Yield Book Advanced Topics

Transcription

1 Yield Book Advanced Topics The Yield Book Inc.

2 Yield Book Advanced Topics Version These materials and the information and methodologies described and incorporated herein are proprietary and confidential to The Yield Book Inc. and may not be disclosed to third parties, or duplicated, or used for any purpose not expressly authorized by The Yield Book Inc. Any unauthorized use, duplication, or disclosure of these materials, information, or methodologies is prohibited by law and will result in prosecution. The Yield Book Inc Inc. 388 Greenwich Street New York, NY (212)816-BOOK The Yield Book is a registered service mark of The Yield Book Inc Throughout this documentation, Yield Book refers to The Yield Book analytical software. Copyright 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004by The Yield Book Inc Inc. All rights reserved.

3 Contents Single Currency Return Attribution: Methodology Overview of Methodology Return Attribution: Page Layout by Steps Individual Security Return Attribution: Example Methodology Example: Scenario Analysis Calculation of Components Current Coupon Spread Introducing Dynamic Portfolios The IRR Method for Averaging Returns Examples Allocation of Returns to Sector and Issue Level Components1-35 Examples: Sector and Issue Allocation Example #2: Treasury and Agency Broken Down Comparison of Sector Weight and Issue Selection Return Attribution: Examples Return Attribution Implementation: Examples Example #1: Static Portfolio using SSB Pricing Example #2: Static Portfolio vs. Index Example #3: Duration Override Example #4: Prepayment Override View Custom Data View Reporting Custom Setup Example #5: Custom Setup Active Portfolios with Transactions Entering Transactions Returns and Attribution on Dynamic Portfolio Entering Transactions using a YbPort Update File Trading Prior to Dated Date in Return Attribution General Notes about Return Attribution Multi-Currency Return Attribution: Methodology Return Attribution on Non-dollar Securities Methodology and New Terms Equations Example: Multi-Currency Portfolio vs. Index Hedge Strategy Notes: Bond Examples i

4 Contents Allocation of Return in Multi-Currency Portfolios Optimization Optimization Terminology General Optimization Procedure Objectives and Constraints Get Started Constraint Definitions Constraint Functions Defining the Constraint Side Per-issue Constraints Constraints Relative to Baseline Portfolios Removing Constraints from Optimization Constraint Files Soft Constraints and Penalty Function Examples Using Optimization in Buy/Sell Mode Example 1: Effective dv01 Neutral Trade Example 2: Hedging Corporates with Treasuries Optimization in Own/Universe/Baseline Mode Example 3: Constructing a Tracking Portfolio Formulating the Problem Example 4: Optimize Portfolio Relative to a Benchmark Example 5: Track a Benchmark using Soft Constraints Reports for Optimization Results Optimization: Examples Example #1: Trade Weighting Example #2: Mortgage Index Tracking Portfolio Example #3: Corporate Index Tracking Example Example #4: Cash Matching ii

5 WORKSHOP Single Currency Return Attribution: Methodology Agenda The Salomon Smith Barney (SSB) Return Attribution Model in the Yield Book calculates and dissects total returns of single or multi-currency fixed income securities, trades, portfolios and/or indices into return attribution factors. The attribution factors explain why the bond achieved the return that it did. The model is designed to calculate and explain returns by decomposing the total return of each security into several attribution components. The attribution components correspond to the effect of the passage of time and various market changes such as yield curve movement, changes in volatility, mortgage prepayment rates, and changes in spreads. The analysis is implemented using SSB s analytic models including: Yield Curves, Term Structure Model, and Mortgage Prepayment Models to measure the effect of these market changes on each security. The model analyzes portfolios and indices by aggregating the issue level return components to the sector level. The sector level aggregation allows the model to measure the effects of portfolio strategies such as sector weighting and issue selection. Highlights In this section of the advanced workshop chapter, we will cover the following: The Layout of the Return Attribution Page Understanding the Return Attribution Model Methodology and the Components of Return on Individual Securities Calculating the Average Return and Portfolio Attribution Components on Static versus Dynamic Portfolios Allocation of Returns to Sector and Issue Decisions Salomon Analytics Inc.

6 Return Attribution Components: Detail Total ROR Benchmark Spread Advantage 1 4 Rolling Yield Market Spread Market 2 3 Parallel Shift Reshape Convexity Advantage Index/ Swap Spread Change Prepay Difference 10 Reshape Advantage Current Coupon Spread Change 11 Volatility Change On-the-Run Spread Change 12 Spread Change 1-2 Single Currency Return Attribution: Methodology

7 Overview of Methodology Overview of Methodology Return Attribution is calculated in three major steps: Step 1: Calculate Issue Level Attribution Components Step 2: Calculate Portfolio Level Attribution Components from the Individual Securities Step 3: Allocate either the Total Return or just the Spread Advantage (non-treasury portion) Return into Sector and Issue Effects. In this section we will cover the first two steps. The third step will be covered in section 3 of this handbook. Step 1: Calculate Issue Level Attribution Components The major dissection of every security s return is to measure what is due to the yield curve exposure or the treasury portion and what is due to everything else. The everything else term, is referred to as spread advantage. This first level break down is shown in the top of the diagram on the opposite page. In order to calculate the treasury component, we must first construct what we call the Matched Benchmark Portfolio (MBP) for the bond. The construction of the MBP will be explained later. The attribution analysis consists of up to 12 scenario analyses for each security or it s MBP. In each scenario, the settlement date is the beginning of the attribution analysis period and the horizon date is set to the end of the attribution analysis period. In each successive scenario analysis, one input is changed and one additional return attribution component is captured. The 12 attribution components are numbered in the diagram on the opposite page. The successive scenario analysis method decomposes the security s total ROR into components corresponding to the effects of various systematic market changes. The remaining return is attributed to spread change. Analytic Assumptions: The Return Attribution methodology requires that you use the following pricing assumptions: Curve Volatility Settle Tsy/Agn/Corp Tsy Model 10% Same Day (begin or end of analysis period) Mortgage Tsy Model Market Same Day (begin or end of analysis period) Single Currency Return Attribution: Methodology 1-3

8 Return Attribution Components: Issue/Sector Total ROR Treasury Spread Advantage Sector Weighting Issue Selection 1-4 Single Currency Return Attribution: Methodology

9 Overview of Methodology The Return Attribution Matrix Dimension by Row: Benchmark vs. Spread Dimension by Column: Yield Effect vs. Market Effects Step 2: Calculate Portfolio Level Attribution from the Individual Security Data Step 3: Allocate Spread Advantage Return into Sector and Issue Affects. Sector Weighting in Sector = Issue Selection in Sector = The twelve issue level attribution components can be categorized and summarized in a two-dimensional matrix as shown on the top of the opposite page. The first dimension in the table is displayed in the rows: the breakdown between Benchmark-like Return Components (as calculated through the MBP) and the Spread-like Components. The second dimension in the table is displayed in the columns: the breakdown between the Yield Effect and the Market Effects. The row and the column totals also provide important measures such as Spread Advantage (i.e. the total incremental return of the security over the MBP). Once the calculation of issue level attribution components are completed, you can combine securities to look at portfolio level components. The method to average these securities depends on whether the portfolio was static or active over the return period. We will explain both averaging methods in detail. Performing the return attribution analysis on an entire portfolio and its corresponding Index allows us to further allocate the portfolio s Spread Advantage return component into Sector Weighting and Issue Selection components as shown in the diagram on the bottom of the opposite page. A detailed example will be covered later, but the basic equations used to calculate these components are: (Index spread advantage in sector - Total Index spread advantage) * (Portfolio Overweight in sector) (Portfolio spread advantage in sector - Index spread advantage in sector) * (Portfolio Weight in Sector) Note: The basic allocation of return into sector and issue level components is done on the Spread Advantage Return, which is the return after the treasury effects (duration and yield curve reshaping) are broken out. Some users may wish to allocate the Total Return into Sector and Issue level components including the treasury portion. This is also available and will be explained and shown in a later example. Before going through a specific example to understand the methodology, let s first see the layout and general procedures of the Return Attribution page (Chapter 4, Page 6) in the Yield Book. Single Currency Return Attribution: Methodology 1-5

10 Return Attribution: Page Layout by Steps 1 Issue Select 2 Pricing 3 Calculate 4 Output 1-6 Single Currency Return Attribution: Methodology

11 Return Attribution: Page Layout by Steps Return Attribution: Page Layout by Steps Please be aware that the steps in the Return Attribution page for calculating return attribution are the same for either a static or an active portfolio. The additional step needed to analyze active portfolios is to define and save transactions to the portfolio. This is done in other pages of the Yield Book, and can be done daily or at the end of a period. Once you are ready to run the attribution on either a static or active portfolio, the following steps are taken in the attribution page, Chapter 4.6. Let s review the steps as circled in the picture on the left: Step 1: Issue Select Retrieve issues, portfolios, or indexes on the buy and/or sell side. You can either retrieve the issues that are sitting in Ch. 4.2 [Receive Buy or Sell from 4.2] or you can retrieve a saved portfolio [Portfolio]. Note about Portfolios with Transactions: The portfolio composition is defined at the beginning of the analysis period and all of the transactions (buys, sells, cash inflows, cash outflows) over the period are saved with the portfolio. Step 2: Pricing Step 3: Calculations Define the begin and end pricing parameters for the calculations. This includes yield curves, settlement dates, and prices of bonds. The easiest way to define these is to use price files [Price File]. If you do not have saved price files of your own and you do not want to use SSB global price files, you have the ability to price the bonds manually through the [Pricing Page]. Run returns only by toggling <ROR> or run returns with return attribution calculations by toggling <RET ATT>. [Read Results] is there to retrieve pre-calculated results. We provide you with pre-calculated results on a daily and monthly basis for the universe of Salomon Index bonds. [Custom Setup] is available for those who wish to customize the partial duration calculation used to calculate the MBP and/or limit the number of attribution factors that are calculated. Step 4: Output The [Print or Copy Summary] generates a canned return attribution summary report of the buys and/or sells. The [Report] button takes you to the template and sector selection page in Ch. 4.2 so you can generate issue level or sector level reports. You may also [Save Results] after calculating for retrieval in the future. Single Currency Return Attribution: Methodology 1-7

12 Return Attribution: Page Layout Single Currency Return Attribution: Methodology

13 Return Attribution: Page Layout by Steps Return Attribution: Page Layout The remaining sections of the Return Attribution page provide information on the inputs and outputs of the return attribution calculation. Each section is circled on the opposite page. Navigation: #5 Data Views: #6 Yield Curve: #7 These navigation buttons are similar to other areas of the Yield Book. You can scroll up and down through the issues, compress issues in or out, sort issues, and focus in on a certain subset of bonds. The data view defines what values are displayed for the issues in the listbox. There are six global views and one Custom view where you can customize a template and read in into this page. The global views will be shown in detail later. The Yield Curves displayed are as of the begin and end of the analysis period. The reinvestment rate defaults to the rate used by the Fixed Income Index group when calculating Index returns. If you click on the box that says [Index] it will change to [User] and the input field will turn yellow for your own input. The parallel shift field displays which point is used to define the amount of the parallel shift for calculating the parallel shift component of the attribution. The default is the 10-year point, but you may change this. We suggest that if you are running return attribution for mortgage securities that you leave the parallel shift at the 10-year point because that is the key rate in the prepayment model. Page Status: #8 Security Listbox: #9 The status shows how many bonds have their begin price, end price and return attribution calculations completed. The boxes will turn green when all bonds are complete. The bottom of the page is a list box for the securities and displays various data depending on the data view you are looking at. The securities can be either on the buy side, the sell side, or the benchmark treasuries used to create the MBP. Single Currency Return Attribution: Methodology 1-9

14 Methodology Example: ABCco 1 2 abc Single Currency Return Attribution: Methodology

15 Individual Security Return Attribution: Example Individual Security Return Attribution: Example Now that we have seen the layout, we will go through an example to explain the SSB Return Attribution Methodology. STEP 1: Turn to Chapter 4.6, toggle on <Buy> and click [Portfolio]. STEP 2: Type abc in the yellow Portid field and click [Search] to find ABCco portfolio. STEP 3: Select ABCco. This portfolio has 6 bonds: 3 corporates, 1 mortgage and 2 treasuries. STEP 4: Click [Read Results]. STEP 5: Click on the file RASEP for the September 99 Results. The page status section shows that the 6 bonds have begin, end and calculated results. The return attribution results file stores both the beginning (8/31/99) and ending (9/30/99) price files as well as the calculated return and return attribution components. STEP 6: Click [Display BMK] to display the Theoretical Benchmark Securities in the listbox. The MBP, created for each security, is made up of bonds from the sixty-one theoretical Benchmark securities, which are now displayed in the listbox. Thirty par bonds, thirty zero-coupon bonds and cash are created from the SSB Treasury Model Curve (see note below) from the beginning of the return period. The par bonds yields (and coupon rates) are set equal to the 1, 2, year yield values of the Treasury Model Curve. The zero-coupon bonds have yields set equal to the 1, 2, 3,...30 year spot rates calculated from the Treasury Model Curve. Note on Treasury Model Curve The Treasury Model Curve is a proprietary 120 point (developed by the SSB Treasury Analysis Group) fitted curve of the most liquid off-the-run non-callable treasuries and strips. The on-the-runs are excluded because they typically trade richer than other issues. It estimates an off-the-run treasury spot curve by finding the set of discount factors that best fit the market prices of all of the off-the-run treasury securities. Single Currency Return Attribution: Methodology 1-11

16 MBP Calculation Single Currency Return Attribution: Methodology

17 Individual Security Return Attribution: Example STEP 7: Click on the bond TCOM 8% 8/1/2005, to display the Matched Benchmark Portfolio. How does the Yield Book select the best match hypothetical security for TCOM Solve for the weight to assign to the best match security (6 year) The Yield Book calculates the effective and partial durations (1, 2, 3, 5, 10, 20, and 30-year points) for the security and for each hypothetical treasury. Then the Yield Book selects the hypothetical Benchmark whose partial duration distribution best matches (using a least sum of squares deviations methodology) the partial duration distribution of the security. The best match security for TCOM is the 6 year. The data in the table comes from the circled fields in the picture on the opposite page. TABLE 1. Calculating the weight of the best match bond Yield Curve Point Partial Duration of TCOM Partials of 6 year par bond Ratio = TCOM Partial / 6yr Partial 1 year year year year year Minimum Ratio year 0 0 N/A 30 year 0 0 N/A Take the minimum ratio of the partial duration of the TCOM bond divided by the partial duration of the 6 year. This is the weight assigned to the best match bond; 82.9% of the MBP is the 6 year par bond. Why take the minimum ratio? Solve for the rest of the MBP If you used the amount indicated by the 5 year partial (93.6% of the 6 year), then the exposure to the 5 year would be.936 * = , which is perfect, but the exposure to the 10 year would be.936 *.9913 = which is too high. The exposure of the bond at the ten year is only By taking the minimum of the ratios and then filling in the rest of the MBP, we do not have to create a more complicated MBP with short positions. The rest of the MBP consists of cash, 1, 2, 3, 5, 10, 20, and 30 year par Treasuries. The weights are calculated so that the MBP has the same effective duration and the same partial duration distribution as the security. The next page will take you through an illustration of this. Single Currency Return Attribution: Methodology 1-13

18 1 2 TCOM versus MBP Single Currency Return Attribution: Methodology

19 Individual Security Return Attribution: Example Methodology Example: TCOM versus MBP In order to see that the MBP has the same partial duration exposure of the bond, we created a portfolio of user bonds representing the hypothetical treasuries in the MBP and set the par amounts equal to the weights as defined on the return attribution page. Let s compare the partial durations of the TCOM bond to the MBP portfolio in Chapter 4.2. AXP versus MBP: Partial Durations STEP 1: Turn to Chapter 4.2, toggle <Buy> and click [Issue]. STEP 2: Type TCOM8,05 in the Ticker/Query field and click [Search]. Click the [B] in so it is yellow and enter a par amount. STEP 3: Toggle <Sell> and click [Portfolio]. STEP 4: Enter mtp in the portfolio ID and click [Search]. Note: This portfolio is made up of the theoretical par bonds (user bonds) which were priced such that the yield was set equal to the par yield on the treasury model curve from 8/31/99. STEP 5: Click on the portfolio to read it in. STEP 6: Click [Pricing]. STEP 7: Toggle <Pricing Files> and click <Select>. STEP 8: Click RA.Sep to retrieve the 8/31/99 pricing assumptions. Remember that the partial duration matching used to calculate the MBP is based on the partial durations calculated from the beginning date of the return period. STEP 9: On the Pricing Page, click Optional Calculations and select Risk We must calculate Risk (partial durations) because user bonds are not in global price files. Remember global price files only contain Salomon source bonds. STEP 10:Click [Update Prices]. Single Currency Return Attribution: Methodology 1-15

20 Partial Duration Swap Report Partial Duration difference is very close to zero. The small differences is due to inaccuracies in constructing the MBP user bonds created for this example. The actual return attribution methodology matches the partial durations exactly Single Currency Return Attribution: Methodology

21 Methodology Example: Scenario Analysis STEP 11:Click [Report]. STEP 12:Click [Template Select]. STEP 13:Type risk swap in the yellow search field and click the global template RSKSWAP. STEP 14:Click [Generate Report]. Methodology Example: Scenario Analysis The next part of the methodology is the explanation of the successive scenario analyses that are run to calculate the attribution components. The table below shows the order of the scenario analysis. In each successive scenario calculation, one input is changed and one additional return attribution component is captured. The return input that is changed is shaded. TABLE 2. Return Attribution Components Calculation Bon d/ MBP Hrz Date Tsy Yield Curve Prepay CC Sprd OTR Sprd Swap Sprd Vol OAS Attribution Component and Description MBP End Beg na na na na na na R1: Bmk Rolling Yield - ROR of MBP holding all parameters (except time) constant. MBP End na na na na na na R2: Bmk Parallel Shift - The effect on the MBP of the parallel shift to the begin Beg + T 10 curve MBP End End na na na na na na R3: Bmk Reshaping - The effect on the MBP of the reshaping of the yield curve Bond End Beg Proj Beg Beg Beg Beg Beg R4: Spread - Difference between Rolling Yield on the bond and the MBP Bond End Proj Beg Beg Beg Beg Beg R5: Convexity Advantage - Difference in the effect of the Beg + T 10 parallel shift on the bond versus the MBP. Bond End Act Beg Beg Beg Beg Beg R6: Prepay Diff - The effect of the difference between the Beg + T 10 actual and the projected prepay Bond End Act End Beg Beg Beg Beg R7: Current Coupon Spread Change - The effect of the Beg + T 10 change in Current coupon spread. Yield Book Keyword RABMRYLD RABMPARA RABMRESH RACREDSPR RACNVADV RAPYDWN RACCSP Bond End Act End End Beg Beg Beg R8: On-the-Run (OTR) Spread - The effect of the return of Beg + T 10 the change in the spread between the OTR curve and the Treasury Model Curve RAONTHERUN Bond End Act End End End Beg Beg R9: Index/Swap - The effect of the change in swap spreads. RAINDEX Beg + T 10 Bond End End Act End End End Beg Beg R10: Reshaping Advantage - The difference in the effect of reshaping on the bond versus MBP. Bond End End Act End End End End Beg R11: Volatility Change - The effect of the change in Market Volatilities Bond End End Act End End End End End R12: Spread Change - The effect of the change in the bond s OAS. RARESHCNV RAVOL RASPRD Single Currency Return Attribution: Methodology 1-17

22 Scenario Analysis Relative Shifts Single Currency Return Attribution: Methodology

23 Methodology Example: Scenario Analysis The process we will go through in the following example is designed to illustrate the methodology and is similar to, but not the same as the process used within the Return Attribution Model. In the example, we will explain several of the return attribution factors by going through four scenario analysis calculations for the TCOM bond and its MBP. STEP 1: Click [Scenario Setup] at the top of the Yield Book. STEP 2: Click [Select] to display the list of scenario files. STEP 3: Click retatwsn, which is a custom scenario file. The default display shows the absolute rates of each scenario. STEP 4: Toggle <Relative> to view relative shifts The relative shifts are based on the settlement Yield Curve, the Treasury Model curve from the begin date, 8/31/99. The first scenario is no change. The second is a parallel shift set equal to the amount that the ten year moved from 8/31/99 to 9/ 30/99 (down 5.6 bps). The ten year is the default for calculating the parallel shift. This can be customized by the user. The 3rd and 4th scenarios are set equal to the actual curve that existed on 9/30/99. STEP 5: Click [Scenario Setup] to take the page down and click [ROR/CF] to bring up the Rate of Return Input Screen. STEP 6: Define the horizon pricing method. Enter 5.9 as the OAS change in the 4th scenario for the TCOM security. The horizon pricing method for the first three scenarios is constant OAS. The horizon pricing method for the fourth scenario is to change OAS by the amount the OAS changed on the bond from 8/31/99 to 9/30/99. In the example, the TCOM s OAS went from a to a for an increase of 5.9bps. STEP 7: Click [Calculate]. STEP 8: Toggle <Total ROR> and <Table>. With these results, we can estimate the Return Attribution Components. Single Currency Return Attribution: Methodology 1-19

24 TCOM: ROR Results and Ret Att Detail R4 R5 R10 R12 R1 R2 R3 Scenario with final yield curve and constant OAS Scenario with final yield curve and OAS change equal to the change in OAS of the bond. A B C D E 1-20 Single Currency Return Attribution: Methodology

