Whitepaper. Government Note and Bond Futures in Fixed Income Portfolio Analysis. White Paper

Transcription

2 Government Note and Bond Futures in Fixed Income Portfolio Analysis Contents Introduction... 2 Portfolio and Benchmark Example... 3 Cheapest-to-Deliver Note or Bond... 5 Futures Hedge Ratios and Portfolio Duration Targeting... 6 Total Return Calculations... 9 Attribution of Portfolio and Benchmark Returns Summary and Conclusions Introduction Government note and bond futures were first introduced in the U.S. in the early 1980s. The Treasury note and bond futures contracts were patterned after the well-known agricultural commodity contracts that were widely traded at the Chicago Board of Trade. As with the agricultural futures, the Treasury futures were designed to provide a derivatives marketplace where hedgers and speculators could manage risk. These futures enabled market participants to mitigate unwanted interest rate exposures in the cash market, offset or enhance cash market volatility, and otherwise reap the benefits of futures price discovery. Treasury note and bond futures were introduced at a time when the U.S. Federal Reserve was targeting money supply, and interest rate volatility was high. Trading activity in interest rate futures markets centers on hedgers and speculators. Hedgers use interest rate futures to adjust portfolio exposures, hedge liability risks, and create synthetic securities. Speculators use them to take positions that they hope will pay off if interest rates change as anticipated. Both groups are necessary for an efficient, well-functioning futures market. Together, they provide the liquidity necessary to ensure an actively traded futures marketplace. One valuable by-product of their trading activity is price discovery. Futures prices and the interest rates associated with them provide valuable indications of what market makers believe those prices and interest rates will be in the future. This information is used by economic policy makers and financial market participants for planning and policy decision making. This paper focuses on government note and bond futures, how they are used in fixed income portfolio management, and how FactSet accounts for them in the analysis and attribution of portfolio total returns. For purposes of illustrating how futures are used in duration management, a sample portfolio and benchmark are introduced as the backdrop for analyzing a futures hedge and futures performance. Specifically, government note futures are added to a portfolio to alter its interest rate exposures relative to a benchmark. The basic terms and conventions of the futures contracts are defined. FactSet data sources, futures-cash relationships, and futures analytics are explored. The paper then focuses on the Copyright 2015 FactSet Research Systems Inc. All rights reserved. 2

3 calculation of futures total returns and the performance and attribution of a portfolio that includes futures. FactSet s analytics and attribution models are used to highlight how futures impact portfolio risk and return in the context of portfolio management versus a benchmark. Portfolio and Benchmark Example The sample portfolio includes multi-currency global bonds and is benchmarked against a multi-currency global index. The sample portfolio consists of U.S. and European government and corporate bonds denominated in GBP, EUR, and USD currencies. At the beginning of the analysis period, the portfolio contained 104 securities and was characterized by the distributions shown in Table 1. Table 1: Portfolio Characteristics Percent Moody s Rating Yield to Maturity OAS Effective Duration Effective Convexity Total A GBP A EUR Baa USD Aa The benchmark is defined to include GBP, EUR, and USD fixed rate securities with final maturities of one year or longer and minimum par amounts outstanding of $300 million for USD securities, 300 million for pan-european securities, and 200 million for GBP securities. The benchmark included over 12,150 securities and was characterized by the distributions in Table 2. Table 2: Benchmark Characteristics Percent Moody s Rating Yield to Maturity OAS Effective Duration Effective Convexity Total Aa GBP 8.14 Aa EUR A USD Aa Compared to the benchmark, the portfolio has a lower allocation to USD, a higher allocation to EUR, and a higher allocation to GBP. On a weighted-average basis, the portfolio exhibits a lower overall quality Copyright 2015 FactSet Research Systems Inc. All rights reserved. 3

