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