25 Calculation of Components Calculation of Components The sequence of Scenario Analyses for return attribution follows the order as defined in the table on page 17. The ROR output can be labelled as shown below: (refer to labels in the ROR output picture on page 20). R1 = ROR of MBP in no change scenario #1 (Benchmark Rolling Yld) =.529 R2 = ROR of MBP in parallel shift scenario #2 =.788 R3 = ROR of MBP in actual scenario #3 =.999 R4 = ROR of bond in no change scenario #1 (Total Rolling Yield) =.601 R5 = ROR of bond in parallel shift scenario #2 =.860 R10 = ROR of bond in actual scenario#4 with no OAS change = R12 = ROR of bond in actual scenario#3 with OAS change =.798 Please note that the numbers produced by the illustrative methodology are close to but do not exactly match those produced by the actual model. Benchmark Rolling Yield Component A (R1) The Benchmark Rolling Yield is the total return (ROR) on the MBP with a no change scenario, (R1) which is equal to.529 Spread Component B (R4/R1) The Total Rolling Yield on TCOM is the ROR on the bond in the no change scenario, (R4) which is.601. The Spread is equal to the Total Rolling Yield (R4) divided by the Benchmark Rolling Yield (R1) or: [( ) 100] = Parallel Shift Component C (R2/R1) The parallel shift component is equal to the ROR of the MBP in the parallel shift scenario (R2) divided by the ROR for the MBP in the no change scenario (R1) or: [( ) 100] = Reshaping Component D (R3/R2) The reshaping component is equal to the ROR on the MBP for the Actual scenario (R3) divided by the ROR on the MBP for the Parallel shift scenario (R2) or: [( ) 100] = Spread Change Component E (R12/R10) The spread change component is equal to the ROR on the bond in the Actual scenario with an OAS change of 5.9 bps (R12) divided by the ROR on the bond in the Actual scenario at a constant OAS: [( ) 100] = Single Currency Return Attribution: Methodology 1-21

26 FNMA Other Change in Swaption Volatility 1-22 Single Currency Return Attribution: Methodology

27 Calculation of Components Convexity Advantage The convexity advantage is equal to the difference in the effect of the parallel shift on the bond (R5/R4) relative to the parallel shift effect on the MBP (R2/R1) = Reshaping Advantage The reshaping component is equal to the difference in the effect of the reshaping on the bond (R10/R5) relative to the reshaping effect on the MBP (R3/R2) = Calculation of Other Attribution Components Let s return to the Return Attribution page and look at a mortgage bond to review the remaining Other attribution components (circled in the picture): volatility, prepay difference, current coupon spread, and OTR spread. Index/Swap is only calculated for floating rate securities. Prepay Difference Volatility Change Current Coupon Spread Change The effect of the difference between the actual and the projected prepays on the bond. This is only calculated for mortgages. The effect of the change in market volatilities on the bond. For mortgages, the important volatilities are the swaptions. Notice on the report on the left page that the 1 year option on the 10-year swap decreased from 16.4 to (-1.3%) over the month. A decrease in vols causes the value of the option to decrease. Since you are short the option on the mortgage, this decrease in option value helps the mortgage; thus a positive effect from volatility change of.228. The current coupon spread change looks at the effect that the change in the current coupon spread has on the bond. The current coupon spread is the spread between the FNMA current coupon and the 10 year on-the-run treasury. For example, let s look at the FNMA 6.5 bond in the ABCCo portfolio as shown on the opposite page. STEP 1: Click on the FNMA 6.5 issue to bring up the Return Attribution details of the bond. STEP 2: Click [Print] to generate a return attribution report of just that one issue. Single Currency Return Attribution: Methodology 1-23

28 Current Coupon Spread Single Currency Return Attribution: Methodology

29 Current Coupon Spread Overall, the mortgage had a spread advantage of basis points. The current coupon spread was or -3.8 basis points. Let s look at what happened to the current coupon spread over that period. You can also calculate a current coupon spread duration on the bond itself. Current Coupon Spread Turn to Chapter 2.2 and click [Hist Data] to go to Historical Data. STEP 1: Click the white menu box next to A1 under the Security/ Issue label. STEP 2: Toggle <Mortgages>. STEP 3: Select FNMA Current Coupon. STEP 4: Click on the white menu box next to A2 under the Security/ Issue label. STEP 5: Toggle <Yield Curves> and select the 10 year (not pictured). STEP 6: Click on the white menu box under the Equation label and select Spread. STEP 7: Set the dates: From 8/31/99, To 9/30/99. STEP 8: Determine which items you would like to display. In this example, we clicked off the yields of the FNMA and the 10 year and said to display just the spread on the bottom. STEP 9: Click [Graph]. For most mortgages, the current coupon spread duration is negative, meaning that when the current coupon spread decreases, the value of the option to prepay increases which hurts the mortgage (prices decrease). When the current coupon spread increases, the value of the option is reduced which helps the mortgage (price increases). Here, the current coupon spread narrowed by 16 basis points from on 8/31/99 to on 9/ 30/99. This increases the value of the prepayment option; therefore hurting the mortgage. The current coupon spread effect was a negative 3.8 bps which hurt the return. Single Currency Return Attribution: Methodology 1-25

30 On-the-Run Spread 1-26 Single Currency Return Attribution: Methodology

31 Current Coupon Spread On-the-Run Spread The On-the-Run spread is the effect of the return of the change in the spread between the OTR curve and the Treasury Model Curve. Date 10 year OTR 10 Year Treasury Model First, lets look at the table of information below: The first two columns of numbers come from the Curve Analysis page as shown on the opposite page. The third column is simply the difference of the first two columns. The fourth column comes from the analysis we did on the current coupon spread on page 24. The current coupon spread effect is calculated by looking at the spread between the FNMA current coupon and the On-the-Run 10 year treasury. Now we are looking at the spread between the FNMA current coupon and the Treasury Model 10 year point. This spread is equal to the CC spread minus the Spread between the 10 year OTR and Treasury Model points as shown: From the table above, we compute this spread to be: = = bps. Spread between OTR and Treasury Model 8/31/ /30/ Change 9 bps 5.57 bps +3.5 bps -16bps Current Coupon Spread FNMA 10yrTsyModelRate = CCSpread ( OTR TreasuryModel) The spread between FNMA current coupon and Treasury Model narrowed by 19.5 bps (versus a narrowing of only 16bps between the FNMA and the 10 year On-the-Run. As discussed above in the Current Coupon Spread, a narrowing of this spread hurst the mortgage. The effect of this 3.5 bps additional narrowing should hurt the mortgage even more. This is shown in the OTR Spread change value of Single Currency Return Attribution: Methodology 1-27

32 Portfolio Level Attribution: Report Single Currency Return Attribution: Methodology

33 Current Coupon Spread Generate the Portfolio Level Attribution Report The individual bond attribution components are averaged using the IRR method (which will be explained in the next section) to compute the portfolio average measures. To generate portfolio reports instead of individual bond reports, do the following: STEP 1: Click [Report]. STEP 2: Click [Template Select]. STEP 3: Enter return att in the yellow search field. STEP 4: Click on Retatt02, the report of ROR components for each bond and the average. STEP 5: Click [Generate Report]. The report displays each of the components and the total return for the period. In addition, the summary levels, TOT TSY for Total Benchmark and TOT SPD ADV for Total Spread Advantage are given. Please see the circled columns on the opposite page. Note: Use the return attribution sector template (RETSEC1 or RETSEC2) and a sector file to generate the return attribution components by sector. Single Currency Return Attribution: Methodology 1-29

34 Introducing Dynamic Portfolios Static vs. Dynamic Portfolios Viewing a Portfolio as a Collection of Investment Segments Transactions: Assumptions about Investment Segments IRR Method for Averaging Returns In a static portfolio where all securities are invested for the entire analysis period, the portfolio average return (and return components) can be derived by calculating the market weighted average return(s) across all securities. This is not true for a dynamic portfolio, which has transactions as well as cash inflows or outflows. An investment segment is a holding in a security from Time A to Time B. If a security is in the portfolio throughout the analysis period, Time A is the beginning of the analysis period and Time B is the end of the analysis period. If a security is purchased and sold within the analysis period, Time A is the purchase trade date and Time B is the sell trade date. For active portfolios, you will define the portfolio composition at the beginning of the analysis period and all of the transactions (buys, sells, cash inflows, cash outflows) over the period. The Yield Book will preprocess the beginning portfolio and transactions into investment segments. The details of how to enter transactions and which type of cash inflows and outflows must be entered versus which are assumed to have occurred by the system will be defined in the next section with examples. In this section, we wish to explain how portfolio averages are calculated for dynamic portfolios. For example, we want to analyze the performance of a portfolio over the month of August, On July 31, 1998, the portfolio consists of 5 million par in each of 3 securities: a treasury, a corporate, and a mortgage. On August 15, the corporate is sold and the proceeds are reinvested in the treasury security. This portfolio in the month of August will consist of 4 investment segments: Investment Segment Security Time A Time B 1 Treasury 7/31/98 8/31/98 2 Mortgage 7/31/98 8/31/98 3 Corporate 7/31/98 8/15/98 4 Treasury 8/15/98 8/31/ Single Currency Return Attribution: Methodology

35 The IRR Method for Averaging Returns The IRR Method for Averaging Returns The first step is to calculate the total return and return attribution components for each investment segment as described in the methodology section of this manual. The portfolio return (and return components) can be averaged via an Internal Rate of Return (IRR) calculation. The IRR method is an AIMR Standards approved method for calculating time weighted rates of return. Its primary advantage is that it does not require the definition of market values for the static securities in the portfolio on the days of transactions, cash inflows, and cash outflows. For this reason, you only need to define the trade price of the bonds you trade on the transaction dates, not all the remaining static securities. The basic calculation is: find R such that: Mi( 1 + R i) ( 1 + R) t = i2 M i ( 1 + R) t i1 where, M i = Market Value (beginning) of investment segment i R i = Return of Investment Segment i R = Internal Rate of Return t i1 = Start time (between 0 and 1) for investment segment i t i2 = End time (between 0 and 1) for investment segment i In a static portfolio where all investment segments span the entire analysis period, the IRR will equal the Market Weighted Average Return. Applying the IRR Method to Averaging Return Attribution Components The attribution components for each investment segment are calculated through a series of scenario analysis return calculations on the security or its Matched Benchmark Portfolio (MBP). The scenario analysis returns are cumulative. That is, in each scenario analysis run, an additional factor is introduced. To calculate the return effect of any of the 12 factors, the first scenario return which includes that factor, is divided by the prior scenario return. The total return for the investment segment is the return of the 12th scenario analysis run (in which all 12 factors are reflected) which, by definition is the product of the 12 Return Attribution Components. Single Currency Return Attribution: Methodology 1-31

36 The portfolio average for each of the 12 return attribution components can be computed through a two-step process. First, calculate the IRR for each of the 12 cumulative scenario returns. The portfolio average for each attribution component can then be calculated by successively dividing the cumulative IRRs. Examples The following three examples will illustrate the IRR calculation for static and dynamic portfolios. In order to simplify the examples, we will consolidate the 12 return components into 2 major return categories: Benchmark Return which is the product of the Benchmark Rolling Yield, Parallel Shift and Reshaping components, and the Spread Advantage which is the product of all the remaining components. Example 1: Static Portfolio The following table displays the returns and major attribution components for each segment of XYZCO over the month of August, Since this is a static portfolio, the average returns can be calculated using a simple market weighted average method, but we will show the IRR method for example: Segment Security Beg Par Beg Mkt (M i ) t i1 t i2 Bmk ROR (R i ) Spread Adv Total Return 1 US TCOM FNMA Step 1: Calculate Portfolio Benchmark Return Using the IRR equation, Mi( 1 + R i) M i ( 1 + R) t = i2 ( 1 + R) t i1 we solve for R such that and since t i2 = 1 and t i1 = 0 for all i, 5594( ) 5280( ) 5112( ) = ( 1+ R) ( 1 + R) ( 1 + R) R = and Portfolio Benchmark Return = 2.640% 1-32 Single Currency Return Attribution: Methodology

37 Examples Step 2: Calculate Portfolio Total Return The portfolio Total Return is solved for using the same equation. Just substitute the Total ROR numbers in place of the Benchmark Return numbers in the above formula and solve for R: 5594( ) ( ) = ( 1+ R) ( 1 + R) ( 1 + R) R = and Portfolio Total Return = 1.281% Step 3: Calculate Portfolio Spread Advantage Return Important Note: Example #2: Dynamic Portfolio Step 1: Define Investment Segments for XYZCO Portfolio in August 1998 The portfolio Spread Advantage Return is calculated by dividing the Total Return by the Benchmark Return: Portfolio Spread Advantage = ( / ) x 100 = % The IRR Method on the other hand, is designed to maintain the cumulative property of the returns so that the product of the component averages will equal the total return average. In this example, we will introduce transactions in the XYZCO portfolio. We will assume that the holdings in the TCOM and FNMA securities were sold on 8/20/98 and all proceeds (including cash generated during the period) were reinvested in the Treasury security. The portfolio would contain 4 investment segments. The market values, par amounts, and returns are shown below: Segment Security Beg Par Beg Mkt (M i ) t i1 t i2 Bmk ROR (R i ) Total Return 1 US TCOM FNMA US Step 2: Calculate Portfolio Benchmark Return Using the IRR equation, we solve for R such that 5594( ) 5280( ) 5112( ) 10425( ) = ( 1+ R) 1 ( 1+ R) ( 1+ R) ( 1 + R) 1 ( 1 + R) 0 ( 1 + R) 0 ( 1 + R) 0 ( 1 + R) this results with R= and Portfolio Benchmark Return = 2.923% Single Currency Return Attribution: Methodology 1-33

38 Step 3: Calculate Portfolio Total Return Step 4: Calculate Portfolio Spread Advantage Calculate Portfolio Total ROR using the same equation as above except substitute the Bmk Return (R) with the Total Return (R) from the table above. This results with portfolio Total Return of 2.501% The portfolio Spread Advantage is calculated by dividing the Total Return by the Benchmark Return. Portfolio Spread Advantage = ( / ) x 100 = % The Benchmark Return in a dynamic portfolio is higher than for the static portfolio due to the fact that the 8/20/98 transaction increased the duration of the portfolio Single Currency Return Attribution: Methodology

39 Allocation of Returns to Sector and Issue Level Components Allocation of Returns to Sector and Issue Level Components Once the individual and portfolio level attribution is completed, you may wish to allocate either the total return or just the total spread advantage component to either issue or sector selection. To allocate return into sector and issue level components, you must choose a benchmark, usually an index. You can allocate total return (relative to the index) or just the total spread advantage return (relative to the index) to either issue or sector selection. The allocation equations are shown below. Sector Weighting in Sector Issue Selection in Sector (Index Return in sector - Total Index Return) * (Portfolio Overweight in sector) (Portfolio Return in sector - Index Return in sector) * (Sector Weight of Portfolio) Note: The basic allocation of return into sector and issue level components is usually done on the Spread Advantage Return (relative to the index), which is the return after the treasury effects (duration and yield curve reshaping) are broken out. Some users may wish to allocate the Total Return (relative to the index) into Sector and Issue level components including the treasury portion. The components for each of these methods are shown on the following page. Single Currency Return Attribution: Methodology 1-35

40 Return Attribution Major Components Allocation of Total Return of a Portfolio with an Index Benchmark Total Return Subtract Index Total Return Total Return Difference Sector Effect Difference Issue Selection Difference Allocation of Spread Advantage of a Portfolio with an Index Benchmark Total Return Treasury Return Spread Advantage Return Subtract Index Treasury Return Subtract Index Spread Advantage Return Spread Advantage Return Difference Duration and Yield Curve Difference + + Sector Effect Difference Issue Selection Difference = Total Return Difference 1-36 Single Currency Return Attribution: Methodology

41 Allocation of Returns to Sector and Issue Level Components The objective is to allocate the portfolio s total return (relative to the index) into three major categories, corresponding to the three major steps in the portfolio management process. Steps in the Portfolio Management Process for Single Currency Portfolios STEP 1: Define the total portfolio duration and yield curve exposure. STEP 2: Define the weight in each sector. The weighting decision can be broad (mortgage vs. corporate vs. treasury) or narrow (utility, industrial, GNMA, FNMA, etc). STEP 3: Select specific issues within each sector. Select Portfolio Duration and Yield Curve Exposure Select Sector Weights Select Specific Issues Step 1 Step 2 Step 3 Treasury Return Sector Weighting Issue Selection The attribution attributed to Step 1 is the average Treasury Return (relative to the index) for the portfolio. The balance of the portfolio return is the Spread Advantage. The Spread Advantage is decomposed into Sector Weighting components for each sector (capturing the return attributable to Step 2 above) and into Issue Selection components (returns attributable to Step 3). Single Currency Return Attribution: Methodology 1-37

42 Sector and Issue Level Attribution: Example # Single Currency Return Attribution: Methodology

43 Examples: Sector and Issue Allocation Examples: Sector and Issue Allocation The Yield Book allows great flexibility in defining the sectors to be used in Sector Level Attribution. The Sector Weighting and Issue Selection components depend on the number of sectors used. In the extreme, if there is only one sector, all of the Spread Advantage is allocated to Issue Selection. In the other extreme, if every security is in a different sector, all of the Spread Advantage is allocated to Sector Weighting. It is very important that you define your sectors based on your portfolio decision making process. In the next two examples, we will apply two different sector files to the ABCco versus the BIGINDEX and you will notice that the results tell a very different story depending on the sector breakdown that is used. Example#1: ABCco vs. BIGINDEX broken down by THREE major industry sectors Compare the ABCco portfolio to the BIGINDEX as of 9/1/99. STEP 1: Toggle Buy in Ch 4.6 and click [Portfolio] and click ABCco as of 9/1/99. STEP 2: Toggle Sell in Ch 4.6 and click [Portfolio], toggle Indexes and click BIGINDEX 9/1/99. STEP 3: Click [Read Results] and select RA.SEPT (not pictured). STEP 4: Click [Report] to obtain the template selection page. STEP 5: Type bmk in the yellow template search field. STEP 6: Select RETBMK template. STEP 7: Click [Sector Select] and choose a sector. In this example, we selected a sector file called MAJOR which is made up of three sectors: Treasury or Agency, Mortgage, and Corporate STEP 8: Click [Generate Report]. Single Currency Return Attribution: Methodology 1-39

44 Sector and Issue Selection: Example #1 Three major industry sectors: Treasury Mortgage Corporate 1-40 Single Currency Return Attribution: Methodology

45 Examples: Sector and Issue Allocation In order to calculate the issue and sector selection, you must have the market weights in each of your sectors for the portfolio and for the index as well as the total spread advantage in each of your sectors for the portfolio and for the index. These are taken from the report shown on the opposite page and summarized in the tables below: Sector Selection Effect: Sector Weighting in Sector = Index spread advantage in sector Total Index spread. advantage X Portfolio Overweight in sector col 1 col 2 col 3 = col 1-2 col 4 col 5 col 6 = col 4-5 col7 = col3*6/100 Sector Market Weight Portfolio Market Weight Index Over or Under Weight Spread Advantage Index Sector Spread Advantage Total Index Difference Sector Weight Effect Tsy/Agn Mortgage Corporates Total Issue Selection Effect: Issue Selection in Sector = Portfolio spread advantage in sector Index spread advantage in sector X Sector Weight of Portfolio col 1 (from above) col 8 col 4 (from above) col 9 = col 8-4 col 10 = (col1*col9)/100 Sector Market Weight Portfolio Spread Advantage: Portfolio Sector Spread Advantage: Index Sector Difference Issue Selection Effect Tsy/Agn Mortgage Corporates Total Total: Sector Sector Weight Effect (col 7 from above) Issue Selection Effect (col 10 fro above) Total Effect Tsy/Agn Mortgage Corporates Total Single Currency Return Attribution: Methodology 1-41

46 Sector and Issue Selection: Example # Single Currency Return Attribution: Methodology

47 Examples: Sector and Issue Allocation Example#2: ABCco vs. BIGINDEX broken down by FOUR major industry sectors Let s say you don t manage your Treasury/Agency allocation as one unit, but as two separate sectors. We will use a new sector file that had four sectors: Treasury, Agency, Mortgage, and Corporate Regenerate the report with the new sector and review the results. Details of how the numbers are calculated are shown in the tables on the next page. Remember, you can customize the sectors that you report on by editing or creating sector files in Chapter 1.5. Single Currency Return Attribution: Methodology 1-43

48 Example #2: Treasury and Agency Broken Down Sector Selection Effect: col 1 col 2 col 3 = col 1-2 col 4 col 5 col 6 = col 4-5 col 7 = col3*col6/100 Spread Advantage : Index Sector Spread Advantage Total Index Difference Sector Weight Effect Sector Market Weight Portfolio Market Weight Index Over or Under Weight Treasury Agency Mortgage Corporate Total Issue Selection Effect: col 1 (from above) col 8 col 4 (from above) col 9 = col 8-4 col 10 = (col1*col9)/100 Sector Market Weight Portfolio Spread Advantage: Portfolio Sector Spread Advantage: Index Sector Difference Issue Selection Effect Treasury Agency Mortgage Corporates Total Total: Sector Sector Weight Effect (col 7 from above) Issue Selection Effect (col 10 from above) Total Effect Treasury Agency Mortgage Corporates Total Single Currency Return Attribution: Methodology

49 Comparison of Sector Weight and Issue Selection Comparison of Sector Weight and Issue Selection Now we can compare the allocation between sector and issue under the two sector files: Table #1 with Three Sectors Sector Sector Weight Effect Issue Selection Effect Total Effect Tsy/Agn Mortgage Corporates Total Table #2 with Four Sectors (Agency separate) Sector Sector Weight Effect Issue Selection Effect Total Effect Treasury Agency Mortgage Corporate Total Notice that in Table #1 using just three sectors, it looks like the decision to overweight Treasury/Agencies was a good sector decision, but you picked poor issues. In Table #2, it shows us that to have overweighted Treasuries and to have underweighted Agencies were both bad decision. This would only be found by breaking the Agency sector out. Single Currency Return Attribution: Methodology 1-45

50 1-46 Single Currency Return Attribution: Methodology

51 WORKSHOP Return Attribution: Examples Agenda This section of the advanced capabilities handbook takes you through several return attribution examples to illustrate the inputs and outputs of the return attribution model. Highlights In this workshop handbook, we will cover Return Attribution examples that teach the following: How to use Salomon Smith Barney (SSB) pre-calculated results for return attribution. How to combine Index pricing and User pricing, where difference between the Index and User pricing is captured as an additional attribution component called User price adjustment. How to enter Duration and Prepayment Overrides to bonds. How to Customize the Calculations in Return Attribution using the Custom Setup. Salomon Analytics Inc.