4 rating, a higher yield to maturity, and a higher option-adjusted spread (OAS) than the benchmark. The effective duration of the portfolio is 0.31 shorter than the benchmark due primarily to the portfolio s concentration of shorter duration EUR denominated securities. Portfolio exposures relative to the benchmark are summarized in Table 3. Table 3: Relative Characteristics Percent Moody s Rating Yield to Maturity OAS Effective Duration Effective Convexity Total 0.00 Lower GBP 3.04 Lower EUR 3.41 Lower USD Lower In Table 3, you can infer several portfolio strategy bets from the relative exposures. First, the portfolio s percentage allocations suggest that the GBP and EUR currency sectors are favored at the expense of USD. Second, an implicit quality bet favors lower-rated securities. Third, the relative durations suggest an expectation that EUR rates are expected to increase and USD rates are expected to decrease. For purposes of introducing government note and bond futures into the portfolio, suppose that the portfolio manager decides to remove the relative interest rate exposures in the EUR and USD sectors. In other words, the manager decides to neutralize the sector duration bets by making each sector s duration equal to that of the respective benchmark sector. This could be accomplished in the cash market by restructuring the bonds in those sectors; however, government note and bond futures can provide a more efficient and cost effective means to target portfolio duration, especially if the cash market bonds are illiquid. Table 4 displays the government note contracts that are used in the example. The Euro-Bund futures contract, traded on the Eurex Exchange, is a widely traded, ten-year physical delivery contract with quarterly settlement dates in March, June, September, and December. Likewise, the U.S. Treasury Note Future contract, traded on the Chicago Mercantile Exchange (CME), is a physical delivery contract settling quarterly in the same months. Both contracts have a notional value of 100,000, a notional coupon of 6%, and settlement at delivery based on an invoice price. The invoice price is calculated as follows: where: + FP = Futures price Invoice Price = FP CF i + AI i + CF i = Conversion factor of the delivered note + AI i = Accrued interest of the delivered note Copyright 2015 FactSet Research Systems Inc. All rights reserved. 4

5 The conversion factor is a quality-adjustment mechanism that takes into account a note s coupon and maturity relative to the 6% coupon bond specified by the contract. The conversion factor system for invoicing notes and bonds effectively broadens the supply of notes and bonds that are deliverable against the futures market and normalizes the process of invoicing at settlement. 1 Table 4: Euro-Bund and U.S. Treasury Note Futures Exchange Ticker Deliverable (Years; Coupon) Type of Settlement Contract Value Delivery Months Euro-Bund Future U.S. Treasury Note Futures Eurex FGBL 8.5 to 10.5; 6% Physical 100,000 CME TY 6.5 to 10.0; 6% Physical $100,000 Mar, Jun, Sep, Dec Mar, Jun, Sep, Dec Cheapest-to-Deliver Note or Bond Although a number of notes are eligible for delivery against the Euro-Bund and U.S. Treasury Note futures contracts, some issues are more likely to be delivered than others. According to contract delivery specifications, traders with short futures positions can decide which eligible note to deliver. Generally they will choose the one that maximizes their profit or minimizes loss upon delivery (i.e., the note with the lowest cash market value relative to the futures invoice price). The note that is most likely to be delivered is often referred to as the cheapest-to-deliver note. Fluctuations in market conditions can lead to changes in what is considered to be the cheapest-to-deliver note. This can impact the interest rate sensitivity of the futures contract and, by extension, the performance results of hedge strategies. For each trading day prior to futures expiration, FactSet calculates the cheapest-to-deliver note based on a Monte Carlo simulation of government rates between the evaluation date and the expiration date of the futures contract. Along each path of the simulation, FactSet determines the cheapest-to-deliver note by comparing the price differential (i.e., cash price versus futures invoice price) to the financing differential (i.e., coupon income versus financing rate). The price differential is called the gross basis, the financing differential is called the carry, and the difference between the two is called the net basis. The note with the lowest net basis is usually cheapest-to-deliver, because it results in the highest profit or lowest loss upon delivery for the traders who are short futures. There are a number of other factors that can complicate the analysis, but they are accounted for in FactSet s calculations. They include the level of prevailing yields relative to the 6% coupon specified by the contracts, changes in yield spreads among deliverable notes, and various delivery-month supply options. 1 For a complete description of the contract specifications and delivery procedures of the U.S. Treasury Note Futures, see U.S. Treasury Futures Delivery Process (CMEGroup.com). You can find similar information for the Euro-Bund Futures by going to the Eurex Exchange website (Eurexexchange.com) and choosing the Trading tab. Copyright 2015 FactSet Research Systems Inc. All rights reserved. 5