52 Example #1: Static Portfolio using SSB Pricing Return Attribution: Examples

53 Return Attribution Implementation: Examples Return Attribution Implementation: Examples The most important thing to do before starting to run return attribution is to decide what pricing to use for bonds that SSB provides pricing on. Three Choices about Pricing 1. Use the SSB price in your total ROR calculation and the attribution calculation. (Example #1 below) 2. Use your own price for the total ROR calculation and the attribution calculation (Example #2-Part A below) 3. Use your own price for the total ROR calculation and the SSB price for the attribution calculation. This is the most commonly used method because you save time on the attribution calculation by using the pre-calculated results and you are able to report actual returns using your own prices. (Example #2-Part B below) This decision determines the sequence in which you perform your calculations and the steps required. Example #1: Static Portfolio using SSB Pricing Problem Assumptions: You wish to use Salomon Smith Barney (SSB) provided Prices for all available bonds. For bonds that SSB does not provide a price, you will use your own user prices. These user prices can be entered either manually using the pricing page or loaded from a pricing file. This example will show the manual method. Using user price files will be shown as part of Example #2. STEP 1: Turn to Chapter 4.6, Toggle <Buy> and click [Portfolio]. STEP 2: Select the portfolio ABCco2 from the listbox. STEP 3: Click [Read Results]. STEP 4: Click RA.SEP What is a Results File? A result file is composed of the return calculation, the attribution components as well as the beginning and ending price files including the partial durations of all the bonds. When you read in a results file, everything is restored to the parameters used when the calculation was completed. Notice in the page status section that there is one unpriced bond for the beginning and ending dates. On the following page we will focus in on this bond and price is manually. Return Attribution: Examples 2-3

54 Return Attribution: Examples

55 Example #1: Static Portfolio using SSB Pricing STEP 5: While toggled on <Buy>, click [Focus] to bring up the Focus Selection page. STEP 6: Click RETATT04, a predefined sector condition that focuses on unpriced securities. STEP 7: Click [Process]. The one unpriced bond, FMCR, is the only bond focused in. Note: Since this sample portfolio is small, it would have been easy to locate the unpriced security without using the focus step. In a large portfolio, it is more difficult to locate the unpriced securities, and requires the focus capability. STEP 8: Click [Pricing Page]. STEP 9: Enter a price of 102 (the begin price) in the new level column for the FMCR bond. STEP 10:Click [Update Buy Prices]. Make sure that if you are pricing a mortgage that you are using the SSB prepayment model in order to calculate an OAS and Effective Duration. (Note: For a CMO, the CMO OAS/EDUR option box must also be turned on). The calculation of the partial durations required for the MTP calculation do not have to be calculated at this point; therefore the RISK option under Optional Calculations need not be on at this time. When the return attribution calculation is run, the risk measures are automatically calculated. Return Attribution: Examples 2-5

56 Return Attribution: Examples

57 Example #1: Static Portfolio using SSB Pricing STEP 11:Toggle <End>. We must also provide a price for the end date. STEP 12:Enter a price of 103 in the new level column for the FMCR bond. STEP 13:Click [Update Buy Prices]. STEP 14:Click [Unfocus]. Notice in the page status that one bond still needs calculations. STEP 15:Toggle on <Ret Att> under the calculations section and Click [Calc Ret Att]. Summary: In this example #1, we used the pre-calculated results from the Return Attribution results file for all bonds which SSB provides a price. For the one user bond, FMCR, we had to enter begin and end user prices and calculate the return and attribution components. The results are: Total Rate of Return Treasury Return.828 Total Spread Advantage.401 Review of Decision about Pricing In most cases when running Return Attribution on your portfolios, you will own some combination of bonds that we have pre-calculated results for and some bonds that we do not have pre-calculated results for. When SSB does not provide pricing and pre-calculated results, it is obvious that you must use your own prices and calculate results for those bonds. When SSB does provide pricing and attribution results for all of your bonds, you have the three choices on what pricing and attribution results to use, see Three Choices about Pricing on page 3. Return Attribution: Examples 2-7

58 2-8 Return Attribution: Examples

59 Example #2: Static Portfolio vs. Index Example #2: Static Portfolio vs. Index Problem Assumptions: In this example, you want the benefit of using the SSB pre-calculated attribution results where available, but you want to use your own pricing to calculate actual returns. We have provided a feature in attribution called Price Adjustment. This feature has the following benefits: 1. You are using your own prices to calculate the returns on your portfolio (so your return matches that which your accounting system reported). 2. The pricing and returns on the index portfolio is as reported by the SSB index. 3. You are using the pre-calculated attribution results provided by SSB in the results file, which saves calculation time. The MTP and successive scenario analyses are already calculated. The difference in returns between a bond that you own that is also in the index is all attributed to the user price difference. What are the steps: Like example#1, we have a bond (FMCR user bond) that SSB does not provide pricing on so we must provide that pricing on our own. In example #1, we entered the pricing manually for those bonds, but in this example we will use user price files. This means we must first create user price files for all bonds. These price files should be saved with the return attribution analytic assumptions (like the return attribution price files). These assumptions are the following: Yield Curve: Treasury model curve Settlement Date: Last day of month if month end, otherwise same day settle Volatility: Market volatilities for mortgages, and 10% single volatility for non-mortgages Ways to create user price files: Price files can be created in one of two ways: YbPort or use the Pricing Page and Pricing Setup. We will use the Pricing Page and Pricing Setup in this example. If you were using YbPort, you would create a ybport file with your month end prices, set Pricing Setup back to month-end, and process the ybport file. Then do the same for your next month-end. Lets create the price files: Return Attribution: Examples 2-9

60 Create User Price File for Begin Date 1 1 2, Return Attribution: Examples

61 Example #2: Static Portfolio vs. Index Create a Price file with user prices as of 8/31/99 for the Begin Date. STEP 1: Turn to Chapter 4.2, Toggle on Buy and select portfolio ABCco2. STEP 2: Click [Pricing Setup]. STEP 3: Change the curve to the Treasury Model. STEP 4: Enter 8/31/99 and click [Load Historical Curve]. STEP 5: Set the Single Global Settlement date to 8/31/99 and turn that option on. STEP 6: Set the volatility controls to the following: Market for Mortgages Single of 10% for Corporates. STEP 7: Click [Pricing Setup] to get back to the bonds. Return Attribution: Examples 2-11

62 Return Attribution: Examples

63 Example #2: Static Portfolio vs. Index Now that Pricing Setup is defined, we must reprice the bonds: STEP 8: Click [Pricing]. STEP 9: Toggle <Pricing Calculations>. STEP 10:Enter beginning levels in the new level column. STEP 11:Click [Update Prices]. Once complete, you will see that the settlement date for every bond has been set to 8/31/99. This is because in Pricing Setup, we have the option box [Use Global Settlement Dates] turned on and the single settlement date is set to 8/31/99. STEP 12:Toggle <Pricing Files>. STEP 13:Enter an ID, as of date and description (optional) STEP 14: Click [Save]. This saves a price file for the begin state. Return Attribution: Examples 2-13

64 17 Create User Price File for End Date 15, Return Attribution: Examples

65 Example #2: Static Portfolio vs. Index Now we must create a price file for the end date. This is done the same way we created the price file for the begin date: Create a Price file with user prices as of 9/30/99, for the End date. STEP 15:Click [Pricing Setup]. STEP 16:Enter 9/30/99 and click [Load Historical Curve]. STEP 17:Set the Single Global Settlement date to 9/30/99 and turn that option on. STEP 18:Click [Pricing Setup] to get back to the bonds. STEP 19:Click [Pricing] for Pricing Calculations. STEP 20:Enter ending levels in the new level column. STEP 21:Click [Update Prices]. STEP 22:Toggle <Pricing Files>. STEP 23:Enter an ID, as of date and description (optional). STEP 24:Click [Save]. This saves a price file for the end state. Note about Price Files: In this example, the user price files were saved with the return attribution pricing assumptions (same day single settlement date, treasury model curve, market volatility for mortgages and single volatility of 10% for non-mortgages). You may have previously saved month-end price files with assumptions that are different. You can still use these price files, but the following adjustments will be made when you calculate return attribution: Settlement Date Different If the settlement dates are not for same day settle, the return attribution calculation will reset the settlement date to the same day and calculate a carry adjusted price from your given price and settlement date (after asking you if this is ok). Volatilities Different If the volatilities or yield curve do not match, but the pricing levels and settlement dates are correct, the return attribution calculation will correct this by using your pricing level as input and calculate new OASs, and effective durations for the bonds. Return Attribution: Examples 2-15

66 1 Calculate ROR and Return Attribution Return Attribution: Examples

67 Example #2: Static Portfolio vs. Index Return Attribution Page Let s just review the setup of the problem: The goal is to use as much of the pre-calculated results as possible from the SSB results file. For the remaining bonds (user bonds, CMOs, Pools) we will user our own pricing from our pricing files and finally, we will use the new Price Adjustment feature in order to maintain the index prices and returns but report our portfolio returns based on our user pricing. The first part of this example is the same as Example#1 except that instead of using the manual pricing input on the pricing page for the non- SSB priced bonds, we want to user price files to set the prices of non-ssb priced issues. We start with reading in our user price files. STEP 1: Turn to Chapter 4.6, Toggle <Buy> and select Portfolio ABCco2. STEP 2: Toggle <Sell>, click [Portfolio], toggle <Indexes> and search for the BIGINDEX as of 9/1/99. STEP 3: Toggle <Begin> and click [Price File]. STEP 4: Select ABCco2 price file as of 8/31/99. STEP 5: Toggle <End> and click [Price File]. STEP 6: Select ABCco2 price file as of 9/30/99. Notice the page status after the user price files have been selected. Our portfolio has 7 bonds that are ready for the return attribution calculation. Example 2 (Part A) - Using User Prices Only Note: if you ran the calculation on these bonds now, you would be calculating ROR and attribution based on your own user prices. This is not shown here, but the results of the calculation on the portfolio (not the index) are given below. These results will be compared to the results of Example #1 and Example #2 - Part B later. Total Rate of Return Treasury Return.829 Total Spread Advantage.497 Now, we can read in the SSB results file. Return Attribution: Examples 2-17

68 Example # Return Attribution: Examples

69 Example #2: Static Portfolio vs. Index STEP 7: Click [Read Results]. STEP 8: Select RA.SEP. The results file reads in the return and attribution results as well as the SSB pricing files for the begin and end dates. Therefore, the bonds that have user prices will be overwritten with the SSB prices if they are in the results file and the bonds that do not have SSB prices will remain priced with the user prices you had in your price files. In this example, all bonds except the FMCR will be overwritten with SSB prices at this point. STEP 9: Toggle on <Ret Att> and click [Calc Ret Att]. Only the bonds that used user prices will have to be calculated. The remaining bonds have pre-calculated results from the results file. In the page status section in this example, you see that out of 7 bonds, 6 are already calculated. The bond that needs to be calculated is the user bond, FMCR. Note: If you wanted to, you can use the [Focus] button here and use the saved sector condition #Retatt2 - securities with retatt not calculated. This is not necessary because the program is smart enough not to recalculate for bonds that already have results. Some users just like to see which specific bonds still need to be calculated. Summary so far: Although, the returns and attribution looks complete, the calculations for the portfolio used the SSB pricing (except for the one user bond which used our user pricing). The results are the same in Example #1: Total Rate of Return Treasury Return.828 Total Spread Advantage.401 This is because we read the results file in after the user price file. The results file contained pre-calculated results on those 6 bonds so when you clicked the [Calculate] button, the system said that you already have these bonds calculated; therefore, no need for further calculation. We now want to adjust the prices on the bonds in your portfolio to use the user prices to calculate the return, which should end up being The next step is to apply the user price adjustment. Return Attribution: Examples 2-19

70 Example 2 (Part B): Apply User Price Adjustments to Portfolio Results After Price Adjustment 2-20 Return Attribution: Examples

71 Example #2: Static Portfolio vs. Index STEP 10:Toggle <Begin> and Click [Adjustments]. STEP 11:Click [Load from Price File]. STEP 12:Click on the begin price file. STEP 13:Click [Update Current]. STEP 14:Toggle <End>. STEP 15:Click [Load from Price File]. STEP 16:Click on the end price file. STEP 17:Click [Update Current]. Then click [Adjustments] to take the adjustment page down. There is no need to calculate again; the total return has immediately been recalculated with your adjusted prices and the difference in the return has been attributed to User Price Diff. Let s look at a comparison of the different examples: Return Attribution: Examples 2-21

72 Example #1: SSB Pricing Example #2 (Part A): - All USER Pricing Example #2 (Part B): SSB Pricing for Attribution; User Pricing for Returns Portfolio Return Total Treasury Effect Total Spread Advantage User Price Difference Example 1 Vs. Example 2 (Part A) Example 2 (Part A) Vs. Example 2 (Part B) Example 1 Vs. Example 2 (Part B) These differ on all measures because #1 used SSB pricing for the total ROR and for the attribution while #2-(Part A) used USER pricing for the total ROR and for the attribution. These have the same total return because we used USER prices for the total return in both cases. The attribution results differ (only slightly) because in #2-Part A we used SSB pricing and in #2 - Part B, we used USER pricing. These have different total returns because in #1 we used SSB pricing while in #2-Part B we used USER prices (applied with Price Adjustment function). The difference in the total returns is equal to the User Price Difference ( =.098) Notice that the Total Treasury Effect is the same because we used SSB pricing for the attribution results. This means that the MTP was calculated based on the same pricing for each. This is where the calculation time is saved. The Total Spread Advantage differs because in #1 we used the SSB pricing for the attribution and in #2 -Part B we used USER prices for the attribution. The Price Adjustment is part of the Total Spread Advantage. Note: How is Price Adjustment Calculated The price adjustment is captured in the category called Other under Total Market Spread. The user price difference for each bond is calculated with the following formula: ( PriceDifference) ( 1 + Return) BeġFullPrice 2-22 Return Attribution: Examples

73 Example #2: Static Portfolio vs. Index Return Attribution: Examples 2-23

74 Example #3: Duration Override Return Attribution: Examples

75 Example #3: Duration Override Example #3: Duration Override What is Duration Override? Duration is a required value on a bond in order to calculate attribution. The duration override feature is to be used for bonds that the option model can not analyze at the given price or for bonds that you disagree with the Yield Book duration number. By utilizing the duration override feature, you can approximate return attribution components for any permissible securities for which the Yield Book is able to calculate a total return. Some examples include: If a bond is trading to call, but the market price is way above the call price. The option model can not run at the given price. You created a user bond to act as a security that the Yield Book does not handle and you want to define your own duration number. Let s say you wanted to change the duration assumption on the SWT bond to 8.5 by using the duration override. What are the steps: STEP 1: First let s click on the SWT bond to look the current assumptions and calculations. The duration is and the MTP is constructed with the 24 year as the best match and filled in with the 1, 2, 3, 5, 10, 20 yr. and cash. STEP 2: Click [Adjustments] to display the adjustments page. STEP 3: Enter duration override of 8.5 in the New column. STEP 4: Click [Update Current]. When this happens, you will loose the calculated attribution for that bond; therefore you must re-calculate for that bond. STEP 5: Click [Calc Ret Att]. STEP 6: Click on the bond again to display the results: Analytic Effect of Using Duration Overide When you enter a duration override, the MTP is constructed using only two key rate treasuries; those that straddle the override duration value. Notice the MTP is now made up of 88.8% of the 10 year and 17.2% of the 20 year. In addition, the return difference versus the MTP (.464) is all attributed to one component: spread change. Return Attribution: Examples 2-25

76 Example #4: Prepayment Override Return Attribution: Examples

77 Example #4: Prepayment Override View Example #4: Prepayment Override View What is Prepayment Override? The prepayment override is used when you have mapped your specific pools to generics and you believe that your specific pools experienced a prepayment rate different than that of the index generic bond that you mapped to. If you do not map your pools to generics, there is no need for the prepayment override because we capture the actual prepays on your pools. A benefit of mapping pools to generics is the saved calculation time by using our pre-calculated mortgage generics results. Let s review the Return Attribution prepayment assumptions first: Return Attribution Prepayment Assumptions Mortgage Generics - uses the index actual paydown assumption. Specific Pools - uses the actual paydown of the pool. This is compared to the projected paydown and if different, there will be a prepay diff component. CMO and ABS - uses the actual paydown of the bond in the return and in the projection; therefore the prepay diff attribution component will be 0. First, let s look at the ROR data view to see the paydowns that were assumed to have occurred on this generic issue. STEP 1: Toggle ROR under data view. The beginning par amount on the generic was 20,000 and the principle amount paid was 235; therefore the index paydown was (235/20000=.01175) 1.175%. Let s assume that we know that our specific pools paid at 2% during this same period. STEP 2: Click [Adjustments]. STEP 3: Set the label for Prepay Override to your preferred choice of input: CPR, PSA, or Paydown% and enter the value. In this example, we want to enter 2 under PYDWN%. STEP 4: Click [Update Current]. STEP 5: Click [Calc Ret Att]. The results now show the principle paydown at 400 instead of 235; or a 2% paydown. This increased the return on the bond from a to Increased paydowns on a discount help the return of the bond. Return Attribution: Examples 2-27

78 Custom Data View Return Attribution: Examples

79 Custom Data View Custom Data View What is the Custom View? There are six global data views on the return attribution page. In order to display a value that does not exist on any of these views, you must use the [Custom View]. [Custom] allows you to retrieve a template from your template list in Ch Templates can only be customized in Ch Let s see how to add the keyword for Return Attribution Index Paydown to a template and view it in the custom view. STEP 1: Click [Send to 4.2] under the Output section. STEP 2: Click [Report]. STEP 3: Enter ret att in the yellow search field to scroll through the templates. Click on the template you wish to customize. STEP 4: Click [Customize Report]. STEP 5: Click [Insert Column], click on the column where you want to insert the keyword and choose a keyword to add. In this example, we are entering the IXPAYDN keyword. We also deleted a few columns. STEP 6: To save this template for use in Ch 4.6, enter a template ID and click [Save]. STEP 7: Turn back to Ch 4.6, toggle in front of <Custom> and click the button [Custom] to bring up the template selection list. STEP 8: Click on the new template. Reporting In addition to the Custom View, you can generate reports directly from the Return Attribution page. [Report] Button [Print Summary] Button When you click [Report] under the Output section of the page, this takes you to the template list in Chapter 4.2 where you can choose a template and sector if required and generate a report. When you click [Print Summary], you will generate the standard return attribution summary table report. Return Attribution: Examples 2-29

80 Custom Setup Parallel Shift Point: Other Options: Option Box to Use the selections you have chosen under [Custom Setup Button] 2-30 Return Attribution: Examples

81 Custom Setup Custom Setup There are several options available to customize the return attribution calculation. We will first review the options and then do an example. Parallel Shift Point: The first is to change the point on the yield curve that is used to determine the parallel shift calculation. The default is the 10 year. This is a yellow field under the Yield Curve display; you can enter another point and recalculate. The remaining options are available under [Custom Setup]. What is Custom Setup We have made several user options available to reduce the time of calculations. Please be aware that these are only helpful in reducing time if you already plan NOT to use our precalculated results. Click [Custom Setup] to see the options. If you wish to apply any of them, after selecting them in the Custom Setup, you must click the option box in front of the Custom Setup button. Partial Duration Points Return Attribution Components WARNING: You may choose any number of partial duration calculations to be used to calculate the MTP. For example, some mortgage users may wish to use only the 2,5,10, and 30yr. You may reduce the number of return attribution components by choosing combined spread other category or combined total spread advantage category instead of the full detail. YOU MUST BE CAREFUL NOT TO MIX RESULTS CALCULATED WITH DIFFERENT ASSUMPTIONS. Return Attribution: Examples 2-31

82 Example #5: Custom Setup Report Before Custom Calculation (after Adjustments) Report After Custom Calculation 2-32 Return Attribution: Examples

83 Example #5: Custom Setup Example #5: Custom Setup Problem Assumption: If you change the parallel shift point, how different would the attribution results be. Assume we are at the same results as in Ex. #4 including all of the user adjustments. We first generate a summary report to see where we stand. Then we will change the assumptions in the calculation and regenerate the results. STEP 1: Click [Print Summary] to print out a summary report. The [Print Summary] button is not shown, but the report output is displayed on the opposite page. STEP 2: Turn the Option Box on and Click [Custom Setup]. STEP 3: Select Combined Total Spread Advantage Category STEP 4: Change the parallel shift point to 5 years. STEP 5: Click [Calc Ret Att]. STEP 6: Click [Print Summary]. Let s compare the results from the table below: Notice that the only change was the allocation between the parallel shift and the reshaping components of the Total Tsy Effect. The parallel shift at the 5-year was -66 basis points while the shift at the 10-year was only -60 basis points. The total treasury return is not affected by changing the parallel shift point. ABCco2 Portfolio Before Custom Calculation After Custom Calculation Diff Total Return Parallel Shift Reshaping Tsy Rolling Yield Total Tsy Effect Spread Advantage Return Attribution: Examples 2-33