6 Changes in the level and shape of the yield curve can change the cheapest-to-deliver note. When this occurs, it can impact the performance of futures hedge strategies and sometimes requires them to be rebalanced. Taking into account the cheapest-to-deliver note, FactSet calculates the partial and effective durations for futures contracts. Holding option-adjusted spreads constant, FactSet shifts the reference yield curve up and down by 100 basis points and recalculates the price as a result of each shift. The average price change versus the starting price adjusted for the yield shift results in the partial and effective durations. Based on these calculations, FactSet calculates the futures durations and partial durations daily and you can use each to construct hedge ratios for purposes of hedging bonds or targeting portfolio duration. Futures Hedge Ratios and Portfolio Duration Targeting Futures are often used by portfolio managers to alter portfolio duration and convexity in anticipation of changes in the level of rates. One method of estimating the number of futures contracts required to achieve a target portfolio duration is as follows: where: N = (D T D P ) (MV + AI) P D F (MV) F + N = number of futures contracts + D T = Target duration of the hedged portfolio + D P = Duration of the unhedged portfolio + (MV + AI) P = Market value and accrued interest of the portfolio + D F = Duration of the futures contract + (MV) F = Notional market value of the futures contract Returning to the portfolio/benchmark example, using Euro-Bund futures the formula above is used to target a EUR sector duration of 5.46 as follows: 69 = ( ) 66,540, ,170 A long position of 69 March 14 Euro-Bund futures contracts increases the effective duration of the EUR sector from 4.20 to 5.46, thereby eliminating the mismatch between the portfolio and benchmark EUR effective durations. A similar calculation is used for the required number of U.S. Treasury Note futures contracts to reduce the effective duration of the USD sector from 5.20 to In this case, 20 March 14 Treasury notes futures are sold to make the duration of the USD sector equal to that of the benchmark. In FactSet, all futures positions are entered in terms of their equivalent notional exposure. Futures notional exposure is equal to the number of contracts times the futures contract value. The notional exposure for a long position of 69 March 14 Euro-Bund contracts is 6,900,000 (69 x 100,000) and the Copyright 2015 FactSet Research Systems Inc. All rights reserved. 6

7 notional exposure for a short position of 20 March 14 U.S. Treasury Note Futures contracts is -$2,000,000 (-20 x $100,000 ). The futures positions that are introduced into the example are shown in Table 5. Table 5: Futures Durations and Convexities 10Y T-Note (CBT) Mar 14 Euro-Bund (EUR) Mar 14 Symbol TYH14-CBTE FGBLH14-EUR Port. Ending Price (Local) Port. Ending Quantity Held -$2,000,000 6,900,000 Port. Ending Market Value -$1,785,941 9,602,730 Port. Ending Weight Portfolio Ending Partial Durations 2- Year Year Year Year Port. Ending Effective Duration Port. Ending Effective Convexity Table 5 shows the futures notional amounts (Port. Ending Quantity Held) required to neutralize the EUR and USD sector durations. The portfolio is long 6,900,000 notional of Euro-Bund futures, equivalent to 69 contracts. The portfolio is short $2,000,000 notional of U.S. Treasury Note futures, equivalent to 20 contracts. Table 5 also shows the partial durations, effective duration, and effective convexity for each futures position. For instance, the Euro-Bund futures have an effective duration of 8.66 and the U.S. Treasury Note futures have an effective duration of The contribution to effective duration and contribution to convexity of the futures positions are calculated as the product of market value percent and the duration/convexity statistics. For instance, the contribution to ending portfolio effective duration of the Euro-Bund futures contracts are: Copyright 2015 FactSet Research Systems Inc. All rights reserved. 7