84 Active Portfolios with Transactions As discussed in the methodology section of this workbook, transactions for active portfolios can be analyzed in Return Attribution as long as the transaction history is saved with the portfolio first. The overall process for calculating returns on active portfolios is as follows: Setup for the Return Attribution Calculation STEP 1: Save a Price File for positions as of the beginning of the analysis period as part of your regular month end processing. STEP 2: During the month, load the transactions on the day of the trades. (Or you can load all of the transactions at once at the end of the month). This is a key step in the return attribution process. The transactions must be entered correctly in order to be taken into account. STEP 3: At the end of the month, create a Price File for positions as of the end of the analysis period (which will then become your beginning price file for next month). Let s review a few terms and then go through some examples of how to enter transactions to a portfolio. Analysis Period The begin and end date of the return attribution analysis period. Investment Segment An investment segment is a holding in a security from Time A to Time B. If a security is in the portfolio throughout the analysis period, Time A is the beginning of the analysis period and Time B is the end of the analysis period. If a security is purchased and sold within the analysis period, Time A is the purchase trade date and Time B is the sell trade date Return Attribution: Examples

85 Active Portfolios with Transactions Transactions: Assumptions about Investment Segments For active portfolios, you will define the portfolio composition at the beginning of the analysis period and all of the transactions (buys, sells, cash inflows, cash outflows) over the period. The Yield Book will preprocess the beginning portfolio and transactions into investment segments. The current pre-processing and return calculation process will make the following implicit assumptions: Important Notes about Cash Assumptions: The current assumptions about cash will be revised with the next update of Return Attribution in the Yield Book. Currently, the assumptions are as follows: 1. Cash generated by an investment segment (coupon payments, partial and/or full principle redemptions s, reinvestment earned) remains with the investment segment until the end of the investment segment period. To reflect a withdrawal of cash prior to the end of an investment segment requires the definition of a transactions where a cash security is sold. For example, do not enter transactions to reflect interest payments or principle payments (coupon payments, called bonds, sinking fund amounts, or mortgage paydown). 2. All cash resulting from selling a security (including cash accumulated during the investment segment period) leaves the portfolio. To reflect a sale of a security in which the proceeds are not reinvested in another security and results in cash kept in the portfolio requires the definition of a transaction where a cash security is bought. 3. Cash inflows into the portfolio, which are immediately invested in a security are reflected by defining an investment segment for the purchased security. Cash inflows into the portfolio that are kept temporarily as cash require a cash investment segment. For example, when cash infusions occur, enter a buy cash trade and when redemptions occur to the portfolio, enter a sell cash trade. Reminder: In a future release, the Yield Book will handle many of these cash transactions without you having to enter them. This is currently in development. Currently, you must enter the transactions as defined above. Return Attribution: Examples 2-35

86 Entering Transactions: Chapter , Return Attribution: Examples

87 Entering Transactions Entering Transactions Transactions can be entered in one of three places in the Yield Book: Chapter 3.2 -Portfolio Definition, Chapter Multiple Portfolio, or in Chapter The YbPort function. Let s see a few examples: Assume that the ABCco2 from 9/1/99 was our beginning portfolio (the same portfolio as we used earlier) and the following events occur over the month of September. A cash inflow of 10,000 to the portfolio on 9/3/99. Sell 5,000 par FNMA 6.5 generic at 95 on 9/9/99 for settle 9/15/99. Buy 15,000 par of FNMA 7 tba generic on 9/9/99 for settle 9/15/99 at 98 using the cash inflow and the proceeds from selling the FNMA 6.5 s. Example #1: Cash Inflow STEP 1: Turn to Chapter 3.2, click [Portfolio Select] and retrieve the base portfolio by clicking on it. You may wish to make a duplicate copy of the base portfolio and save transactions to this portfolio. For example, make a duplicate of ABCco and name it ABCcoT for Transaction. This way you have preserved your month-end holdings portfolio. Once the portfolio is selected, the Issue Selection is the default right-hand page. If you buy or sell a bond, you must search the bond in again. STEP 2: On the issue selection page, search for CASHUSD. STEP 3: Enter 10,000 in the par amount field. The [Enter Transaction] button turns yellow to reminder you to enter the transaction information before clicking save. STEP 4: Click [Enter Transaction]. STEP 5: Enter the trade price as a dollar price, the trade date and the settlement date of the trade. All three fields are required. STEP 6: Click [Save]. The trade prices and dates move from the new column to the current column. STEP 7: Click [Enter Transaction] to take the transaction entry screen down and retrieve the Issue Selection page again. Return Attribution: Examples 2-37

88 Entering Transactions: Chapter Return Attribution: Examples

89 Entering Transactions Example #2: Sell 5,000 par FNMA 6.5 generic and buy 15,000 par of FNMA 7 TBA. STEP 8: Search for FNMA 6.5 (the same one you have in portfolio) because you are selling 5,000 par of your current position. STEP 9: Search for FNMA 7.5 tba since you are buying 15,000 par. STEP 10:Search for CASHUSD (not pictured). STEP 11:Click [Enter Transaction] Enter the transaction data: Sell 5000 par of FNMA 6.5 at on 9/9/99 settle 9/15/99. Buy par of FNMA 7 at 98 on 9/9/99 settle 9/15/99. Balance of trade is in cash (see next step) STEP 12:Enter transaction for the CASH part of the trade. Proceeds from sale of FNMA 6.5 less payment on buy of FNMA 7 leaves you with short 9941 in cash to complete the trade. Since we have a cash balance sitting in the portfolio, we will use that. Enter in amount for cashusd with trade and settlement date 9/15/99. STEP 13:Click [Save] to save all of the transaction data. Return Attribution: Examples 2-39

90 Returns and Attribution on Dynamic Portfolio 14 View of Transactions Return Attribution: Examples

91 Returns and Attribution on Dynamic Portfolio Returns and Attribution on Dynamic Portfolio Once all of your transactions are saved with the portfolio, we can run the analysis on the dynamic portfolio in Chapter 4.6. In this example, we will just run the analysis on the ABCco2T portfolio only (ignoring the index). STEP 14:Toggle Buy, click [Portfolio] and select ABCcoT, Next we go through the same procedures as we normally do when running attribution. Price for begin and end, use result files, then add adjustments. The steps are written below, but not pictured. Also, notice that if you toggle on <Trans> you will see the transactions that you saved with the portfolio. STEP 15:Read in Beginning User Price File (8/31/99). STEP 16:Read in Ending User Price File (9/30/99). STEP 17:Read in Result File for September. STEP 18:Enter Begin and End Price Adjustments using Price Files. STEP 19:Enter Duration and Prepay Adjustments. STEP 20:Click [Calc Ret]. You will receive a message telling you that some segments require a carry adjustment. Do you wish to continue? This message relates to the transactions you just entered where the trade date and settlement date are different. (Your saved price files already the settlement date equal to the month end date). What is the Carry Adjustment? The trade date defines the time interval over which the security is affected by market changes. The settlement date defines the time interval over which the security accrues yield. The current methodology is to carry adjust the settlement date price to the trade date by solving for a price such that the return for the security from the trade date to the settlement date is equal to a finance rate. The analytics then assume that the security accrues yield from the trade date. This is offset by the carry adjusted price which has the impact of reducing the accrual (over the delay period) to the finance rate so that the total return is unaffected. This issue is most relevant for mortgage securities where Settlement and Trade dates may be a month apart. STEP 21:Click [Yes] and the calculation will continue. Return Attribution: Examples 2-41

92 Attribution Results Results of Calculation on Static Portfolio Results of Calculation on Dynamic Portfolio 2-42 Return Attribution: Examples

93 Returns and Attribution on Dynamic Portfolio Now that the calculation is complete, we can review the output First, overall we can see that these trades did not help the portfolio at all. The overall return on the dynamic portfolio was compared to a return on the static portfolio. Return Attribution: Examples 2-43

94 Entering Transactions: YbPort 1, Return Attribution: Examples

95 Entering Transactions using a YbPort Update File Entering Transactions using a YbPort Update File Let s do the same example using a YbPort update file. An update file with transactions looks a lot like a portfolio file excpet that the update file includes only those issues and par amounts that must be changed in, or added to the existing portfolio along with the trade prices, trade dates, and settlement dates for each entry. STEP 1: Turn to Chapter 3.5, click [Edit] and create the file directly on the yellow input screen as shown below. You may also create this file in another program outside of the Yield Book such as Excel and upload the file through Ch 1.2. STEP 2: Enter the contents of the file as shown below: The update file format is identical to the portfolio file format, except that a + must precede the portfolio name. You must append the letters td to the date to indicate trade date and the letters sd to indicate settle date in a transaction entry. The trade date is mandatory. We will assume that td=sd if the settlement date is not entered in the file. STEP 3: Enter a file name and click [Save]. STEP 4: Click [Edit] again to get out of edit mode, select the file on the right, choose your pricing options. STEP 5: Click ont eh file in the list box on the right. You should see the file name appear on the left page. Make your ybport option selections. STEP 6: [Process] on the right page to Process. You can see the results of the update by turning to Ch. 3, Pg. 2 and retrieving the portfolio. Please note that par amounts are not consolidated automatically after a transaction update. Instead, a bond is added to the listbox showing a negative par amount (if sold) and a positive par amount (if bought). Return Attribution: Examples 2-45

96 Trading Prior to Dated Date in Return Attribution Currently, return attribution cannot be calculated on bonds that are traded before their dated dates (i.e. buying when issued securities or buying newly issues bond prior to the dated date). Since all trades are carry adjusted from the settle date to the trade date and the Yield Book cannot settle the bond before the dated date, the following error message will appear: Begin settle date inconsistent with Global. Two methods may be used to approximate such a trade. Based on the strengths and weaknesses of each method, the user should decide which method is appropriate for his/her application. Method 1: Assume trade date is the dated date. Assume the trade is completed on the dated date at the given price. Advantage: 1. Since no accrued occurs before the dated date, the returns on the bond are correct. Disadvantages: 1. If the dated date is after the end of the period, the bond will need to be left out of that analysis period. 2. The attribution may be incorrect due to the fact that the yield curve and other data will be different on the dated date than on the trade date. Specifically, this means that the return attribution allocated between yield curve changes and spread change will be incorrect. The magnitude of the error will be proportional tothe magnitude of the move in the Yield Curve between the trade date and dated date. Method 2: Substitute a User Bond You can create a user bond where you define the dated date on the issue to be equal the trade date. Advantage: 1. The attribution of market affects will be approximately correct because the yield curve and other date will use the values associated with the trade date. Remember to use the user bond in the attribution instead of the actual bond. Disadvantage: 1. The accrued will be incorrect because of the adjustment in the dated date. This means the accrual income received and the full price calculations will be incorrect; thus an there will be an error in the computation of total return. This error will be proportional to the number of days between the trade date and the dated date. The error will be relatively small if the actual trade date is close to the actual dated date. Method 1 should be more appropriate if the number of days between the trade date and dated date is large or if the yield curve did not move significantly between the two dates. Method 2 will be more appropriate if the number of days between trade date and dated date is small and the yield curve did move significantly between the two dates Return Attribution: Examples

97 General Notes about Return Attribution General Notes about Return Attribution 1. If you do not map your specific pools to generics, always enter your amounts for the pools in ORIGINAL face. If you forget to do this, and enter current face, the Yield Book will compute the original face from your current face input and base the rest of the calculations on that original face. 2. Review the general assumptions the Yield Book makes about cash. See Important Notes about Cash Assumptions: on page Currently, intra-day trade effects are not captured. The Return Attribution Methodology uses Yield Curves and other market parameters as of the 3:00 P.M. market close. To correctly attribute the return into components, the trade prices defined for the securities should also be as of the 3:00 P.M. market close (not necessarily the price you actually completed the trade at). In situations where the security is purchased (or sold) during a volatile day at a point where the Yield Curve was significantly different from the close, the actual trade price may be significantly different from the 3:00 P.M. valuation. To allow this price difference to be reflected in the Total Return of the portfolio, the user can input the trade price in the price adjustments field. 4. Currently, there is no ability to enter price adjustments to the sell side portfolio, even if it is not an index. 5. We are currently working on implementing return attribution for nondollar bonds. Return Attribution: Examples 2-47

98 2-48 Return Attribution: Examples

99 WORKSHOP Multi-Currency Return Attribution: Methodology Agenda As you have seen so far, the Salomon Smith Barney (SSB) Return Attribution Model in the Yield Book calculates and dissects total returns of multi-currency fixed income securities, trades, portfolios and/or indices into return attribution factors. The attribution factors explain why the bond achieved the return that it did. The first section focused only on US dollar securities. Now we move on to other currencies including looking at multi-currency portfolios. The model analyzes portfolios and indices by aggregating the issue level return components to the market and sector level. The market level aggregation allows the model to measure the effect of portfolio strategies such as forex hedging, inter market weighting and intra market performance. The sector level aggregation allows the model to measure the effects of portfolio strategies such as sector weightings and issue selection. Highlights In this section of the advanced workshop chapter, we will cover the following: Understanding the Return Attribution Model Methodology and the Components of Return for Securities whose local currency is not equal to the base currency. Computing Portfolio versus Index Return Attribution on Multi-Currency Portfolios including Allocation of Returns in Multi-Currency Portfolios. Salomon Analytics Inc.

100 Return Attribution on Non-dollar Securities In addition to the local market attribution factors, the return attribution model computes the currency effect on the bond and the portfolio. The steps required to run multi-currency portfolio attribution are the same as running single-currency portfolio attribution except for the following: The Yield Book must be in International Mode - set in Pricing Setup in Return Attribution Mode (after going to the Return Attribution Page). A base currency must be selected in Pricing Setup. The default hedging strategy is assumed to be 100% hedged for both the buy and sell side portfolios. If your hedging strategy is anything other than 100% hedged in every currency, then you will define the % hedged for each currency on the Return Attribution Adjustments page (an example will be shown). Return Attribution cannot currently handle currency forwards; instead, enter the % hedged for each currency. Pre-calculated Data: Partial Durations and Results Global return attribution price files contain partial durations on nondollar securities for Salomon source bonds. Monthly result files on the WGBI since 12/31/99 are available. Notice a few updates to the Return Attribution page for multi-currency analysis: Return Attribution Page: Yield curve - the yield curve displayed is the global curve from [Pricing Setup] when in single currency mode. To view a different curve go to [Pricing Setup], turn to single currency mode, and select the curve of your choice. Note: If all securities on Chapter 4.6 are in a single currency, that currency s yield curve is automatically displayed. Base Currency - the base currency is displayed as defined in [Pricing Setup]. To change the base currency, go to [Pricing Setup], turn to international mode, and select the currency from the menu box. View Mode - The multi-currency view mode has been updated to show several new terms which will be explained in the next section. Adjustments - There is a new feature in the adjustments page for multi-currency portfolios. The adjustment is used for entering your currency hedge percentage if it is anything other than 100%. 3-2 Multi-Currency Return Attribution: Methodology

101 Methodology and New Terms Methodology and New Terms The individual security local return and attribution factors for non-dollar bonds are computed in the same way as the US dollar securities. In general, a matched government bond portfolio is created for each security using hypothetical bonds generated from the yield curve associated with the currency denomination of the bond. Then a succession of scenario analyses are performed to capture each of the rolling yield and market effect components which explain the bond s local return. Finally, the currency is taken into account to compute the base currency return. The currency effect is broken down into two major components: Total 100% Hedged 1 Forex (FX) Return (ROR) FX Advantage - the difference between the Total Base Return given the actual hedge and the Total Base Return assuming 100% hedged. Total Hedged FXROR The Total Hedged FX ROR can be broken down into two components: Hedge Premium ROR and Unhedged Market ROR The 100% currency hedge assumes a hedge on the beginning market value times the local rolling yield return. The exchange rate locked in at the beginning of the analysis period for the end of the analysis period is based on the interpolated market forward quotes and is called the forward exchange rate. The Hedge Premium ROR is the ratio of the forward exchange rate divided by the spot exchange rate. The Unhedged Market ROR measures the currency effect of having hedged the local rolling yield ROR only. If the Local Market ROR is anything other than zero, then a portion of the local ROR is unhedged and there will be an Unhedged Market ROR component. The Total Hedged FX ROR plus 2 the Total Local ROR equals the Total Hedged Base ROR assuming you are 100% hedged. FX Advantage The FX Advantage measures the effect of your actual hedging decision. If you are anything other than 100% hedged, then there is a FX Advantage. The FX Advantage plus the Total 100% Hedged Base ROR equals the Total Base ROR based on your actual hedge. Total Actual Hedged Base ROR As mentioned above, the Total Actual Hedged Base Total ROR is equal to the Total Hedged Base ROR plus the FX Advantage. 1. For simplicity, when we use the term hedged, the assumption is 100% hedged unless otherwise stated, such as a specific % hedge or Actual hedge 2. Since the YB actually compounds returns, the plus term is used to simplify the discussion. Multi-Currency Return Attribution: Methodology 3-3

102 Equations We will now go through the equations: Notice that the Yield Book keyword is denoted in () in the left margin. Hedge Premium ROR (RAHDGPREM) forward exchange rate begin exchange rate Unhedged Market ROR (RAUHDGMKT) end exchange rate forward exchange rate Local Market ROR Local Market ROR This is the currency effect due to the fact that the ROR was different than the Rolling Yield ROR on the bond, but the hedge is only on the Rolling Yield ROR. The Hedge Premium ROR plus the Unhedged Market ROR equals the Total Hedged FX ROR shown below: Total Hedged FX ROR (RAHDGFXTOT) Hedge Premium ROR Unhedged Market ROR The Total Hedged FX ROR plus the Total Local Market ROR equals the Total Hedged Base ROR shown below: Total Hedged Base ROR (RAHDGBRET) Total Local ROR Total Hedged FX ROR So far, we have calculated the Total Hedged FX ROR. If the actual hedge is 100%, then the analysis is complete. If the actual hedge is anything other than 100%, then another factor called the FX Advantage accounts for the difference between the Total Actual Hedged Base ROR and the Total Hedged Base ROR. First let s compute the Total Actual Hedged Base ROR. 3-4 Multi-Currency Return Attribution: Methodology

103 Equations Total Actual Hedged Base ROR (RAACTHDGBRET) The Total Actual Hedged Base ROR can be expressed in two ways: The first equation shows that the Total Actual Hedged Base ROR is the sum of the Total Unhedged Base ROR and the Total Actual Hedged ROR (the ROR of hedging forward contracts accounting for the fact that only the Rolling Yield ROR is hedged and it is hedged at the forward exchange rate). The formula is: Total Unhedged Base ROR + Actual Hedged ROR Tot Local ROR Unhedged FX ROR (% hedge) Rolling Yield foward exchge rate end exchge rate begin exchge rate where Unhedged FX ROR = end exchange rate begin exchange rate The second equation (below) shows that the Total Actual Hedged Base ROR can also be expressed as the Total 100% Hedged Base ROR plus the FX Advantage: Total 100% Hedged Base ROR FX Advantage Once the Total Actual Hedged Base ROR is calculated from the first equation, the second equation can be used to solve for the FX Advantage, or the difference between the Total Actual Hedged Base ROR and the Total 100% Hedged Base ROR. Solving for FX Advantage, the equation is: FX Advantage (RAFXADV) Total Actual Hedged Base ROR Total 100% Hedged Base ROR Multi-Currency Return Attribution: Methodology 3-5

104 1 Portfolio vs. Index Example Steps for Return Attribution Multi-Currency Return Attribution: Methodology

105 Example: Multi-Currency Portfolio vs. Index Example: Multi-Currency Portfolio vs. Index This example looks at a Euro based investor (base currency is the Euro) whose benchmark is the G-5 (US, France, Germany, UK, and Japan) portion of the World Broad Investment Grade Index (WBIG) as of 8/1/00. The return period is for the month of August 2000 (7/31/00-8/31/00). The benchmark is assumed to be 100% currency hedged at the beginning of the period. The portfolio (INTPORT) was constructed by re-weighting the benchmark with the following adjustments: Portfolio INTPORT Characteristics Overweight France by 5.104% - holding all index issues Underweight Japan by 5.104% - holding all index issues In the US market, INTPORT has no government bonds, instead their market weight was invested in Agencies. The agency sector in US is represented by only one bond. Hedging strategy - All currencies are 100% hedged except for British Pound which is completely unhedged. In order to focus on the new terminology, we assume there are no transactions. Steps to Run Attribution To get started with a multi-market (currency) portfolio, first put the Yield Book into International mode and define the base currency. STEP 1: Turn to Chapter 4.6 to be in Return Attribution Mode and toggle <Begin>. This step is necessary before going into Pricing Setup so that Pricing Setup is in Return Attribution Begin Mode instead of the global Pricing Setup when not in Return Attribution Mode. STEP 2: Click on [Pricing Setup]. STEP 3: Toggle <International> mode and select the base currency (EURO in this case). Multi-Currency Return Attribution: Methodology 3-7