8 Contribution to Effective Duration = Market Value(%) Effective Duration 0.49 = ( 5.70 ) 8.66 (Euro-Bund futures) 100 The notional exposure of the Euro-Bund futures contributes 0.49 to the effective duration of the portfolio. You can perform a similar calculation to estimate the Euro-Bund futures contribution to the effective duration of the EUR sector where it resides. The weights are scaled to reflect the percentage that the Euro-Bund futures notional amount represents within that sector. For example, the Euro-Bund futures contribute 1.26 to the EUR sector s effective duration, increasing it to The effect of the Euro-Bund futures strategy is to neutralize the EUR sector s relative interest rate sensitivity to changes in EUR rates. At the portfolio level, the impact of the Euro-Bund and U.S. Treasury Note futures strategies are illustrated in Figure 1 and Figure 2. Figure 1 displays the portfolio results excluding futures and Figure 2 shows similar output including futures. Figure 1: Portfolio Excluding Futures versus Benchmark In Figure 1, notice the discrepancy in the ending effective durations of the EUR and USD sectors, and 0.14 respectively. In the example, the Euro-Bund and U.S. Treasury Note futures were included in the portfolio specifically to neutralize these discrepancies. The results of including the futures are shown in Figure 2. Figure 2: Portfolio Including Futures versus Benchmark As Figure 2 shows, the duration discrepancies in the EUR and USD sectors have been eliminated. With the inclusion of the futures in those currencies, the portfolio is duration neutral versus the benchmark Copyright 2015 FactSet Research Systems Inc. All rights reserved. 8

9 with respect to changes in EUR and USD interest rates. However, the effective duration remains 0.11 longer than that of the benchmark at the portfolio level. This is due to the fact that the portfolio is overweighted in GBP and EUR and the effective durations of those sectors are longer than the effective duration of the USD sector, which is underweighted. Total Return Calculations The real economic value and impact of derivative positions, including futures, is best measured by the notional exposure of those securities. The notional exposure approach adjusts for the actual market risk and exposure of futures contracts by decomposing them into a market component and a funding component. In FactSet, the futures market component is measured by the notional value and sensitivities of the futures contracts. The funding component is measured by the corresponding cash offset position. The introduction of the cash offset funding component guarantees that the overall market value of the portfolio is not distorted by the notional exposure of the futures contract. In other words, the weight of the combined position futures and cash offset is zero upon initiation. The notional exposure approach is also used for calculating futures total returns. Otherwise, futures returns would be infinite or undefined because futures contracts have zero market value at initiation and very small market values thereafter related only to mark-to-market margin variations. The weight and total return calculations for futures are as follows: Beginning Weight = Notional B i i Notional Bi and Total Return = Notional E i Notional Bi Notional Bi where: + Notional Bi = Beginning quantity Price Bi + Notional Ei = Ending quantity Price Ei Portfolio total return is the product of the beginning weights and total returns, across all holdings: ( Notional B i Notional Bi i Portfolio Total Return = ) ( Notional E i Notional Bi Notional Bi ) = ( Notional E i Notional Bi ) i Notional Bi For futures, the beginning notional exposures in the equation above cancel out. The return contribution becomes the futures gain/loss divided by the total portfolio market value. Futures generate no coupon or principal cash flows, and therefore, consist entirely of price return. In FactSet, price return is always displayed in local currency terms. In a multi-currency portfolio, total return is reported in a user-selected reporting currency and includes a currency return component: Currency return is calculated as: Total Return = Price Return + Currency Return Currency Return = Total Return (report currency) Total Return (local currency) Copyright 2015 FactSet Research Systems Inc. All rights reserved. 9

10 To calculate total return in a reporting currency that is different than the local currency, FactSet applies exchange rate adjustments to both the local price and local coupon returns as follows: where: + FX e = Ending FX rate Currency Adjusted Total Return = (P e P b ) (P b + AI b ) (FX e FX b ) + FX b = Beginning FX rate In the multi-currency portfolio example, a reporting currency is selected and the local returns are converted to reporting currency returns. This is shown in Figure 3 for the portfolio, excluding the futures contracts. The holding period is 31 days, the price and coupon returns are in local currency, and the total returns and variations in total returns are in EUR. Figure 3: Total Return Components & Contributions Portfolio Excluding Futures versus Benchmark The Return Components section of Figure 3 shows portfolio price return, portfolio coupon return, and portfolio currency return. The Total Returns & Contributions section shows total returns for the portfolio and benchmark as well as the contributions to total returns by currency sector. Finally, the Variation section shows the difference in total return between the portfolio and the benchmark. For the period, the portfolio total return was one basis point less than the benchmark total return. Positive relative performance in the EUR sector (+0.32) was more than offset by negative relative performance in the GBP and USD sectors (-0.19 and -0.09, respectively). Figure 4 shows similar data for the portfolio, including the Euro-Bund and Treasury Note futures. Copyright 2015 FactSet Research Systems Inc. All rights reserved. 10