106 , Multi-Currency Return Attribution: Methodology

107 Example: Multi-Currency Portfolio vs. Index Select the Buy and Sell Side Portfolio and Benchmark Select a portfolio as the buy side and an index as the sell side. In this example, we have selected a portfolio on both the buy and sell sides. This is because we created a custom index which is saved as a portfolio not as an index. STEP 4: In Chapter 4.6, toggle <Buy> and click on the portfolio. STEP 5: Toggle <Sell> and click on the portfolio used to represent the index. Pricing for Begin and End Dates Price the bonds manually using the [Load Yield Curve] and [Pricing Page] buttons or use a previously saved price file for the begin and end dates using the [Price File] button. In this example, we use the SSB provided month-end pricing files. STEP 6: Under Pricing, toggle <Begin> to price for the beginning. STEP 7: Toggle <RA.Monthly> to display the list of price files. STEP 8: Click RA.Aug to price for 7/31/00. STEP 9: Toggle <End> to price for the end date. STEP 10:Toggle <RA.Monthly> to display the list of price files. STEP 11:Click RA.Sept to price for 8/31/00. STEP 12:Under the Calculations section, toggle on <RetAtt> to run both the returns and the attribution and click [Calc Ret Att]. Default is 100% hedged for all currencies on buy and sell side. Once this is complete, the returns and attribution results are provided assuming 100% hedged portfolio and index. The Total 100% Hedged Base ROR (.066) is equal to the Total Actual Hedge Base ROR (.066). This is because the % hedge column is 100% for all bonds. Therefore, the FX Advantage, which measures the effect of a hedge percent different from 100%, is 0. If the currency strategy is 100% hedged, the analysis is complete; otherwise go to Step 13 on the next page to enter hedge percentages by currency. Multi-Currency Return Attribution: Methodology 3-9

108 Sell side remains 100% Hedged Buy Side: 100% hedged except for GBP Multi-Currency Return Attribution: Methodology

109 Example: Multi-Currency Portfolio vs. Index Enter Hedge Percentage: Adjustments STEP 13:To enter currency hedge percentages for the BUY side, toggle the <Buy>. STEP 14:Click [Adjustments]. STEP 15:Toggle <Currency % Hedged>. STEP 16:Enter the % hedged in the New Hedging column and click [Update Current]. In this example, enter 0 in for GBP to be completely unhedged in GBP. Notice that this is the hedge input for the BUY side since we are toggled on Buy. All other percentages are equal to the default and do not need to be defined. This is also the case on the sell side. STEP 17:Click [Adjustments] to refresh the screen and display the newly computed results. Notice that the overall portfolio has a FX Advantage of.072. Only the bonds with currency equal to GBP have a FX Advantage term. Now there is a new Total Actual Hedge Base ROR term (.732) which takes into account the FX Advantage. Multi-Currency Return Attribution: Methodology 3-11

110 GBP on Buy Side is 200% Hedged GBP on Buy Side is -100% Hedged 3-12 Multi-Currency Return Attribution: Methodology

111 Hedge Strategy Notes: Hedge Strategy Notes: The hedge percentage does not have to be between 0 and 100. To reflect a leveraged bet that the currency will depreciate, enter a hedge % greater than 100. To reflect a leveraged bet that the currency will appreciate, enter a hedge % less than 100, including a negative %. Two examples are shown below: 200% Hedge GBP In the above example, to reflect the GBP was going to depreciate relative to the EURO, you could hedge the GBP at 200%. If the GBP did depreciate relative to the EURO, you would have a positive FX Advantage due to being overhedged. In this example, the opposite occurred. The GBP appreciated relative to the EURO. The EURO/GBP rate went from per 1 GBP to per 1 GBP. The result is a negative FX Advantage. Since you were invested in GBP, which appreciated, it would have been better not to hedge back into EURO. If you had hedged 100%, then the FX Advantage would equal 0. Instead you bet on the EURO relative to the GBP and this negative FX Advantage decreases the Total Actual Base ROR. Total Hedged Base ROR =.660 FX Advantage = Total Actual Hedge Base ROR = % Hedge GBP To bet that the GBP would appreciate versus the EURO, you could underhedge the GBP to EURO by entering a percentage less than 100. In this example, we enter Since the GBP did appreciate versus the EURO, it was good to underhedged the GBP. There is a positive FX Advantage which helps the Actual Hedge Base Total ROR. Total Hedged Base ROR =.660 FX Advantage =.143 Total Actual Hedge Base ROR =.803 Now let s return to the original problem where all currencies are 100% hedged except for GBP, which is 0% hedged. Multi-Currency Return Attribution: Methodology 3-13

112 Example: AA 7.25, Multi-Currency Return Attribution: Methodology

113 Bond Examples Bond Examples AA 7.25,05 This is a US dollar bond 100% hedged to the EURO. There should be a Total FX Return but no FX Advantage. Hedge Premium ROR forward exchange rate begin exchange rate ( / ) - 1 * 100 = Unhedged Market ROR end exchange rate forward exchange rate Local Market ROR Local Market ROR = Total Hedged FX ROR Hedge Premium ROR Unhedged Market ROR [( ) * ( )] -1 * 100 = Total Hedged Base ROR Total Local Market ROR Total Hedged FX ROR [( ) * ( )] -1 * 100 = Total Actual Hedged Base ROR Since the hedge is 100%, there is no FX Advantage. The Total Actual Hedged Base ROR is equal to the Total Hedged Base ROR calculated above ( ). The total local (USD) return was 1.223, (rolling yield return of.577 and local market return of.642). The hedge hurt the rolling yield by because the forward exchange rate was lower (1.0768) than the begin exchange rate (1.0792). The end exchange rate increased to The Euro came down relative to the dollar so it was good not to hedge the local market return. This is reflected in the unhedged market being a positive.028. Multi-Currency Return Attribution: Methodology 3-15

114 Example: BTY 7.125, Multi-Currency Return Attribution: Methodology

115 Bond Examples BTY 7.125,03 This is a GBP denominated bond and we are 0% hedged to the EURO. This means there should be a FX Advantage. Hedge Premium ROR forward exchange rate begin exchange rate (1.6137/1.6163) - 1 * 100 = Unhedged Market ROR end exchange rate forward exchange rate Local Market ROR Local Market ROR = Total Hedged FX ROR Hedge Premium ROR Unhedged Market ROR [( ) * ( )] -1 * 100 = Total Hedged Base ROR Total Local Market ROR Total Hedged FX ROR [( ) * ( )] -1 * 100 = This bond returned less than its rolling yield due to negative market effects. The Unhedged Market Return is negative since the negative market return implies the bond was overhedged and the forward exchange rate (1.6137) was lower than the end exchange rate of (1.6365). Finally, as shown on the next page, the currency decision not to hedge GBP helped by because the Euro depreciated relative to the GBP over the month. Multi-Currency Return Attribution: Methodology 3-17

116 Example: BTY 7.125, Multi-Currency Return Attribution: Methodology

117 Bond Examples Actual Hedged Base Total ROR Total Unhedged Base ROR + Actual Hedged ROR Tot Local ROR Unhedged Currency ROR (% hedge) Rolling Yield foward exchge rate end exchge rate begin exchge rate In this example, since the hedge % is 0, the Total Actual Hedged Base ROR is equal to the Total Unhedged Base ROR. = [( ) * ( ) -1] * = To solve for the FX Advantage, we use the formula: FX Advantage (RAFXADV) = Total Actual Hedged Base ROR Total 100% Hedged Base ROR ( / ) -1 * 100 = Multi-Currency Return Attribution: Methodology 3-19

118 BOBL 4.25,04 This is a EUR denominated bond (same as our base currency) so there should be no currency effect at all; both Total FX Return and FX Advantage should be 0. The local return equals the base return Multi-Currency Return Attribution: Methodology

119 Allocation of Return in Multi-Currency Portfolios Allocation of Return in Multi-Currency Portfolios Once the individual security returns and attribution factors are calculated, the portfolio totals are computed. Then the portfolio is compared with a benchmark, usually an index, in order to allocate the return due to Intra- Market effects on a single-currency portfolio or due to Inter-Market effects on a multi-currency portfolio. From now on, when we use the term market in return attribution on multi-currency portfolios, it is assumed that market means the bond market in a given currency. (i.e. all bonds which trade off of a particular yield curve). Intra-Market We refer to Intra-Market allocation within one currency or yield curve market. In this case, we allocate the total spread advantage difference from the index (not including the total treasury effect) into two components when comparing to a benchmark (as described in section 1 of this workbook). Sector Selection Issue Selection Inter-Market We refer to Intermarket allocation when there are multiple markets or it is a single market portfolio but the base currency differs from the currency of the bonds in the portfolio. In this case, we allocate the Total Actual Hedged Base ROR to three components: FX Strategy Allocation Inter-Market Weight Allocation Intra-Market Return Allocation, which as stated above can in turn be allocated to yield curve, hedging, sector weighting, and issue effects. The method employed by the Yield Book to allocate returns is based on the following six step model of the Portfolio Management Process. Steps in the Management Process of Multi- Currency portfolio: STEP 1: Select a benchmark, which is usually an index STEP 2: Select Market Weights for each Market (Currency Market) STEP 3: Select FX Exposure (Hedge %) for each Market STEP 4: Select Duration and Yield Curve Exposure for each Market STEP 5: Select Weights within each Market STEP 6: Select Issues within each Market Multi-Currency Return Attribution: Methodology 3-21

120 Multi-Currency Return Attribution Allocation Report Multi-Currency Return Attribution: Methodology

121 Allocation of Return in Multi-Currency Portfolios Steps to Generate the Multi-Market Allocation Report STEP 1: Click [Report]. STEP 2: Select the template RETBMKMM Multi-Market Benchmark template. STEP 3: Select the Currency Sector File with ID PROF13. STEP 4: Click [Generate Report]. The template is broken down into four major sections: Local Returns - local currency returns Total 100% Hedged Base Returns Total Actual Hedged Base Returns Allocation of Base Return Difference FX Strategy Allocation measures the effect of the currency strategy on the portfolio base return relative to the benchmark. It is calculated as FX Strategy = Allocation FX Advantage of Market in Portfolio X Market Weight in Portfolio FX Advantage of Market in Index X Market Weight in Index Inter-Market Weight Allocation measures the effect of market under or over weighting decisions. It is calculated for each market by: Inter-Market Weight = Allocation Weight of Market in Portfolio Weight of Market in Index X 100%Hdg ROR of Market in Index 100% Hdg ROR of Entire Index Intra-Market Return Allocation measures the effect of yield curve, hedging, sector weighting and issue selection decisions within individual markets. It is calculated for each market by: Intra-Market Weight of Market Return Allocation = 100% Hedged Return 100% Hedged Return in Portfolio X of Market in Portfolio of Market in Index Multi-Currency Return Attribution: Methodology 3-23

122 Let s go through the examples using the report just generated. The mount to be allocated is 17.8bps. This is the difference in the Actual Hedged Base Total ROR between the portfolio and the index. FX Strategy Allocation If the hedge is 100% in every currency, then the FX Allocation is zero since the index is 100% hedged in every currency. To the extent that the portfolio hedge differs from 100% in a particular currency, there will be a FX Allocation. In this example, the FX is 7.1bps of the total 17.8 bps. col 1 col 2 col 3 col 4 col 5 col 6 = col 1 * col 3 col 7 = col 2 * col 4 col 8 = col 6 - col 7 Market Mkt Wt Portfolio Mkt Wt Index FX Adv Portfolio FX Adv Index %Hedged Portfolio Euro British Pound *5.06% = FX Allocation US Dollar Japanese Yen Total Inter-Market Weight Allocation The difference between the Total Hedged Base ROR in a particular market (currency sector) in the index and the Total Hedged Base ROR in the entire index is used to measure the effect of market weighting. The market weight allocation accounts for 3.6 bps of the col 1 col 2 col 3 = col 1- col 2 col 4 col 5 col 6 = col 4-5 col 7 = col 6 * col3 100% Hedged Return of Index Market 100% Hedged Return of Entire Index Market Market Weight Portfolio Market Weight Index Over/ Under Weight 100% Hedged Return Diff Euro British Pound US Dollar Japanese Yen Total Market Weight Effect In summary, column 6 tells us if the market was a good one to be in or not, so, the only market to be in was the US dollar. We had a very small underweight in that market which makes the effect 0. In addition, even 3-24 Multi-Currency Return Attribution: Methodology

123 Allocation of Return in Multi-Currency Portfolios though the British Pound was not a good market to be in, the very small overweight had no effect. Japanese Yen was a bad market to be in and it was underweighted that so there is a positive market weight effect of.062. This is decreased by due to the overweight in Euro which was also a bad market to be in. Intra-Market Return Allocation The Intra-Market Allocation compares the portfolio return within a market to the index return within that market. The return measure used is the Total 100% Hedged Base ROR so it looks at the difference between the Total Hedged Base ROR of a particular market in the portfolio and the Total Hedged Base ROR of the same market in the index. It is a measure of the yield curve, hedging, sector weighting, issue selection, and currency hedging decisions within an individual market.this accounts for the remaining 7bps of the 17.8 total. col 1 col 2 col 3 col 4 col 5 = col 3-4 col 7 = col 5 * col1 100% Hedged Return of Portfolio Market 100% Hedged Return of Index Market Sector Market Weight Portfolio Market Weight Index 100% Hedged Return Diff Euro British Pound US Dollar Japanese Yen Total Intra-Market Return Allocation To see the Intra-Market Return further broken down into the yield curve, sector and issue selection components in each market, focus on a specific market and generate a return attribution benchmark report using a sector file of your choice. The example on the next page uses the US Dollar market portion of this portfolio. Multi-Currency Return Attribution: Methodology 3-25

124 Single Currency Return Attribution Allocation Report Multi-Currency Return Attribution: Methodology

125 Allocation of Return in Multi-Currency Portfolios STEP 1: Click [Focus] to bring up the focus selection input field. STEP 2: Enter focus selection criteria and click [Process]. STEP 3: Click [Report]. STEP 4: Select the Return Attribution Intra-Market Benchmark Comparison Template STEP 5: Choose a sector file. STEP 6: Click [Generate Report]. Recall in the multi-currency report that the total outperformance of the US market between the portfolio and the index was 13.3 basis points. (1.394 Total 100% Hedge Base ROR in portfolio versus Total 100% Hedge Base ROR in index). That 13.3 basis points of return is made up of: Local outperformance in US = 12.9bps + Unhedged Market Effect =.5bps 13.4bps The single currency report allocates the 12.9 basis points to Total Treasury Effect (-1.4bps) and Total Spread Advantage (14.1bps). Finally, the 14.1 bps of Total Spread Advantage is allocated between sector and issue selection depending on the sectors chosen. Multi-Currency Return Attribution: Methodology 3-27

126 3-28 Multi-Currency Return Attribution: Methodology

127 WORKSHOP Optimization Agenda The optimization page in the Yield Book is a flexible, linear programming tool that can be used to solve a variety of problems. Applications include trade weighting and portfolio optimization relative to a benchmark. The layout of the optimization page is extremely adaptable to many different problem formulations. Highlights Optimization Terminology Page Layout and Navigation General Procedure Problem Formulation and Working with Constraints Once the basic concepts are defined, the following step-by-step examples will be explained: Trade Weighting Optimization: Issues defined on the buy and sell sides will be used to create an optimum combination of long and short positions that is effective dv01 neutral. Hedging Corporate Securities: Similar to trade weighting, this example demonstrate how to hedge corporates along different portions of the curve by shorting treasuries. Creating a Tracking Portfolio: A universe of issues will be used to construct a portfolio that tracks the treasury index. Portfolio Optimization Relative to a Benchmark: An existing portfolio will be used with universe issues to create a new optimum portfolio that meets constraints defined relative to a benchmark and issuer level constraints. Salomon Analytics Inc.

128 Optimization and Constraints Definitions Objective Sector Conditions Constraints (#1,3,4,5) Modes Optimization Tips Define only one objective (the goal) for optimization. Use optimization constraint templates to help define one or more constraints. Scrutinize results -- optimization can be used to hone in on mispriced securities. Save the current optimization universe (click on the [Operations] button) for future optimizations. Use the optimization Report templates to generate useful reports on your results Optimization

129 Optimization Terminology Optimization Terminology The following terms are used in the Yield Book to describe optimization procedures: Buy/Sell Mode Own/Univ/BL Mode This mode of optimization is used mostly for trade weighting (long and short positions). Issues defined on the buy and sell sides are considered for the optimum solution. Constraints may be placed on either the buy side, the sell side, or the difference (buy - sell). This mode is used for portfolio optimization that may include constraints relative to a benchmark. In general, an owned portfolio is used in conjunction with a universe to construct an optimum net portfolio relative to a baseline. U, Universe The optimization universe includes all issues deemed acceptable to be included in the solution. Own BL, Baseline Objective Constraints Sector Condition This label is applied to owned issues, usually bonds that are currently included in a portfolio. These bonds may not necessarily be part of the solution portfolio. Issues tagged BL are part of the baseline index or portfolio. The baseline is used to benchmark the optimization results. bl is also used to define boundary conditions in constraints. The objective function is the goal of the optimization. Typically maximize or minimize, the objective is set on the Optimization Constraints Definition page in 4.2. Constraints impose requirements on the optimal results. They can be defined on the Optimization Constraints Definition page in 4.2. There are both Soft and Hard Constraints. Soft Constraints will be described at the end of the methodology section as it is a more advanced feature. Sector conditions focus a constraint on a specific set of issues. The condition is defined as part of the constraint definition. The sector condition s0 means all issues and is the default value. Optimization

130 General Optimization Procedure 1 toggles Constraints & Objectives Optimization

131 General Optimization Procedure General Optimization Procedure The procedure for a variety of Optimization problems is generalized in the following steps described below and illustrated on the opposite page. In the next section we will present four specific examples in detail. STEP 1: Go to Ch. 4.2 On the left page in the Yield Book, there is a toggle for the mode of optimization. Select either Buy/Sell or Own/Univ/BL, depending on your problem. STEP 2: Retrieve Issues and Benchmark. In Buy/Sell mode, simply retrieve portfolios or issues on each side by using the buy/sell toggles. In Own/Univ/BL mode, first toggle on the own/univ side and retrieve the owned issues by retrieving a portfolio through portfolio select. Keep the toggle on own/univ to read in the universe issues. They must be retrieved through the domain on the issue selection page. Then toggle on the baseline side and, using portfolio select, retrieve the portfolio or index that will be used for the benchmark. STEP 3: Click on the [Optimization] button to enter optimization mode. This step displays the Optimization Constraints Definition page on the right side. This page is used for most of the problem formulation. Both the objective function and constraints will be defined on this page. STEP 4: Define an objective and/or constraints for Optimization. Default constraint templates will appear automatically, depending on the mode of optimization. A constraints file may be retrieved or the constraints may be created. Problem formulation and constraint definition will be covered in detail in the next sections. STEP 5: Click on [Calculate] Optimization

132 Objectives and Constraints Constraints (#1,3,4,5) Objective Optimization

133 Objectives and Constraints Objectives and Constraints Objectives and constraints pose the problem for optimization. The Yield Book provides the tools to define the problem and to find the best solution. The Objective The objective is the goal of optimization. You will likely know what the objective of the optimization and be able to express it in plain language. Since the objective and constraints syntax is similar, you can define the objective in the Optimization Constraints Definition page of the Yield Book, using defined keywords and values. You can also choose from several constraint templates provided by the Yield Book. The templates contain pre-defined objectives and constraints, which can be modified or made inactive depending upon the goal of optimization. Objective Examples What are Constraints? One example of an objective would be to minimize the cost (total market value) of the resulting optimum selection of issues. Another example is to maximize the overall Yield To Maturity of the results. Constraints impose restrictions and conditions on the optimization results. You can formulate these constraints based on your optimization problem, then define them in the Yield Book using the Optimization Constraints Definition page. Constraints can be applied to the following items: The universe of optimization issues ( All securities included in Ch. 4.2 listbox ). Constraints for these issues are defined in the Optimization Constraints Definition page. For these constraints, the value of the sector condition should be s0, which means apply this constraint to all issues. See the example on the opposite page. A sector of issues. A sector condition in the constraint definition, describes the set of issues that are the focus of the constraint. An individual issue. Per-issue constraints are defined in Ch. 4.2 in the left page listbox Optimization

134 Get Started 1 & Optimization

135 Get Started Get Started How to Get There Define an Objective and Constraints Constraint Templates Click on [Optimization] in Ch. 4.2 to display the Optimization Constraints Definition page, where constraints for all issues or for sectors of issues are defined. There must be only one objective in an optimization, but there may be many constraints. Objectives and constraints are defined in the same table, in any order, on the Optimization Constraints Definition page in Ch The Yield Book will load pre-defined generic constraint templates into the constraints table according to the type of optimization being performed. You may modify, delete, or add to these commonly used constraints by following the procedure described below. Constraint definition pages are illustrated on the opposite page. STEP 1: Click on the left-most white (Keyword) box in the Constraint Definitions table, as indicated below. STEP 2: Enter search criteria for the keyword, then click on the appropriate selection STEP 3: Click on successive white boxes, moving left to right, to modify default values STEP 4: In the final right-most box, enter a boundary condition to apply to the subject of the constraint. An example is shown below. More detailed information on boundary conditions follows Boundary Condition Optimization

136 Constraint Definitions Constraint definitions for sectors of issues consist of the following components: Keyword Weighting Factor Function Sector Condition Side/Position Boundary Condition Keyword Weighting The keyword is the subject of remaining constraint definition components (for example, the EFFDUR keyword applies the constraint definition to the effective duration value, the YTM keyword applies the constraint to the Yield To Maturity value). The weighting factor can be selected from five possible values: Par Amount Market Value Macauley Duration x Market Value Modified Duration x Market Value Effective Duration x Market Value Function Sector Condition Side/Position Boundary Condition Click on this field in the constraint definition to toggle between Total (sum total) and Avg (average) aggregation functions. Select sectors from the Sector Constraint page to apply to constraints. The default value is s0 (All sectors). Use this field to define the side or, in the case of trade weighting optimization, the position of the issues affected by the constraint. Select from the following: Can be a numeric value, a keyword or an expression limiting the subject of the constraint. For example, < 100 means limit the value of the subject of the constraint to less than or equal to Optimization

137 Constraint Functions Constraint Functions The format for defining a constraint on the Optimization Constraints Definition page provides flexibility and precision. When selecting appropriate values and keywords for constraint fields, the aggregation function must first be specified as either Total or Average. The aggregation function can be changed by clicking in the Tot/Avg field of the Constraints Definition table: Referring to the constraint definition examples above, suppose the following two issues appeared in the optimization universe: NAME FPRICE YTM EFFDUR PARAMT MKTVAL BondA ,000 25,000 BondB ,000 75,000 Following are descriptions of the sample constraints applied to the two-issue portfolio above: Constraint #1 - Market Value: To constrain the market value of the optimization results, use the FPRICE keyword with the Total function. Market Value is calculated by: ( FPRICE PARAMT ) Optimization

138 Using BondA and BondB for the portfolio issues, the Market Value is: FPRICE(BondA) x PARAMT(BondA) + FPRICE(BondB) x PARAMT(BondB) = 100% x 25, % x 60,000 = 25, ,000 = 100,000 Constraint #2 - Effective Duration: To constrain the average effective duration of the optimization results, use the EFFDUR keyword with the Avg function. Effective Duration is calculated by: (EFFDUR MKTVAL ) MKTVAL Using BondA and BondB for the portfolio issues, the average Effective Duration is: EFFDUR(BondA) x MKTVAL(BondA) + EFFDUR(BondB) x MKTVAL(BondB) MKTVAL(BondA) + MKTVAL(BondB) = 9.0 x 100% x 25, x 125% x 60, % x 25, % x 60,000 = 9.0 x 25, x 75,000 25, ,000 = Optimization

139 Constraint Functions Effective Duration Dollars Often used in trade weighting problems, the effective duration dollar keyword (EFFDUR$) is expressed in a constraint in the following way: If the EFFDUR$ keyword is selected from the keyword search listbox, the above constraint will appear in the Constraints Definition table. The constraint requires that the long and short issues EFFDUR$ values be equal (Diff = 0), where EFFDUR$ is calculated by: ( EFFDV01 PARAMT ) NOTE: By convention, the value entered in the right-most field will be multiplied by 1000, so the number entered must be expressed in thousands to be interpreted as a value in millions. Optimization

140 Optimization Defining the Constraint Side

141 Defining the Constraint Side Defining the Constraint Side Define the focus of the constraint in the Side field of the Optimization Constraints Definition table. The Side field and the Sector field together define the set of issues to which a constraint is applied during optimization. There are different choices for each side depending on which optimization mode is toggled. In Buy/Sell mode, the choices are fairly straightforward. Constraints may be placed on the buy side, the sell side, or the difference (buy - sell). In Own/Univ/BL mode, there are more choices: Net Buy Sell Keep Long, Short, & Diff INet IBuy Net is probably the most commonly used side because constraints are often defined to govern the properties of the optimum (net) portfolio. It is a very direct way to construct a portfolio with a given set of characteristics. The buy side in Own/Univ/BL mode refers to constraints placed on issues to buy in the optimization. An example is the requirement to buy a certain market value from the universe to be added to an owned portfolio. Sell refers to the owned issues. A constraint may be placed that requires a given amount of the owned portfolio to be sold. The keep side also refers to owned issues, it can be used to set the amount of the owned issues that cannot be sold. In Own/Univ/BL mode, there is a toggle that enables short positions to be a part of the net portfolio. When this toggle is on, constraints can be defined on the long and short sides of the net portfolio. Issuer-Level Net: This side refers to issuer net and is used to place constraints on the different issuer sectors of the net portfolio. An example would be to set a constraint that places a limit on the market value of the bonds from each issuer that can be included in the net portfolio. Issuer-Level Buy: Similar to the buy, this side is used to set issuer level constraints on the bonds to be bought from the universe. The par amount purchased from each issuer (in addition to what is already included in the owned portfolio) can be limited by placing a constraint on this side. Optimization

142 General Constraint Syntax The table below describes the syntax for entering boundary conditions for sectors of issues or for individual issues: Constraint Syntax Description Lower Bound > value Greater than or equal to value Upper Bound < value Less than or equal to value Value value Set equal to value Range val1/val2 Defines a range of values from val1 to val2 Examples of the above boundary conditions: 1.In this example, the total market value (FPRICE x Par Amt.) of issues selected from the optimization universe must be less than or equal to 5, 000, The example below requires that the total market value (FPRICE x Par Amt.) of all issues in the Net portfolio be exactly 5,000,000 after optimization. 3.Using a range boundary condition below, the Total Market Value of securities in sector #4 is constrained to lie between 95% and 105% of that sector s total market value distribution in the baseline portfolio Optimization

143 Per-issue Constraints Per-issue Constraints The following Boundary Value expressions can be used for per-issue constraints (left page of Ch. 4.2 of the Yield Book): The boundary conditions are entered in the right-most column (Par($M)). To constrain the Market Value instead of the Par Amt, use the letter m to force the value. The example conditions are described below: Boundary Condition Syntax Constraint Example Upper Bound < value Buy a maximum of $10,970,000 par amount of Issue #1. Lower Bound > value Buy an amount greater than or equal to $100,000 par amount of Issue #2 Exact Value value Buy exactly $1,000,000 of market value of Issue #3 The m in constraint boundary value 1000m for Issue #3 forces the value in that field to apply to the Market Value of the issue. If a per-issue boundary condition is not entered, the Yield Book will assume $5 billion par amount as the default Upper Bound (unless a sector condition on the Constraints Definition page includes the issue). This means that if there is no defined boundary condition for an issue, no greater than $5 billion of the issue can be bought. Global upper and lower bounds may be set as keyword constraints. The keywords are OPTLOW- ERBND and OPTUPPERBND. They can be chosen like any other constraint keyword and may be applied to specific sides. Optimization

144 Constraints Relative to Baseline Portfolios Baseline portfolios can be used as the benchmark in optimization problems. The baseline is usually an index. The baseline can be used to constrain the overall performance of optimum portfolios. Below are sample constraint definitions which use the baseline ( bl or BL ) to place a boundary condition on a keyword. Two examples below constrain the total market value (FPRICE x Par Amt): Constraint definition #10 requires that the Total market value of the results be equal to the total market value of the baseline portfolio or issue. Constraint definition #12 requires that the total market value of the results be equal to the total market value of the baseline plus $5 million. Constraint definitions #5 and 6 are used to constrain the deviation of nominal returns across included scenarios from the baseline returns. The effect of these constraints produces the following result: The minimum return across all included scenarios is kept at its highest possible value relative to the baseline return value. In general, using the maxmin condition maximizes the worst case results of optimization and using the maxmin-bl condition maximizes the worst case difference between optimum portfolio returns and baseline returns Optimization

145 Constraints Relative to Baseline Portfolios Examples below constrain the total market value and the average effective duration: Constraint definition #13 requires that the sector-defined percentage of the total Market Value of the net portfolio lies in the range from 95-to-105 percent of the equivalent percentage of the baseline total market value (bld = baseline distribution). Constraint #14 requires that the value of the average effective duration of the net portfolio lies between 0.25 above the baseline (bl) and 0.25 below the baseline. Optimization

146 Removing Constraints ACTIVE CONSTRAINTS INACTIVE CONST. (White numbered box) Loading and Saving Constraint Files INACTIVE CONSTRAINT Blank Boundary Condition Optimization

147 Removing Constraints from Optimization Removing Constraints from Optimization If you use default constraints loaded by the Yield Book, you may want to remove some of the definitions from the optimization. The procedure is outlined below. If the yellow field is blank, the constraint is automatically inactive. Deactivate a Constraint Delete Constraints To remove a constraint from the optimization, click on the green numbered box to the left of the constraint keyword. The box will turn white. A white numbered constraint box means that the associated constraint is inactive and is not considered during optimization. To delete the constraint from the constraints definition table click on the [Compress] button. Note that you don t have to remove the constraint from the constraints definition table to make the constraint inactive (see Deactivate a Constraint above). Constraint Files Constraint files are specific to the mode of optimization. The file selections in the Constraint File listbox will reflect the current mode. For example, if <Own/Univ/BL> is toggled, then the constraint files in the listbox will only be those constraints used in the Own/Univ/BL mode. Load Constraint File Save Constraints File To retrieve a constraints file, click on the [Cons. Files] button in the Constraints Definition page, then click on a file name in the listbox to select it. The constraints will be loaded into the table of constraint definitions. To save a constraints file, click on the [Save] button, located below the [Cons. Files] button on the Constraints Definition page. Enter a file id, date, and description and click [Generate Constraints File] to save the constraints. Optimization

148 Soft Constraints and Penalty Function The constraints spoken about so far are known as hard constraints, which means that the specific parameters must be met. Now we introduce the concept of soft constraints. Soft constraints allow the user to relax the hard constraints by putting a penalty on deviating from the constraint. A description of an example is the best explanation. A detailed example of the steps will be shown as example #5 at the end of this section. Example Use of Soft Constraints Assume that the optimization problem is to create a portfolio which maximized OAS versus the index subject to the constraints of having the same partial duration exposure as the index across specific industry sectors. This means that the partial duration of the mortgage sector of the portfolio must equal the partial duration of the mortgage sector of the index. The input on the constraint page is bl on all of the keywords for the partial durations in each sector. The optimizer must create a portfolio which has the exact same partial durations as the benchmark in each sector. These may be tight constraints. To loosen them, the constraint syntax of bl+/-.05 is entered to relax the constraint of an exact match to one within.05 up or down; basically entering a range for the partial durations. There are two problems with this problem formulation. First, the optimizer values the partial duration that exactly matches the baseline and the partial duration that is.05 above or below the baseline equally. There is no incentive for the optimizer to get closer to the baseline as long as it is within.05 up or down. In addition, the optimizer does not distinguish between going above or below the baseline target, while this may be something that the user would like to influence. Second, the relaxation of the constraint (entering the range) is probably not required on every constraint, but with a large number of constraints, it is very tedious to determine which subset of constraints are the best ones to relax. The solution here is to use soft constraints and a penalty function. New Objective: Minimize the constraint penalty (CONSPENALTY) By entering soft constraints and a penalty function the partial duration constraints ( bl ) become targets where any deviation from the target will produce a penalty score, which increases as the deviation becomes larger. To keep the deviation from the desired target as low as possible, the minimization of the sum of the penalty scores for the set of constraints becomes the objective function. There is a new keyword called CON- SPENALTY Optimization

149 Soft Constraints and Penalty Function How to Enter the Penalty Function Minimizing the constraint penalty is only valuable if you calculate a penalty for deviating from the target level. The penalty function is defined as the following; Penalty = Deviation Exponent Standard Tolerance where... Deviation is the absolute difference between the result and the target.the deviation is then weight adjusted before being used in the above formula. Exponent is currently defined as 1, however quadratic penalties may be added in the future. Standard Tolerance is used to standardize the penalty units. For example, without the tolerance, the penalty calculated for a market value deviation would be many times greater than the penalty calculated for a partial duration deviation. This inconsistency would bias the penalty function. Note: The starting point for entering a tolerance level should be the range that is used to loosen hard constraints depending on the keyword. For example, a tolerance level for OAS may be 5 while a tolerance level for partial duration may be.05. If no tolerance level is entered, the default is infinity; therefore the penalty for deviation would be zero. Users should always define the standard tolerance levels when using soft constraints in order to give the constraint penalty sum a value. There is a standard tolerance level for deviations below the target (lower bound) and a standard tolerance level for deviations above the target level (upper bound). If breaking the upper bound is more important than breaking the lower bound, then the standard tolerance level for the upper bound should be lower than that of the lower bound. The solution may go outside of the standard tolerance levels and that will be accounted for in the penalty function. As you can see from the formula, the higher the tolerance, the lower the penalty and vice versa (the higher the tolerance, the lower the penalty). If you wish to place a new set of hard constraints to limit the deviation, you must use the Max Divergence input field. Max Divergence is the allowable range for a value. When defined, it becomes a hard constraint and the solution will never violate it. Optimization

150 Optimization in Buy/Sell Mode Optimization

151 Examples Using Optimization in Buy/Sell Mode Examples Using Optimization in Buy/Sell Mode Buy/Sell mode in optimization is most useful for problems which involve trades and have direct constraints on long and short positions. The basic procedure for optimization in this mode is outlined below and two detailed step by step examples will follow. The first example will involve constraints commonly used in trade optimization, such as effective dv01 neutral and equal market value on the buy and sell side. The second example will demonstrate how to use the optimization page for hedging corporates with treasuries. General Trade Weighting Optimization Procedure: STEP 1: In Ch. 4.2, click the Buy/Sell toggle ON STEP 2: Retrieve Long position issues into the BUY side STEP 3: Retrieve Short position issues into the SELL side STEP 4: Click on the [Optimization] button to display the default constraints file STEP 5: Define constraint values STEP 6: Calculate Optimization

152 Retrieve the Issues Optimization

153 Example 1: Effective dv01 Neutral Trade Example 1: Effective dv01 Neutral Trade The problem: Suppose you have two bonds that you must sell and would like to buy issues with similar characteristics. The trade must be effective dv01 neutral, the difference in oas must be as high as possible, and you do not want to include any cash for this trade. This problem description can be easily formulated for optimization. Once the issues are selected on the buy and sell sides, the goal and each of the requirements can be translated into an objective function and constraints. Retrieve the Issues: STEP 1: In Ch. 4.2, click on the Sell side toggle Retrieve the issues that are to be sold on the sell side. STEP 2: Click on the [Issues] button] STEP 3: Enter search criteria and click on [Search to Sell] Search to sell the 5 and 10 year on-the-run treasuries. STEP 4: Click on [Include All] to add the positions STEP 5: In Ch. 4.2, click on the Buy side toggle STEP 6: Click on the [Issues] button STEP 7: Enter search criteria and click on [Search to Buy] STEP 8: Click on [Include All] to add the positions Optimization

154 Load the Constraints File 2 3 Enter the Objective Function and Constraints Optimization

155 Example 1: Effective dv01 Neutral Trade Load the Constraints File The Short Generic Trade Weighting constraints file contains predefined constraints commonly used for Trade Weighting optimization. The right-most column (used for boundary values) is left blank. When the Buy/Sell toggle is ON, the Short Generic Trade Weighting constraints are the default constraints, and will appear automatically on the Constraints Definition page in optimization mode. STEP 1: In Ch of the Yield Book, click on [Optimization] STEP 2: On the right (Optimization Constraints Definition) page, click on [Cons. Files] STEP 3: Select the Short Generic Trade Weighting template We can now alter the Short Generic Trade Weighting constraints file to reflect our problem. Formulating the Problem Objective Function: Constraints: Enter the Objective Function and Constraints The goal of the problem is to maximize the difference between the buy side and sell side oas. This translates to the objective of maximizing the average oas on the diff (buy-sell). The other requirements can be expressed as constraints. The first additional requirement is that the effective dv01 of the buy side must equal that of the sell side. This is the same as setting the effective dv01 on the diff side to zero. The other condition is that no cash is to be included, so the buy and sell sides should have the same market value. Since you already know exactly what you are selling, you can set the market value diff to zero and the market value of the sell side will be constrained. STEP 1: Enter the objective by typing max into line 8, the oas of the diff. STEP 2: To neutralize the effective dv01, enter zero for the effdv01 on the diff on line 6. STEP 3: Enter the market value constraint by setting the diff to zero, shown in line 3. STEP 4: Make sure that all other constraints are off. Optimization

156 Enter Per-Issue Constraints and Calculate Results Optimization

157 Example 1: Effective dv01 Neutral Trade Enter Per-Issue Constraints Calculate To specify the amounts of each individual issue, enter the values to be sold in the issue listbox on the left page. STEP 1: Click on [Calculate] The Yield Book will calculate a solution based on the defined set of universe issues and the given constraint definitions. When processing is completed, a detailed display in the Constraints Definition page will display actual values calculated for Trade Weighting. To change the constraints and universe inputs and re-calculate, click on [Return to Input]. Click on [Detail] to view the Buy, Sell, and Diff results. Optimization

158 1 Prepare the Issues Optimization

159 Example 2: Hedging Corporates with Treasuries Example 2: Hedging Corporates with Treasuries The Problem: You currently own a portfolio of corporate bonds and would like to hedge by using U.S. treasury issues to reduce the exposure to shifts in interest rates along different portions of the yield curve. You have already calculated the risk measures on your portfolio and the several treasury issues that are candidates for the problem. The main goal is choose bonds so the partial durations of the resulting portfolio are neutral. Similar to trade weighting, this hedging example will be performed in buy/sell mode. Though the intent of the problem is to be partial duration neutral, it is not the objective function, but rather a series of constraints. It is a common circumstance where the practical goal of the optimization is really just a constraint, not the objective function. However, an objective function must always be entered in optimization. In these cases where the objective function is not obvious or even important to the practical aspects of the problem, remember that you can always maximize or minimize a keyword that may not have a large effect on the solution. When the constraints are extremely tight, it is common to find that there is only one solution, so whether you maximize or minimize on a specific keyword the solution remains the same. In this case, we will maximize the difference of yield to maturity. Prepare the Issues Retrieving issues on the buy and sell sides is covered in detail in Example #1. For this example, use the following general guidelines to prepare the issues for optimization: STEP 1: Retrieve or construct a portfolio of corporates on the Buy side. STEP 2: On the sell side, search for treasuries that are candidates for this problem. STEP 3: Once all of the bonds are included in the listbox, use the pricing page or read in a pricing file to obtain the partial durations. It is important to make sure that the keywords used in an optimization are defined for all issues in the problem. If this is not the case, those issues whose values are not calculated will be excluded from the optimization. In this example, we will be entering direct constraints on the partial durations of the issues, so it is crucial that those values are defined. Optimization

160 1 Enter the Objective Function and Constraints 2,3 4, Optimization

161 Example 2: Hedging Corporates with Treasuries Formulating the Problem Objective Function: Constraints: Enter the Objective Function and Constraints The objective function of this example is to maximize the yield on the difference. Since the buy side issues are set, this is the same as minimizing the yield of the issues in the short position. So the same objective can be defined by minimizing the yield on the sell side or maximizing yield on the diff. The desire to reduce exposure to changes in rates along the curve can be translated into constraints placed on the partial dv01s for the relevant points. For each partial dv01 keyword, the diff will be set to zero. A market value constraint will be added as well. Once the issues are defined in the list box and the risk measures have been calculated, we can enter the problem on the Constraints Definition page. The Short Generic Trade Weighting constraints file will be used as a starting point and the partial duration constraints will be added. STEP 1: On the Constraints Definition page, retrieve the Short Generic Trade Weighting constraints file from the constraints file list. STEP 2: Enter the objective by typing max for the ytm diff, as shown in line 4. STEP 3: Set the diff of the market value to zero in line 3. STEP 4: Add the relevant partial dv01 keywords for constraints. The step-by-step procedure for adding constraints can be found in the earlier section on defining objective and constraints. STEP 5: Set the side on the partial dv01 keywords to diff and set each zero. At this point, all of the constraints are defined. Remember that the additional lines in the constraints list will remain inactive as long as no value is entered in the yellow field on the right. You may wish to reduce the constraints file to show only the lines relevant to this problem by compressing the blank constraints out of the list. At this point, the active list can be saved as a constraint file for future use with similar problems. Optimization

162 Calculate and Review Results Modify Constraints Optimization

163 Example 2: Hedging Corporates with Treasuries Calculate STEP 1: Click on [Calculate] STEP 2: Review the Solution Because of the tight constraints involving partial durations, the solution may be not feasible. If this is the case, try entering a small range for the partial dv01 constraints instead of zero. In this type of problem, you may be willing to tolerate a small difference in certain partial dv01 points. If you do not wish to alter the constraints, you can always consider adding different issues or cash to the sell side. Just remember to calculate the risk measures on any additional issues before recalculating. Show Detail As shown in the last example, the solution may be displayed with detail on or off. By using the [Operations] button, the solution can also be transferred to problem mode so it can be saved as a portfolio for further analysis. Solution Optimization

164 Optimization in Own/Universe/Baseline Mode 5 1, Optimization

165 Optimization in Own/Universe/Baseline Mode Optimization in Own/Universe/Baseline Mode Own/Univ/BL mode in optimization is extremely flexible and is mostly used for problems involving a portfolio and a benchmark. An owned portfolio can be used in conjunction with a universe to create a net portfolio that satisfies constraints that reference a particular benchmark. A starting portfolio is not required, it is also possible to construct a portfolio that matches a benchmark from a universe of issues. There are many possibilities in this mode of optimization, including the ability to constrain the amounts that you want to buy, sell, or keep in the net portfolio. It is also possible to define constraints on the issuer level, so you can limit the amount purchased of each issuer in the universe. The general procedure for optimization in own/univ/bl mode is outlined below and two step-by-step examples will follow. The first example will use the optimization page to construct portfolio that tracks the Treasury Index. This problem will be kept at a relatively basic level so the fundamentals of own/univ/bl mode are understood. The second example will be similar in objective, however we will add more pieces to the problem so that some of the additional features are utilized. General Procedure: Portfolio Optimization STEP 1: Retrieve a Portfolio This step is optional, if you are not starting with an owned portfolio, you can skip to step 2. STEP 2: Select issues for the Optimization Universe These universe issues must be retrieved through issues select. STEP 3: Retrieve a Baseline Portfolio or Index STEP 4: Define the Objective and Constraints STEP 5: Calculate the Optimum Portfolio Optimization