11 Figure 4: Total Return Components & Contributions Portfolio Including Futures Versus Benchmark The portfolio s total return for the holding period was 3.07%, up 10 basis points from the 2.97% shown in Figure 3. The total return of the portfolio relative to the benchmark also increased by the same amount. The futures added to portfolio total return, but how? To answer this question, we turn to the attribution of portfolio and benchmark performance. Attribution of Portfolio and Benchmark Returns FactSet s performance attribution model explains benchmark-relative performance based on factors of attribution, portfolio exposures relative to the benchmark, and changes in market conditions. FactSet provides users with flexibility to choose the attribution factors and how the attribution is displayed. This paper describes a basic approach where the attribution factors are chosen to match portfolio strategy variables commonly employed by fixed income managers. The relationship between those strategy variables and the factors of attribution are summarized in Table 6, which shows the configuration of FactSet s basic attribution model. Table 6: Basic Performance Attribution Factors Portfolio Strategy Strategy Variable Attribution Factor (Effect) Interest rates Effective Duration Shift Yield Curve Partial Durations Twist Sector Allocation Sector weight (%) Allocation Bond Selection Bond Weight (%) Selection Currency Currency weight (%) Currency The attribution factors include shift, twist, allocation, selection, and currency. For a full explanation of FactSet s attribution methodology, reporting configurations, and calculation details, see A Flexible Copyright 2015 FactSet Research Systems Inc. All rights reserved. 11

12 Benchmark Relative Method of Attributing Returns for Fixed Income Portfolios. 2 One advantage of FactSet s approach is that a common methodology and set of calculations are used for all security types, including government note and bond futures. For government note and bond futures, the most relevant attribution factors are shift and twist since futures are primarily interest rate sensitive instruments. Shift return is calculated as: Shift Return = 1 E Duration Δ Shift Point E Convexity (Δ ShiftPoint ) 2 Twist return is calculated as: where: + E Duration = Effective Duration ( 1 E PartialDuration1 (Δ PartialPoint1 Δ ShiftPoint )) + ( 1 E PartialDuration2 (Δ PartialPoint2 Δ ShiftPoint )) + ( 1 E PartialDuration3 (Δ PartialPoint3 Δ ShiftPoint )) + ( 1 E PartialDurationN (Δ PartialPointN Δ ShiftPoint )) + Δ ShiftPoint = Change in the Yield of a UserDefined Yield Curve Shift Point + E Convexity = Effective Convexity + E PartialDuration# = Effective Partial Duration at a Specific Yield Curve Point + Δ PartialPoint# = Change in the Yield of a Specific Yield Curve Point Shift and twist returns represent the portion of total return explained by changes in the level of interest rates and changes in the shape of the yield curve, respectively. Shift and twist returns exclude spread and carry components and are calculated independently of the benchmark. Subtracting shift and twist return from total return results in Residual Return: Residual Return = Total Return (Shift Return + Twist Return) Residual return represents the portion of unexplained total return. It includes return components such as spread, income, paydown, carry (accretion and roll down), volatility, inflation, and basis. 3 Residual return is primarily basis and carry for government bond futures. 2 Kwasniewski, Stanley J., CFA A Flexible Benchmark Relative Method of Attributing Returns for Fixed Income Portfolios. 3 These components comprise the optional factors in FactSet s fixed income attribution model. Clients who wish to analyze the full range of total return components can add these additional attribution factors to their analysis. For a full description of this methodology, please see A Flexible Benchmark Relative Method of Attributing Returns for Fixed Income Portfolios. Copyright 2015 FactSet Research Systems Inc. All rights reserved. 12

13 Residual returns are used to quantify allocation and selection effects, both of which are calculated relative to the benchmark, as follows: Allocation Return = [(W i W i ) (RR i RR)] i where: Selection Return = [W i (RR i RR i )] i + W i = Weight of Group i in Portfolio + W i = Weight of Group i in Benchmark + RR i = Residual Return of Group i in Benchmark + RR = Overall Benchmark Residual Return + RR i = Residual Return of Group i in Portfolio Returning to the portfolio example, Figure 5 shows performance attribution for the portfolio (excluding futures) versus the benchmark. The portfolio and benchmark returns are shown in both local and EUR currency terms and the attribution results are in local terms. Figure 5: Basic Attribution of Portfolio (excluding Futures) versus Benchmark Over the holding period the portfolio total return in EUR was 2.97% one basis point less than the total return of the benchmark. The attribution results indicate that the shift (-0.10), twist (0.05), allocation (0.01), selection (0.14), and currency effects (-0.10) were largely offsetting in the aggregate. As described previously, the Euro-Bund futures were purchased to lengthen the EUR sector duration by 1.26 and U.S. Treasury Note futures were sold to shorten USD sector duration by As changes in the portfolio of cash bonds occurred throughout the holding period, the futures positions were adjusted accordingly. During the holding period, both the Euro and U.S. interest rates declined. Figure 6 shows the total return and performance attribution results, when futures are included in the portfolio. Copyright 2015 FactSet Research Systems Inc. All rights reserved. 13

14 Figure 6: Basic Attribution of Portfolio Including Futures versus Benchmark By comparing Figure 5 (excluding futures) to Figure 6 (including futures), the impact of the futures derivative strategy is evident. Portfolio total return increased relative to the benchmark by 10 basis points ( ) as a result of the strategy. Specifically, the Euro-Bund futures added 35 basis points ( ) to the local total return of the EUR sector, while the U.S. Treasury Note futures subtracted 5 basis points ( ) in local return from the USD sector. At the portfolio level, the net result was an increase in EUR total return by 10 basis points ( ). The attribution reveals why. The shift effect of the EUR sector increased by 13 basis points ( ) because the long Euro-Bund futures positions added duration in that sector, and EUR rates declined. Conversely, the shift effect of the USD sector decreased from to basis points because the short position in U.S. Treasury Note futures reduced the effective duration of that sector and USD rates declined. At the portfolio level, the weighted-average shift effect increased by 12 basis points ( ). The original purpose of adding the futures to achieve duration neutrality paid off. Despite declines in EUR and USD benchmark rates, there was minimal impact at the portfolio level relative to the benchmark due to changes in rates. Further analysis of Figure 5 and Figure 6 reveals that the impact on twist effects at the portfolio and currency sector levels were negligible. Likewise, the allocation effect did not change at the portfolio level because the futures position had no impact on the portfolio sector weights. The selection effect of the EUR sector increased slightly as a result of adding the Euro-Bund futures because the contract had a higher residual return over the period than the index sector where it resided. In summary, the attribution indicates minimal shift effect impact on relative performance as a result of declining EUR and USD rates when futures are included in the portfolio. The government note futures effectively neutralized the relative interest rate exposures. Summary and Conclusions Government note and bond futures are often used by portfolio managers to hedge durations and alter interest rate exposures of global bond portfolios. Recognizing that futures constitute leveraged positions, FactSet applies a notional-exposure approach to calculate their contributions to portfolio analytics, returns, and attribution. Futures are coupled with cash-offset positions so that the combined positions net out so as not to distort the market value and weight relationships within the portfolio. According to this approach, futures contribute to the portfolio s interest rate sensitivity and total return without impacting the portfolio s market values. The analytics and returns calculated by FactSet constitute the basis for calculating performance attribution for portfolios that include futures versus benchmarks. As this paper shows, the attribution of relative portfolio performance can be calculated and reported at a basic level that relates the factors of attribution to primary investment strategies or on a more Copyright 2015 FactSet Research Systems Inc. All rights reserved. 14

15 advanced level by enabling a high degree of user choice and configuration of attribution factors. Whichever approach is taken, FactSet accurately measures and accounts for the impact of government note and bond futures within the context of portfolio analysis and performance attribution. Copyright 2015 FactSet Research Systems Inc. All rights reserved. 15