166 Select Issues for the Optimization Universe Optimization

167 Example 3: Constructing a Tracking Portfolio Example 3: Constructing a Tracking Portfolio The problem: Select Issues for the Optimization Universe Using the Treasury Index as a benchmark, create a portfolio that matches several characteristics of the index, such as effective duration, convexity, and partial durations. The net portfolio should have returns over different scenarios where the worst case (the lowest return) is as high as possible. There is 50 million available to create the portfolio and we are starting from scratch, there are no issues currently owned. To retrieve candidate issues for the net portfolio, we must read in the universe issues. For this problem, we will choose from issues that are included in the benchmark. Once retrieved, they are tagged U to indicate universe and have only the default upper bound of 500 million on their net values in the optimized result. STEP 1: Set the optimization mode to Own/Univ/BL STEP 2: Click the Own & Univ toggle ON. STEP 3: Click on the [Issues] button. STEP 4: On the right page, enter search criteria to select universe issues OR STEP 5: Click on the [Domain] button to select an saved Optimization Universe or Index STEP 6: For this problem, set the domain to the Treasury Index STEP 7: Click [Search to Buy] and make sure that you are copying blank amounts so no values are set on the universe issues. STEP 8: On the left page, click on the [Include All] button Optimization

168 Retrieve the Baseline Optimization

169 Example 3: Constructing a Tracking Portfolio Retrieve the Baseline The Treasury Index will be used as the baseline index in this example. Retrieving the baseline is very similar to retrieving an index on the sell side. STEP 1: Click the Baseline toggle ON STEP 2: Click on [Portfolio] to select a baseline index OR click on [Issues] to search for a set of issues STEP 3: On the right page, select an index or search for a set of issues to use as a baseline STEP 4: For this problem, use the portfolio selection to choose the TSYINDX as the baseline. STEP 5: On the left page, click on the [Include All] button Prepare the Issues As shown in the last example, it is important to have the keywords that are going to be used in the optimization defined. The risk measures must be calculated on the bonds so the partial duration constraints can be used. In addition, the returns of the index and the universe issues must be calculated over the different scenarios so the objective function can reference the nominal return keywords. Use the following general guidelines for preparing the issues: STEP 1: Calculate the partial durations on all issues. STEP 2: Define several scenarios in the Scenario Setup support page. STEP 3: Use the ROR/CF page in Chapter 4.2 to calculate returns for the defined scenarios. Now that all of the necessary values have been calculated for the universe and baseline issues, we can translate the problem into an objective function and a series of constraints to be defined on the optimization page. Optimization

170 Enter the Objective Function and Constraints Optimization

171 Formulating the Problem Formulating the Problem Objective Function: Constraints: Enter the Objective Function and Constraints The intent of this optimization is to create a portfolio that tracks the treasury index. In the problem definition, one of the goals was to keep the worst case of the returns as high as possible over several scenarios. The maxmin objective across several scenarios will accomplish this goal. This syntax is described in the earlier section on defining the objective and constraints. It will maximize the minimum returns across the scenarios on the net portfolio. The constraints in this problem will include effective duration, convexity, oas, and partial durations. The previous example showed us how to create additional constraints with new keywords. The main difference here is that instead of having a buy/sell side and matching by setting the diff to zero, we will be directly entering constraints that define the characteristics of the net (solution) portfolio. Because we want to match the baseline on these constraints, we can use the baseline constraint syntax. STEP 1: On the Constraints Definition page, select the Total ROR constraints file from the constraints file list. This file contains lines for the market value of the net portfolio and the nominal return of the net portfolio for seven scenarios. We can add the additional constraints in the same way as Ex. 2 STEP 2: Add the Other Constraint Keywords Define keywords for the effective duration, the effective convexity, the oas, and the partial durations. A detailed explanation on adding constraints is provided in the earlier section on defining objective and constraints. STEP 3: Enter the Objective Function by typing maxmin on the bcnomret keywords for each defined scenario, as shown on lines 2 through 8. STEP 4: Enter the market value constraint by setting the net market value to on line 1. STEP 5: Enter the remaining constraints relative to the baseline. To set the values of the net portfolio to those of the baseline, simply type bl for each constraint. Optimization

172 Calculate and Review Results Optimization

173 Formulating the Problem Calculate and Review Results STEP 6: Click on [Calculate] STEP 7: Review the Results If the problem is not feasible, the constraints that are set to the exact baseline values may be relaxed by entering a small range relative to the baseline value. STEP 8: Transfer the Solution using Operations (optional) As shown in buy sell mode, it is possible to use operations to transfer the solution back to a portfolio that can be analyzed further. In own/univ/bl mode, the process is slightly different. Often the net portfolio will be compared to the benchmark in analysis and the [Transfer Solution to Buy and Sell Sides] button in operations will transfer whatever is currently displayed in the yellow to the buy side and whatever is displayed in the green side to the sell side. The default for solution mode is to have the net portfolio populate the yellow side and the baseline populate the green side, so when this button is clicked, the net portfolio will become the portfolio on the buy side and the benchmark will populate the sell side. Optimization

174 Retrieve the Owned Portfolio Optimization

175 Example 4: Optimize Portfolio Relative to a Benchmark Example 4: Optimize Portfolio Relative to a Benchmark The Problem: Retrieve the Owned Portfolio Suppose you own a portfolio of corporate bonds and would like to optimize it so that it matches the corporate index in oas, effective duration, and effective convexity. You do not want to sell more than 20 million of the currently owned portfolio and the market value of the net portfolio must be 75 million. In addition, there are limits on how much you can hold of one company, so you can buy no more than 5 million of each issuer. The worst case returns of the net portfolio should be as high as possible. STEP 1: Go to Ch. 4.2 STEP 2: Click the Own/Univ/BL toggle ON STEP 3: Click the Own/Univ toggle ON if it isn t already selected STEP 4: Click on the [Portfolio] button STEP 5: On the right page, select a portfolio or search for a portfolio id STEP 6: Notice that the portfolio issues are loaded into the left page under type Own. The Par Amounts are displayed in the right-most column. During Optimization, each Par Amount will be used as the upper bound for the Net amount of each issue. STEP 7: On the left page, click on the [Include All] button Optimization

176 Select the Optimization Universe and Baseline 2 5 3, Optimization

177 Example 4: Optimize Portfolio Relative to a Benchmark Select the Optimization Universe To retrieve candidate issues for the net portfolio, we must read in the universe issues. For this problem, we will choose from the 1 to 10 year Corporate Index. You can also retrieve issues by using search criteria. STEP 1: Click the Own & Univ toggle ON. STEP 2: Click on the [Issues] button. STEP 3: On the right page, enter search criteria to select universe issues OR Click on the [Domain] button to select an saved Optimization Universe or Index STEP 4: For this problem, set the domain to the Corporate 1-10 Index. You may enter a desired rating range as well. STEP 5: Click [Search to Buy] and make sure that you are copying blank amounts so no values are set on the universe issues. STEP 6: On the left page, click on the [Include All] button Retrieve the Baseline STEP 7: Click the Baseline toggle ON STEP 8: Click on [Portfolio] to select a baseline index OR click on [Issues] to search for a set of issues STEP 9: On the right page, select an index or search for a set of issues to use as a baseline. For this problem, use the portfolio selection to choose the CORPONLY Index as the baseline. STEP 10:On the left page, click on the [Include All] button Optimization

178 1 Enter the Objective Function and Constraints Optimization

179 Example 4: Optimize Portfolio Relative to a Benchmark Prepare the Issues Make sure that the values that are defined in the optimization are calculated for each issue. This includes calculating scenario rate of return on the owned portfolio, the universe issues, and the Corporate Index. Formulating the Problem Objective Function: Constraints: The objective in this optimization is the same as in Example 3, we are trying to maximize the minimum returns across scenarios. The constraints in this problem include matching the effective duration, effective convexity, and oas of the net portfolio to the Corporate Index. We can enter the same type of constraints as in Example 3 for these keywords. There are also some requirements that place limits on the market value of specific parts of the problem. One is that the most that can be sold from the owned portfolio is 20 million. We can place an upper bound constraint on the sell side to accomplish this. The market value of the net portfolio must also be set to 75 million. Also, there is a maximum of 5 million for each issuer, so the net portfolio must be constrained by issuer level market value as well. This can be done with the INet side, which stands for Issuer Net. An upper bound of 5 million must be set for this constraint line. Enter the Objective Function and Constraints STEP 1: On the Constraints Definition page, select the Total ROR constraints file from the constraints file list As in Example 3, we will use this constraints file as a starting point and add additional lines. A detailed procedure for editing constraints can be found in the earlier section on defining the objective and constraints. STEP 2: Insert two more lines for additional market value (full price * par) constraints. Set one side as Sell and the other as INet. These two are in addition to the Net side, which is already defined. STEP 3: Insert the remaining constraint keywords - effective duration, effective convexity, and oas. At this point, all of the constraint keywords are chosen. The objective and constraints values must now be entered. Optimization

180 Enter Objective and Constraint Values Calculate Results Optimization

181 Example 4: Optimize Portfolio Relative to a Benchmark Enter Objective and Constraint Values STEP 1: Enter maxmin on the nominal return keywords to define the objective function. STEP 2: Set the market value on the net portfolio by setting the Net side to STEP 3: Set the constraint on the amount that can be sold from the owned portfolio by entering <20000 on the Sell side of the market value. STEP 4: Use the INet side to set market value constraints on the issuer level. By entering <5000, we are limiting the market value of each issuer in the net portfolio. STEP 5: Enter the remaining constraints values by setting the effective duration, effective convexity, and oas equal to the baseline. Type bl on the Net side for these constraints. Calculate Results STEP 6: Click on [Calculate] and Review the Results As shown in previous examples, a problem that is initially not feasible can altered by relaxing the constraints. You may be willing to accept a small range around your initial constraints instead of definite values. You may also find that by relaxing constraints, the value of your objective function is higher (or lower, depending). Several iterations with constraint adjustments give you a better sense of the problem and how sensitive your objective is relative to the constraints. In addition, the universe itself should be scrutinized. It may be beneficial to change some of the issues in the universe. Optimization

182 Select Optimization Universe Select Baseline Optimization

183 Example 5: Track a Benchmark using Soft Constraints Example 5: Track a Benchmark using Soft Constraints The Problem: Select the Optimization Universe Suppose you must create a portfolio that tracks the bigindex where the objective is to minimize the constraint penalty of deviating from the index subject to certain constraints. The hard constraints are that the overall effective duration and effective convexity exactly match the baseline, the portfolio has a market value of 100 million, and the market value distribution across specific industry sectors is the same as the baseline. The soft constraints are that the portfolio should having the same (or as close as possible) partial durations as the index in specific sectors. To retrieve candidate issues for the net portfolio, we must read in the universe issues. For this problem, we will choose bonds in the Bigindex with an outstanding amount of 300 billion or higher and a coupon greater than 0. STEP 1: Click the Own & Univ toggle ON. STEP 2: Click on the [Issues] button. STEP 3: Click on the [Domain] button to select the Bigindex. STEP 4: Enter the search criteria for the outstanding amount.01+ in the coupon field STEP 5: Click [Search to Buy] and make sure that you are copying blank amounts so no values are set on the universe issues. STEP 6: On the left page, click on the [Include All] button. Retrieve the Baseline STEP 7: Click the Baseline toggle ON. STEP 8: Click on [Portfolio] to select a baseline index. STEP 9: Click on the Bigindex. Optimization

184 Optimization

185 Example 5: Track a Benchmark using Soft Constraints Enter the Hard Constraints STEP 10:Enter the hard constraints on the overall sector. 100,000 for the market value constraint bl on average effective duration and average effective convexity to match the baseline effective duration and convexity. The next constraint is a market value constraint on specific sectors instead of on the overall sector. The constraint is have the optimal portfolio have the same market value distribution as the index in each of the corporate sectors. STEP 11:Click [Select Sectors] to retrieve the sector file list and choose sector PROF09 which has detailed corporate sectors. STEP 12:On the FPRICE keyword, click [S0] to bring up the sector constraint page on the left. STEP 13:Include all the sectors that you want. STEP 14:Type the constraint bld on the right hand page. STEP 15:Click [Generate Constraints] on the left hand page to create that bld constraint for every included sector. STEP 16:Enter the partial duration constraints In this example, the constraint is to have the same partial duration as the baseline in each of the corporate sectors. This means you must create a bl constraint for each sector for each of the seven partial duration keywords (pdur1, pdur2, pdur3, pdur5, pdur10, pdur20, and pdur30). Note: If you tried to calculate (after entering an objective such as maximize OAS, the result would be infeasible due to the constraints being too tight on the partial durations. Instead of lightening these constraints by entering a range around the bl (bl-.05/bl+.05), we can use soft constraints and a constraint penalty. Optimization

186 Optimization

187 Example 5: Track a Benchmark using Soft Constraints Enter Soft Constraints Soft Constraint Page Layout When toggled on Own/Univ/Bl mode for Optimization as opposed to Buy/Sell mode, the [Soft Constraints] button will automatically appear on the constraints definition page. STEP 17:Click [Soft Constraints] to retrieve the soft constraint input page, which is described below: A list of in/out buttons to tell if the soft constraint is included or not. Notice that these buttons are distinct from the in/out buttons to the left of the keyword which designate whether the hard constraint is included or not. After the in/out buttons, there is a column labelled Exp for exponent in the penalty equation. As described earlier, the exponent is currently defined as 1, however quadratic penalties may be added in the future. A button labelled [Tolerance] to enter the upper and lower tolerance for each soft constraint. When the Tolerance button is clicked it will then show [Max Divergence] to enter upper and lower bounds. STEP 18:Enter the tolerance level for the soft constraint on PDUR1 and to apply this to all sectors, click [S0], include the sectors and click [Generate Constraints]. Do this for each of the partial duration keywords. We use.05 as the upper and lower tolerance for each keyword. STEP 19:Add the keyword Conspenalty to the listbox and enter MIN. This defines the objective to minimize the constraint penalty. STEP 20:Click the option box in front of the label for Soft Constraints to use them. STEP 21:Click [Calculate]. Note: In this example, we have not entered a maximum divergence upper or lower bound. Optimization

188 Optimization OPTIMIZATION RESULTS

189 Example 5: Track a Benchmark using Soft Constraints Review Results The results tell you that the constraint penalty has a total of 6 and on the left hand page you can see that the optimal portfolio has 136 and the overall effective duration and convexity match the baseline. This is because we kept hard constraints on those values. To view the soft constraint results, click on the [Soft Constraints] button to view the columns labelled Deviation and Penalty: Deviation is the amount the partial duration in the sector of the optimal portfolio deviated from the partial duration in that sector of the baseline. For many of them, the number is 0, thus the penalty is 0. The penalty is calculated according to the formula: Penalty = Deviation Exponent Standard Tolerance Notice the Gas/Utility sector had an absolute deviation of After the weight adjustment, the penalty is 1.86 which rounds to 2 on the screen. Optimization

190 Reports for Optimization Results Optimization

191 Reports for Optimization Results Reports for Optimization Results There are two report templates for portfolio optimization reports, OPT- TRACK and ISSUES09. Use OPTTRACK when the portfolio is optimized against a baseline. Use ISSUES09 to report on all issues involved in transactions (buy/sell) during optimization. STEP 1: Click on the [Report] button in Ch. 4.2 of the Yield Book (left page). STEP 2: Click on the [Template Select] button STEP 3: A listbox of templates will appear on the right page. Select OPTTRACK or ISSUES09 STEP 4: Click on the [Generate Report] button to create the corresponding report Optimization

192 Optimization

193 WORKSHOP Optimization: Examples Agenda This section of the advanced capabilities handbook takes you through several optimization examples to illustrate the types of trade weighting and portfolio optimization problems you can solve using the Yield Book. In addition, the advanced feature, return attribution is used to evaluate the optimization results. Highlights The optimization examples will teach the following: How to calculate a duration-neutral trade, evaluate the trade performance using return attribution analysis and re-optimize the trade. Create an Index tracking portfolio using the SSB Mortgage Index and evaluate the portfolio in return attribution. Create an Index tracking portfolio using the SSB Corporate Index, evaluate the portfolio in return attribution and re-optimize. Cash Matching Example Salomon Analytics Inc.

194 Example #1: Trade Weighting Optimization: Examples

195 Example #1: Trade Weighting Example #1: Trade Weighting Problem Assumptions: In the July 31, 1998 Bond Market Roundup: Strategy Report, John Melesius recommends buying CWE and selling TXU. We will use the optimizer to identify calculate and evaluate specific trades. STEP 1: Turn to Ch 4.2 and toggle on the <Buy/Sell> mode, then toggle <Sell>. STEP 2: Enter TXUE 6.75,7/1/05 in the Ticker/Query and click [Search]. STEP 3: Toggle Buy and click [Domain]. STEP 4: Toggle <Indexes>, enter bigindex in the yellow search field and click on the BIGINDEX as of 8/1/98. Now the BIGINDEX is set to the DOMAIN. STEP 5: Enter CWE in the Ticker/Query and click [Search to Buy]. Do not click [Include ALL] for these bonds. We will select the bonds to buy using a scatter graph on the next page. STEP 6: Click [Pricing] and toggle <Pricing Files>. STEP 7: Click [Select]. STEP 8: Choose the UNIV.AUG. This retrieves the pricing levels and the pricing assumptions back to July month-end when the trade idea was recommended. Optimization: Examples 5-3

196 9, Optimization: Examples

197 Example #1: Trade Weighting Scatter Graph STEP 9: Click [Profile]. STEP 10: Toggle <Scatter>. STEP 11: Toggle Effective Duration for the Horizontal axes and OAS for the vertical axis. STEP 12: Click [Graph]. You can now look for bonds that have a duration around the TXUE bond and higher OAS s. Click on a dot in the graph to highlight what bond it is. When you find the bond you want to include in the analysis, click the white box to the right of the bond and it will say either B or S depending on which side the bond was on. We have selected the CWE /15/2018 and the CWE /15/04. STEP 13: Click [Profile]. This takes you back to the bonds. You should see the two CWE bonds on the sell side and the TXUE on the buy side. Optimization: Examples 5-5

198 , Optimization: Examples

199 Example #1: Trade Weighting STEP 14: Click [Compress] to remove the non-included CWE bonds from the buy side. Run the Optimization STEP 15: Click [Optimization]. STEP 16: Click [Cons.Files] to retrieve the list of available files. STEP 17: Click SHORT GENERIC TRADE WEIGHTING (cons02). STEP 18: Define the constraints: FPRICE (sell) = 10,000 FPRICE (Diff) = 0 EFFDV01 (Diff) = 0 STEP 19: Define the objective: OAS (Diff) = max STEP 20: Click [Calculate]. STEP 21: Click [Operations]. Optimization: Examples 5-7

200 2, Optimization: Examples

201 Example #1: Trade Weighting Review Trade in Return Attribution page, 4.6 Now that we have created a duration neutral trade and maximized OAS, we can evaluate how the trade performed over the month of July using the return attribution page. Although this is still example #1, we have started the steps over at 1 again to make it easier to follow along. STEP 1: Enter 4.6 in the yellow field in the Turn To Support button at the top of the Yield Book and click the white part of the button. STEP 2: Toggle <Buy> and click [Receive Buy from 4.2]. STEP 3: Toggle <Sell> and click [Receive Sell from 4.2]. STEP 4: Click [Read Results] to retrieve a list of result files. STEP 5: Click RAAUG. Next we will evaluate what happened? Optimization: Examples 5-9

202 5-10 Optimization: Examples 5 year

203 Example #1: Trade Weighting What happened to the Trade? Yield Curve Difference Return Attribution Summary Report To evaluate what happened to this trade, let s look at the return attribution results and what happened to the Yield Curve between 7/31/98 to 8/31/ 98. The pictures on the opposite page show these results. Use [Curve Analysis] at the top of the Yield Book to compare the Treasury Model Curve from two different dates. Notice that a bull steepening scenario occurred. The short-end of the curve rallied by more than the long end. The summary report shows us that we lost 1 basis point by doing this trade. This was due to the reshaping that occurred to the yield curve over the month. Let s focus on the Diff column in the report as circled on the opposite page. The reshaping component accounted for 23 basis points of underperformance of the CWEs versus the TXUE. This is because the biggest rally in the curve was in the five year which is what we sold in order to buy the barbell around it. The overall return of both sides of the trade was hurt by the widening of OAS, but the CWE s widened by less than the TXUE which helped us. This is reflected in the Total market spread difference of 21 basis points. If we had tested this trade idea in a reshaping scenario similar to the one that actually occurred, we could have better positioned ourselves. Let s go through that now. First, we will run scenario analysis to show how the trade would perform in reshaping scenarios and then use them in the optimizer to weight the trade better. Optimization: Examples 5-11

204 6, Optimization: Examples

205 Example #1: Trade Weighting Back to Scenario Analysis in Chapter 4.2 Let s go back from Return Attribution (Ch 4.6) to Ch 4.2 to run the scenario analysis. STEP 1: Click [Scenario Setup] STEP 2: Click [Select] and click on the Scenario ID cmb1mo. These are the reshaping scenarios generated from the Treasury Analysis Group s principle component analysis. The scenarios are displayed based on their relative shifts to the settlement yield curve. STEP 3: Click [Scenario Setup] again. STEP 4: The Turn To box should have the bookmark of 4.2 in it, so click the Turn To. STEP 5: Click [ROR/CF]. STEP 6: Click [Calculate]. The assumption is that OAS is held constant over the period. The analysis tells you that this trade would not have been a good idea in scenarios 5 (bull intermediate) and 6 (bull steepener). Scenario 6 is like the scenario that actually occurred from 7/31/ 98 to 8/31/98. Optimization: Examples 5-13

206 1 3 4 Output of ROR , Optimization: Examples

207 Example #1: Trade Weighting Re-Optimize Let s start over with the optimization with this information in mind. STEP 1: Click [Clear Buy]. STEP 2: Search for all CWE bonds in the BIGINDEX. (not shown) STEP 3: Click [ROR/CF] STEP 4: Click [Calculate] (button not shown, but output is) STEP 5: Click [Optimization] STEP 6: Click [Cons.File]. STEP 7: Select the file named nomretbs. If you do not have this constraint file, you can customize one of the existing ones by adding the constraint keywords that are missing. STEP 8: Define constraints: FPRICE (sell) = 10,000 FPRICE (Diff) = 0 EFFDV01 (Diff) = 0 EFFCNVX (Diff) >0 NOMRET.1 (Diff) >0 NOMRET.2 (Diff) >0 NOMRET.3 (Diff) >0 NOMRET.4 (Diff) >0 NOMRET.5 (Diff) >0 NOMRET.6 (Diff) >0 STEP 9: Define objective function: NOMRET.7 (Diff) MAX STEP 10: Click [Calculate]. Optimization: Examples 5-15

208 , Optimization: Examples

209 Example #1: Trade Weighting Review Trade Results in Return Attribution Now that we have a new trade, let s review the results in the return attribution page again. STEP 11: Click [Operations]. STEP 12: Enter 4.6 in the yellow field in the Turn To Support button at the top of the Yield Book and click the white part of the button. STEP 13: Toggle <Buy> and click [Receive Buy from 4.2]. STEP 14: Toggle <Sell> and click [Receive Sell from 4.2]. STEP 15: Click [Read Results] and choose RAAUG as before. STEP 16: Click [Copy Summary] or [Print Summary] to generate the summary report. What happened? Optimization: Examples 5-17

210 Example # Optimization: Examples

211 Example #2: Mortgage Index Tracking Portfolio Example #2: Mortgage Index Tracking Portfolio Problem: Define the Baseline: Construct a $100 million dollar mortgage portfolio that has the same characteristics as the 10/1/99 Mortgage Index. This means you have the money to invest starting 10/1/99. You would like the portfolio to have the same duration and at least the same convexity as the 10/1/99 Mortgage Index. You think that a good idea for the month of September would be to buy bonds such that you maximize OAS. In addition, you want to make sure that the effective duration distribution across various mortgage sectors is very close to the baseline because this is a tracking portfolio. STEP 1: In Chapter 4.2, toggle <Own/Univ> mode. STEP 2: Toggle <Baseline> and click [Portfolio]. STEP 3: Toggle <Indexes> and search in the Mortgage Index as of 10/ 1/99. STEP 4: Toggle <Own &Univ>. STEP 5: Click [Issue Select]. STEP 6: Click [Domain]. STEP 7: Toggle <Indexes> and select Mortgage Index as of 10/1/99. The Mortgage Index is now your searchable domain. STEP 8: Click [Search to Buy]. This reads all of the securities in the Mortgage Index into the left hand page as the universe.. Remember to always read your universe in through the Domain button. Optimization: Examples 5-19

212 Optimization: Examples

213 Example #2: Mortgage Index Tracking Portfolio Define the Universe STEP 9: Click [Include All] to include all of the mortgages bonds in the universe. STEP 10: Click [Pricing]. STEP 11: Toggle <Pricing Files>. STEP 12: Click [Select]. STEP 13: Click UNIV.OCT. STEP 14: Click [Optimization]. Optimization: Examples 5-21

214 Optimization: Examples

215 Example #2: Mortgage Index Tracking Portfolio Run the Optimization STEP 15: Define constraints by entering the following: FPRICE (NET) = EFFDUR (NET) = bl (this says you want the effdur of your portfolio to be equal to that of the baseline portfolio) EFFCNVX (NET) > bl (this says you want the effective convexity of your portfolio to be greater than that of the baseline). STEP 16: Define the objective function: OAS (NET) MAX Note: the default constraint file that is displayed on the optimization page is the Short Generic Constraints file. STEP 17: Click [Select Sectors]. Sector files are used in optimization problems to define constraints or an objective on a particular sector instead of the overall portfolio. STEP 18: Click the sector file named MTGSECws. This is a customized mortgage sector file. STEP 19: Click on the next empty white menu box to add another constraint. Type FPRICE in the yellow field to find the full price keyword, select it and enter the constraint: FPRICE (NET).99bld/1.01bld. STEP 20: Click [S0]. STEP 21: Click [Include All] STEP 22: Click [Generate Constraints]. This will create the constraint that you want the market value in each sector of your portfolio to be between 99 and 101% of the market value of each sector in the index. It is a sector distribution constraint. STEP 23: Click [Calculate]. Optimization: Examples 5-23

216 Optimization: Examples

217 Example #2: Mortgage Index Tracking Portfolio You receive an error message stating: Infeasible solution because of these constraints: Check the coefficients for each bond. The constraints that have errors are highlighted in red. These two constraints (#7 and #8) are on sectors that do not have any issues in the Mortgage Index. This is because they are treasury sectors. STEP 24: Click the #7 and #8 to exclude them for the optimization calculation. STEP 25: Click [Return to Input] and [Calculate] again. The solution is feasible. Now we will transfer these bonds into the return attribution page to analyze the results. STEP 26: Click [Operations]. Optimization: Examples 5-25

218 Optimization: Examples

219 Example #2: Mortgage Index Tracking Portfolio Evaluate the Portfolio over the month in Return Attribution STEP 27: Turn to Chapter 4.6. STEP 28: Toggle on <Buy>, click [Receive Buy from 4.2], and then toggle on <Sell> and click [Receive Sell from 4.2]. STEP 29: Click [Read Results]. STEP 30: Click RAOCT. This will read in the results for the month of October. You can see that the tracking portfolio outperformed the Mortgage Index by 37 basis points. This was all due to the spread change component. The fact that our objective in the optimization was to maximize OAS turned out to be a good idea! Optimization: Examples 5-27

220 2 Example # Optimization: Examples

221 Example #3: Corporate Index Tracking Example Example #3: Corporate Index Tracking Example Problem: Define the Baseline Construct a $100 million dollar corporate portfolio that has the same effective duration and convexity as the 10/1/99 Corporate Index priced as of September 99 month end. At first, the only constraint is that the bonds have at least 200 million in outstanding amounts. Later we will impose additional constraints after comparing the results in return attribution. STEP 1: Turn to Own/Univ/BL mode and toggle on <Baseline>. If your baseline is an index that is currently stored on the Yield Book, you can simply retrieve it through the portfolio button as in the prior example for the mortgage index. In this example, the index has already been deleted from the database. The major indexes (BIGINDEX, WGBI, etc.) are maintained on the database for 13 months while the sub-indices are only stored for two months at a time. In this case, we can use the BIGINDEX from 10/1/99 and search only for the Corporates. Let s start: STEP 2: Click [Issue], and click [Domain]. STEP 3: Toggle <Indexes>, enter bigindex in the search field and select the index. This defines the domain as the index. Then you can enter additional search criteria on the Issue Selection page. STEP 4: Change the Copy None to Copy Amounts by clicking on [None] and selecting <Copy Amounts>. When you search, the bonds will be retrieved on the left page with the par amounts that are owned in the index; therefore the average index characteristics will be calculated. Later you will see that when reading in bonds into the universe instead of the baseline, you will want them to come in with no amounts. The optimizer will then solve for the optimal amounts. STEP 5: Define the rating range. To retrieve just the corporate issues from the Bigindex, we can put in a S&P range of AAA to un-rated. STEP 6: Click [Search to Buy] to retrieve the issues. STEP 7: Click [Include All] to include the bonds in the baseline. Optimization: Examples 5-29

222 Optimization: Examples

223 Example #3: Corporate Index Tracking Example Define the Universe STEP 8: Toggle <Own & Universe>. STEP 9: Click [Issue]. STEP 10:Define the search criteria: Bigindex from 10/1/99 is the Domain Copy Amounts should say NONE S&P Range is AAA to un-rated Enter 200+ in the outstanding amount to limit the bonds in the universe only to issues with more than 200 million in outstanding. STEP 11:Click [Search to Buy] to retrieve the bonds in the universe. STEP 12:Click [Include All]. Now we can reprice all of the bonds as of 9/30/99 using a global price file. Read Pricing Files STEP 13:Click [Pricing]. STEP 14:Toggle <Pricing Files>. STEP 15:Click [Read] to display the list of price files. STEP 16:Toggle RA.Monthly. STEP 17:Select RA.Oct for 9/30/99 pricing. Now you are ready to do the optimization. Optimization: Examples 5-31

224 , RetAtt Results Optimization: Examples

225 Example #3: Corporate Index Tracking Example Optimization STEP 18:Click [Optimization]. STEP 19:Enter the constraints and objective: Full Price 100,000 (market value of 100 million) EFFDUR bl (same average effective duration as baseline) EFFCNVX bl (same average effective convexity as baseline) OAS max (Ojbective - maximize the average OAS) STEP 20:Click [Calculate]. STEP 21:Click the Display Both off to view the optimal portfolio. The optimizer chose 3 bonds. Assuming you put that trade on for the month of October, let s evaluate that portfolio versus the baseline in Return Attribution for the month. Evaluate Results in Return Attribution Page STEP 22:Turn to Chapter 4.6 and Toggle <Buy> and click [Receive Buy from 4.2] STEP 23:Toggle <Sell> and click [Receive Sell from 4.2]. STEP 24:Click [Read Results]. STEP 25:Click RA.OCT to read in the returns and attribution results for October. You notice that this turned out to be a poor portfolio. The portfolio return underperformed by 256 basis points. What happened? The only attribution factor that was pretty well matched was the parallel shift factor. This is because in the optimization, we said to match the baseline. Let s see how we can use the optimizer to create a portfolio that similar attribution component risks as the baseline. Let s start with the reshaping risk which we see is a mismatch of 25bps. Optimization: Examples 5-33

226 Optimization: Examples

227 Example #3: Corporate Index Tracking Example Re-optimize to match reshaping risk To match the reshaping risk we can use the partial duration keywords in the optimization. STEP 26:Go back to Chapter 4.2 and click [Return to Input] on the Optimization page. STEP 27:Click one of the empty keyword boxes to bring up the keyword list. STEP 28:Type in pdur in the yellow search field to find the partial duration keywords. There are seven partial durations. Add one at a time to the optimization page. STEP 29:Enter bl as the constraint for each partial duration to constrain them to match the baseline. STEP 30:Click [Calculate]. The optimizer now picks 10 bonds. Let s review in return attribution again. Turn back to Chapter 4.6. STEP 31:While toggled on <Buy>, Click [Receive Buy from 4.2] to retrieve the 10 bond portfolio. The sell side has not changed since it is still the baseline. In addition, there is no need to read the result file again. Notice that the reshaping component is now much closer to the index. In addition, we are now only underperforming the index by 189 bps. Now, that we have matched the exposure to the yield curve (parallel and reshaping components), let s look at ways to more closely match the spread advantage components. For example, we will now add several other constraints to the optimization including: Match the spread duration dollars of various corporate sectors to better match spread duration component. To do this we will have to constrain spread duration and market value across the sectors. Match the quality sectors versus the index. Let s continue on. Optimization: Examples 5-35

228 Define Market Value Constraint across all Sectors that have at least 1 bond Define Spread Duration Constraint across Sectors that have at least 50 bonds Optimization: Examples

229 Example #3: Corporate Index Tracking Example Re-optimize with sector constraints To constrain sectors other than the overall sector, we must bring in a sector file and define constraints for each sector. A few examples will be shown. Click [Return to Input] again. STEP 32:Click [Select Sectors]. STEP 33:Type industry in the sector search field. STEP 34:Choose PROF09. STEP 35:To constrain the market distribution across sectors, add the keyword FPRICE to the list and enter.99bld/1.01bld to say you want the market value in each sector in your portfolio to be between 99and 101% of the market value in each sector in the baseline. STEP 36:Click [S0 (All)] to bring up the sector list. STEP 37:Click [Include All] to include all sectors in this sector file. Click the sectors you wish to eliminate to exclude them. In this case, we have clicked off the sectors that have 0 issues. STEP 38:Click [Generate Constraints]. The constraint of.99bld/1.01bld on market value will be written for each included sector as seen in the picture on the bottom of the opposite page. We will do the same thing for the spread duration except we will only apply this to sectors that have at least 50 bonds in them. The number of bonds in each sector can be seen on the sector file page. STEP 39:Add the keyword sprddur and enter bl as the constraint. STEP 40:Click [S0 (All)] to bring up the sector list. STEP 41:Click [Include All] to include all sectors in this sector file. Then click the sectors you wish to eliminate to exclude them. In this case, we have clicked off the sectors that have less than 50 issues. STEP 42:Click [Generate Constraints]. The constraint of bl for spread duration will be written for each of the included sectors. Optimization: Examples 5-37

230 Define Index Quality Constraints across Sectors that have at least 100 bonds Remaining Constraints and Objective 50 Results Final Attribution Results on Optimal Portfolio Optimization: Examples

231 Example #3: Corporate Index Tracking Example Constrain the index quality across sectors. STEP 43:Add the keyword ixql (for index quality rating) and enter bl as the constraint. STEP 44:Click [S0 (All)] to bring up the sector list. STEP 45:Click [Include All] to include all sectors in this sector file. Click the sectors you wish to eliminate to exclude them. Here, we have clicked off the sectors that have less than 100 issues. STEP 46:Click [Generate Constraints]. The constraint of bl for index quality rating will be written for each of the included sectors. STEP 47:Define an upper bound constraint per ISSUE: Set the keyword OPTUPPERBND to 1000 meaning that you can buy no more than 1 million of any one issue. STEP 48:Define an upper bound constraint per ISSUER: Add the keyword FPRICE and change the side to say INET (for ISSUER amount) instead of NET. Enter <2000 to constrain the amount per issuer to less than 2 million. STEP 49:Define the objective function: Maximize the overall quality of the optimal portfolio. In the early part of the problem we had the objective as maximize OAS. This must be eliminated since there can be only one objective. In this case we made the OAS a constraint to match the baseline (bl). STEP 50:Click [Calculate]. Let s review in Return Attribution page one last time. STEP 51:While toggled on <Buy>, Click [Receive Buy from 4.2] to retrieve the final 140 bond portfolio. Now, most of the attribution factors are more closely matched. The only difference is spread change. The portfolio outperforms by 10bps which accounts for the overall return outperformance versus the index. This is all due to issue selection. Optimization: Examples 5-39

232 4 5 Example #4: Cash Matching 2 3 1, Optimization: Examples

233 Example #4: Cash Matching Example #4: Cash Matching Problem: Define the Cash Flow Schedule in Cash Flow Setup You have a stream of liabilities starting 12/31/98 to 12/31/2017 which must be funded at the minimum cost. Find the portfolio that does the best cash matching across three scenarios: unchanged, +100, -100 as of 9/30/ 98. STEP 1: Click [Cash Flow Setup]. STEP 2: Click [Edit], click [Clear]. STEP 3: Enter schedule for scenario 1: Date Liability Reinvestment 12/31/98, /31/2017 STEP 4: Click [Generate]. STEP 5: Define the next two scenarios with the assumptions shown in the picture on the opposite page. After each scenario is generated, you must click [Clear] and enter the next scenario number in the scenario field. STEP 6: Click [Cash Flow Setup] to exit the setup page. STEP 7: Turn to Chapter 4.2 and toggle <Own/Univ/BL> mode. STEP 8: Click [Issue]. STEP 9: Click [Domain] and toggle <Indexes>. STEP 10: Choose TSYINDEX 10/1/98, click [Search to Buy] and [Include All]. Note: The [Search to Buy] and [Include All] are not pictured. STEP 11: Click [Pricing] and toggle <Pricing Files>. STEP 12: Click [Select]. STEP 13: Click the Univ.Oct. file Optimization: Examples 5-41

234 , Optimization: Examples

235 Example #4: Cash Matching Run Scenario Cash Flows on the Universe STEP 14: Click [Scenario Setup]. STEP 15: Click [Clear All]. STEP 16: Enter three scenarios: 0, -100, +100, immediate over 1 month STEP 17: Click [Generate]. STEP 18: Click [Scenario Setup] to exit the setup page. STEP 19: Click [ROR/CF]. STEP 20: Toggle on Scenario Cash Flow under Optional Calculations. In order to do cash matching, you must first run cash flows in all scenarios on all bonds in the universe. You will see later that if we add more bonds to the universe, we will have to recalculate cash flows on the additional bonds. STEP 21: Click [Calculate]. Now we are ready to move on to the optimization. Optimization: Examples 5-43

236 1 5 2 Make sure Short Constraints File Only one bond was selected Optimization: Examples

237 Example #4: Cash Matching Start the Optimization Now that we are starting the optimization, we will restart the numbering of the steps to make the example easier to follow: STEP 1: Click [Optimization]. STEP 2: Make sure the Short Constraint file is selected. STEP 3: Enter the objective function: FPRICE (NET) = MIN STEP 4: Toggle on Cash Match vs. Liabilities at the bottom of the page. Notice that all three scenarios are already clicked on by default. STEP 5: [Calculate]. Notice that the optimizer chose only one issue, a very high coupon bond. This solution does not look good. STEP 6: Click [Scenario CF] STEP 7: Click [Table] View the cash flows for all three scenarios and you can see that it is driven by the coupon income for the first payout. We need to add TBills to the universe. Optimization: Examples 5-45

238 Optimization Output Optimization: Examples

239 Example #4: Cash Matching STEP 8: Click [Return to Input]. Retrieve TBills into the universe. STEP 9: Click [Issue] STEP 10:Click [Domain] STEP 11: Change the security type box to TBILL by clicking on the white menu box and selecting TBILL. STEP 12: Click [Search to Buy]. STEP 13: Click [Include All]. Steps are not shown in the pictures since you did these in the early parts of this example. Remember for each new bond that we bring into the universe, you must read in the Univ.Oct price file and run scenario cash flows before you can use those bonds in the optimization. STEP 14:Click [Pricing] and toggle <Pricing Files>. STEP 15: Click [Select]. STEP 16: Click the Univ.Oct. file STEP 17: Click [ROR/CF]. STEP 18: Toggle on Scenario Cash Flow under Optional Calculations. STEP 19: Click [Calculate]. STEP 20: Click [Optimization]. STEP 21: Click [Calculate]. We have improved the results by buying 15 issues instead of one, but the match still looks inefficient as you can see in the cash flow table on the opposite page. Let s try to add mortgages to the universe. Optimization: Examples 5-47

240 Optimization: Examples

241 Example #4: Cash Matching Steps 22, 23, and are not shown in the pictures since you did these in the early parts of this example. Remember for each new bond that we bring into the universe, you must read in the Univ.Oct price file and run scenario cash flows before you can use those bonds in the optimization. STEP 22: Click [Return to Input]. Retrieve GNMA TBAs into the universe. STEP 23: Click [Issue] STEP 24: Enter GNMA in the Ticker/Query and tba in the description field. STEP 25: Click [Search to Buy]. STEP 26: Click [Include All]. STEP 27: Click [Pricing] and toggle <Pricing Files>. STEP 28: Click [Select]. STEP 29: Click the Univ.Oct. file STEP 30: Click [ROR/CF]. STEP 31: Toggle on Scenario Cash Flow under Optional Calculations. STEP 32: Click [Calculate]. STEP 33: Click [Optimization]. STEP 34: Click [Calculate]. The cash matching looks a little better, but we have bought a lot of one issue. We need to add an upper bound constraint. Optimization: Examples 5-49

242 Optimization: Examples

243 Example #4: Cash Matching STEP 35: Click [Return to Input] - not pictured. STEP 36: Click on one of the white menu fields for constraints and enter bound in the yellow input field to scroll through the available keywords. Click on OPTUPPERBND. STEP 37: Enter STEP 38: Click [Calculate] again. STEP 39: Click [Scenario CF]. STEP 40: Click [Table] to look at the results. Make sure you have the item End Balance in the table. End Balance is equal to the amount of cash available minus the liability schedule. It looks like the balances are too high which implies reinvestment risk. Let s try to eliminate that. We will do this by adding a maximum ending balance constraint to the cash flow schedule in [Cash Flow Setup]. Optimization: Examples 5-51

244 42 41, 44, Optimization: Examples

245 Example #4: Cash Matching Back to Cash Flow Setup STEP 41: Click [Cash Flow Setup] at the top of the book. STEP 42: Click [File Select]. STEP 43: Choose a customized cash flow file named optimizws, which has a maximum balance constraint of 20,000 every period. STEP 44: Click [Cash Flow Setup] to take the page down. STEP 45: Click [Return to Input] and [Calculate] again. STEP 46: An infeasible solution is found; therefore the maximum balance constraint will not be allowed. STEP 47: Click [Cash Flow Setup] again and re-select the first cash flow file. We are going back to our original liability schedule. The last thing we will try is to add some TINTs to the portfolio to try to help the end balances. Optimization: Examples 5-53

246 Optimization: Examples

247 Example #4: Cash Matching Steps 48, 49 and are not shown in the pictures since you did these in the early parts of this example. Remember for each new bond that we bring into the universe, you must read in the Univ.Oct price file and run scenario cash flows before you can use those bonds in the optimization. STEP 48: Click [Return to Input] - not pictured. STEP 49: Click [Issue]. STEP 50: Enter TINT in the Ticker/Query. STEP 51: Click [Search to Buy]. STEP 52: Click [Include All]. STEP 53: Click [Pricing] and toggle <Pricing Files>. STEP 54: Click [Select]. STEP 55: Click the Univ.Oct. file STEP 56: Click [ROR/CF]. STEP 57: Toggle on Scenario Cash Flow under Optional Calculations. STEP 58: Click [Calculate]. STEP 59: Click [Optimization]. STEP 60: Click [Calculate]. STEP 61: Click [Scenario CF]. STEP 62: Click [Table] to look at the results. The cash match looks better and we have used the minimum amount of cash at $257,371, the lowest number we have seen through all of these iterations. Good job - take the rest of the day off! Optimization: Examples 5-55

248 5-56 Optimization: Examples

249

250 The Yield Book Inc. Systems Help: Analytics Help: FAX (212) 816-TECH (8324) (212) 816-BOOK (2665) (212)