Chapter 23 Active Bond Portfolio Management Strategies

Chapter 23 Active Bond Portfolio Management Strategies
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Learning Objectives After reading this chapter, you will understand the five basic steps involved in the investment management process the difference between active and passive strategies what tracking error is and how it is computed the difference between forward-looking and backward-looking tracking error the link between tracking error and active portfolio management the risk factors that affect a benchmark index the importance of knowing the market consensus before implementing an active strategy Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Learning Objectives (continued)
After reading this chapter, you will understand the different types of active bond portfolio strategies: interest-rate expectations strategies, yield curve strategies, yield spread strategies, option-adjusted spread-based strategies, and individual security selection strategies bullet, barbell, and ladder yield curve strategies the limitations of using duration and convexity to assess the potential performance of bond portfolio strategies why it is necessary to use the dollar duration when implementing a yield spread strategy how to assess the allocation of funds within the corporate bond sector why leveraging is used by managers and traders and the risks and rewards associated with leveraging how to leverage using the repo market Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Overview of the Investment Management Process
Regardless of the type of financial institution, the investment management process involves the following five steps: setting investment objectives establishing investment policy selecting a portfolio strategy selecting assets measuring and evaluating performance Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Overview of the Investment Management Process (continued)
Setting Investment Objectives The first step in the investment management process is setting investment objectives. The investment objective will vary by type of financial institution. Establishing Investment Policy The second step in investment management process is establishing policy guidelines for meeting the investment objectives. Setting policy begins with the asset allocation decision so as to decide how the funds of the institution should be distributed among the major classes of investments (cash equivalents, equities, fixed-income securities, real estate, and foreign securities). Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Selecting a Portfolio Strategy Selecting a portfolio strategy that is consistent with the objectives and policy guidelines of the client or institution is the third step in the investment management process. Portfolio strategies can be classified as either active strategies or passive strategies. Essential to all active strategies is specification of expectations about the factors that influence the performance of an asset class. Passive strategies involve minimal expectational input. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Selecting a Portfolio Strategy Strategies between the active and passive extremes have sprung up that have elements of both extreme strategies. For example, the core of a portfolio may be indexed, with the balance managed actively. Or a portfolio may be primarily indexed but employ low-risk strategies to enhance the indexed portfolio’s return. This strategy is commonly referred to as enhanced indexing or indexing plus. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Selecting a Portfolio Strategy In the bond area, several strategies classified as structured portfolio strategies have commonly been used. A structured portfolio strategy calls for design of a portfolio to achieve the performance of a predetermined benchmark. Such strategies are frequently followed when funding liabilities. When the predetermined benchmark is the generation of sufficient funds to satisfy a single liability, regardless of the course of future interest rates, a strategy known as immunization is often used. When the predetermined benchmark requires funding multiple future liabilities regardless of how interest rates change, strategies such as immunization, cash flow matching (or dedication), or horizon matching can be employed. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Selecting a Portfolio Strategy Given the choice among active, structured, or passive management, the selection depends on the client or money manager’s view of the pricing efficiency of the market the nature of the liabilities to be satisfied Pricing efficiency is taken to describe a market where prices at all times fully reflect all available information that is relevant to the valuation of securities. When a market is price efficient, active strategies will not consistently produce superior returns after adjusting for risk and transactions costs. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Selecting Assets After a portfolio strategy is specified, the fourth step in the investment management process is to select the specific assets to be included in the portfolio, which requires an evaluation of individual securities. It is in this phase that the investment manager attempts to construct an efficient portfolio. An efficient portfolio is one that provides the greatest expected return for a given level of risk, or, equivalently, the lowest risk for a given expected return. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Measuring and Evaluating Performance The measurement and evaluation of investment performance is the fifth and last step in the investment management process. This step involves measuring the performance of the portfolio, then evaluating that performance relative to some benchmark. The benchmark selected for evaluating performance is called a benchmark or normal portfolio. The benchmark portfolio may be a popular index such as the S&P 500 for equity portfolios or one of the bond indexes. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Tracking Error and Bond Portfolio Strategies
Before discussing bond portfolio strategies, it is essential to understand an important analytical concept. When a portfolio manager’s benchmark is a bond market index, risk is not measured in terms of the standard deviation of the portfolio’s return. Instead, risk is measured by the standard deviation of the return of the portfolio relative to the return of the benchmark index. This risk measure is called tracking error. Tracking error is also called active risk. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Tracking Error and Bond Portfolio Strategies (continued)
Calculation of Tracking Error Tracking error is computed as follows: Step 1: Compute the total return for a portfolio for each period. Step 2: Obtain the total return for the benchmark index for each period. Step 3: Obtain the difference between the values found in Step 1 and Step 2. The difference is referred to as the active return. Step 4: Compute the standard deviation of the active returns. The resulting value is the tracking error.  The tracking error measurement is in terms of the observation period.  If monthly returns are used, the tracking error is a monthly tracking error.  If weekly returns are used, the tracking error is a weekly tracking error. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit 23-1 (see Overheads and 23-16) shows the calculation of the tracking error for two hypothetical portfolios assuming that the benchmark is the Lehman U.S. Aggregate Index. Portfolio A’s monthly tracking error (in Overhead 23-15) is 9.30 basis points where the monthly returns of the portfolio closely track the return of the benchmark index—that is, the active returns are small. In contrast, for Portfolio B (in Overhead 23-16), the active returns are large, and thus, the monthly tracking error is large—79.13 basis points. The tracking error is unique to the benchmark used. Exhibit 23-2 (see Overheads and 23-18) shows the tracking error for the portfolios using the Lehman Global Aggregate Index. The monthly tracking error for Portfolio A (in Overhead 23-17) is basis points compared to 9.30 basis points when the benchmark is the Lehman U.S. Aggregate Index; for Portfolio B (in Overhead 23-18), it is basis points for the Lehman Global Index versus basis points for the Lehman U.S. Aggregate Index. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Calculation of Tracking Error for Two Hypothetical Portfolios: Benchmark Is the Lehman U.S. Aggregate Index (Portfolio A) Observation period = January 2007–December 2007; Benchmark index = Lehman U.S. Aggregate Index Portfolio A Month in 2007 Portfolio Return (%) Benchmark Index Active January -0.02 -0.04 0.02 February 1.58 1.54 0.04 March 0.00 April 0.61 0.54 0.07 May -0.71 -0.76 0.05 June -0.27 -0.30 0.03 July 0.91 0.83 0.08 August 1.26 1.23 September 0.69 0.76 -0.07 October 0.95 0.90 November 1.08 1.04 December 0.28 -0.26 Sum 0.041 Mean 0.0034 Variance 0.0086 Standard Deviation = Tracking error 0.0930 Tracking error (in basis points) 9.30 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Calculation of Tracking Error for Two Hypothetical Portfolios: Benchmark Is the Lehman U.S. Aggregate Index (Portfolio B) Observation period = January 2007–December 2007; Benchmark index = Lehman U.S. Aggregate Index Portfolio B Month in 2007 Portfolio Return (%) Benchmark Index Active January -1.05 -0.04 -1.01 February 2.13 1.54 0.59 March 0.37 0.00 April 1.01 0.54 0.47 May -1.44 -0.76 -0.68 June -0.57 -0.30 -0.27 July 1.95 0.83 1.12 August 1.26 1.23 0.03 September 2.17 0.76 1.41 October 1.80 0.90 November 1.04 1.09 December -0.32 0.28 -0.60 Sum 3.42 Mean 0.2850 Variance 0.6262 Standard Deviation = Tracking error 0.7913 Tracking error (in basis points) 79.13 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Calculation of Tracking Error for Two Hypothetical Portfolios: Benchmark Is the Lehman Global Aggregate Index (Portfolio A) Observation period = January 2007–December 2007; Benchmark index = Lehman Global Aggregate Index Portfolio A Month in 2007 Portfolio Return (%) Benchmark Index Active January -0.02 -0.98 0.96 February 1.58 2.06 -0.48 March -0.04 0.24 -0.28 April 0.61 1.13 -0.52 May -0.71 -1.56 0.85 June -0.27 -0.44 0.17 July 0.91 2.03 -1.12 August 1.26 1.23 0.03 September 0.69 2.24 -1.55 October 0.95 1.63 -0.68 November 1.08 1.91 -0.83 December 0.02 -0.31 0.33 Sum -3.119 Mean Variance 0.5782 Standard Deviation = Tracking error 0.7604 Tracking error (in basis points) 76.04 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Calculation of Tracking Error for Two Hypothetical Portfolios: Benchmark Is the Lehman Global Aggregate Index (Portfolio B) Observation period = January 2007–December 2007; Benchmark index = Lehman Global Aggregate Index Portfolio B Month in 2007 Portfolio Return (%) Benchmark Index Active January -1.05 -0.98 -0.07 February 2.13 2.06 0.07 March 0.37 0.24 0.13 April 1.01 1.13 -0.12 May -1.44 -1.56 0.12 June -0.57 -0.44 -0.13 July 1.95 2.03 -0.08 August 1.26 1.23 0.03 September 2.17 2.24 October 1.80 1.63 0.17 November 1.91 0.22 December -0.32 -0.31 -0.01 Sum 0.26 Mean 0.0217 Variance 0.0142 Standard Deviation = Tracking error 0.1192 Tracking error (in basis points) 11.92 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Two Faces of Tracking Error Calculations computed for a portfolio based on a portfolio’s actual active returns reflect the portfolio manager’s decisions during the observation period. We call tracking error calculated from observed active returns for a portfolio backward-looking tracking error. It is also called the ex-post tracking error and the actual tracking error. The portfolio manager needs a forward-looking estimate of tracking error to reflect the portfolio risk going forward. The way this is done in practice is by using the services of a commercial vendor or dealer firm that has modeled the factors that affect the tracking error associated with the bond market index that is the portfolio manager’s benchmark. These models are called multi-factor risk models. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Two Faces of Tracking Error Given a manager’s current portfolio holdings, the portfolio’s current exposure to the various risk factors can be calculated and compared to the benchmark’s exposures to the factors. Using the differential factor exposures and the risks of the factors, a forward-looking tracking error for the portfolio can be computed. This tracking error is also referred to as predicted tracking error and ex-ante tracking error. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Tracking Error and Active Versus passive strategies We can think of active versus passive bond portfolio strategies in terms of forward-looking tracking error. In constructing a portfolio, a manager can estimate its forward-looking tracking error. When a portfolio is constructed to have a forward-looking tracking error of zero, the manager has effectively designed the portfolio to replicate the performance of the benchmark. If the forward-looking tracking error is maintained for the entire investment period, the active return should be close to zero. Such a strategy—one with a forward-looking tracking error of zero or very small—indicates that the manager is pursing a passive strategy relative to the benchmark index. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Risk Factors and Portfolio Management Strategies Forward-looking tracking error indicates the degree of active portfolio management being pursued by a manager. Therefore, it is necessary to understand what factors (referred to as risk factors) affect the performance of a manager’s benchmark index. The risk factors affecting the Lehman Brothers Aggregate Bond Index have been investigated. A summary of the risk factors is provided in Exhibit 23-3 (see Overhead 23-23). Risk factors can be classified into two types: A systematic risk factor is a force that affect all securities in a certain category in the benchmark index. A nonsystematic risk factor refers to risk that is not attributable to systematic risk factors. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit 23-3 Summary of Risk Factors for a Benchmark
Systematic Risk Factors Non-Systematic Risk Factors Term Structure Risk Factors Non-Term Structure Risk Factors Issuer Specific Issue Specific sector risk quality risk optionality risk coupon risk MBS sector risk MBS volatility risk MBS prepayment risk Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Risk Factors and Portfolio Management Strategies Systematic risk factors, in turn, are divided into two categories: term structure risk factors and non-term structure risk factors. Term structure risk factors are risks associated with changes in the shape of the term structure (level and shape changes). Non-term structure risk factors include sector risk, quality risk, optionality risk, coupon risk, MBS sector risk, MBS volatility risk, and MBS prepayment risk. Sector risk is the risk associated with exposure to the sectors of the benchmark index. Quality risk is the risk associated with exposure to the credit rating of the securities in the benchmark index. Optionality risk is the risk associated with an adverse impact on the embedded options of the securities in the benchmark index. Coupon risk is the exposure of the securities in the benchmark index to different coupon rates. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Risk Factors and Portfolio Management Strategies The last three non-term risks (MBS sector risk, MBS volatility risk, and MBS prepayment risk) are associated with the investing in residential mortgage pass-through securities. MBS sector risk is the exposure to the sectors of the MBS market included in the benchmark. MBS volatility risk is the exposure of a benchmark index to changes in expected interest-rate volatility. MBS prepayment risk is the exposure of a benchmark index to changes in prepayments. Nonsystematic factor risks are classified as nonsystematic risks associated with a particular issuer, issuer-specific risk, and those associated with a particular issue, issue-specific risk. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Determinants of Tracking Error Once we know the risk factors associated with a benchmark index, forward-looking tracking error can be estimated for a portfolio. The tracking error occurs because the portfolio constructed deviates from the exposures for the benchmark index. A manager provided with information about (forwarding-looking) tracking error for the current portfolio can quickly assess if the risk exposure for the portfolio is one that is acceptable if the particular exposures are being sought Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Active Portfolio Strategies
Manager Expectations Versus the Market Consensus A money manager who pursues an active strategy will position a portfolio to capitalize on expectations about future interest rates, but the potential outcome (as measured by total return) must be assessed before an active strategy is implemented. The primary reason for this is that the market (collectively) has certain expectations for future interest rates and these expectations are embodied into the market price of bonds. Though some managers might refer to an “optimal strategy” that should be pursued given certain expectations, that is insufficient information in making an investment decision. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Active Portfolio Strategies (continued)
Interest-Rate Expectations Strategies A money manager who believes that he or she can accurately forecast the future level of interest rates will alter the portfolio’s sensitivity to interest-rate changes. A portfolio’s duration may be altered by swapping (or exchanging) bonds in the portfolio for new bonds that will achieve the target portfolio duration. Such swaps are commonly referred to as rate anticipation swaps. Although a manager may not pursue an active strategy based strictly on future interest-rate movements, there can be a tendency to make an interest-rate bet to cover inferior performance relative to a benchmark index. There are other active strategies that rely on forecasts of future interest-rate levels. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Yield Curve Strategies (pp ) The yield curve for U.S. Treasury securities shows the relationship between their maturities and yields. The shape of this yield curve changes over time. Yield curve strategies involve positioning a portfolio to capitalize on expected changes in the shape of the Treasury yield curve. A shift in the yield curve refers to the relative change in the yield for each Treasury maturity. A parallel shift in the yield curve is a shift in which the change in the yield on all maturities is the same. (p. 529) A nonparallel shift in the yield curve indicates that the yield for maturities does not change by the same number of basis points. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Yield Curve Strategies (pp ) Historically, two types of nonparallel yield curve shifts (p. 529) have been observed: a twist in the slope of the yield curve and a change in the humpedness of the yield curve. A flattening of the yield curve indicates that the yield spread between the yield on a long-term and a short-term Treasury has decreased; a steepening of the yield curve indicates that the yield spread between a long-term and a short-term Treasury has increased. The other type of nonparallel shift, a change in the humpedness of the yield curve, is referred to as a butterfly shift. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Yield Curve Strategies Frank Jones analyzed the types of yield curve shifts that occurred between 1979 and 1990. He found that the three types of yield curve shifts are not independent, with the two most common types of yield curve shifts being a downward shift in the yield curve combined with a steepening of the yield curve an upward shift in the yield curve combined with a flattening of the yield curve. These two types of shifts in the yield curve are depicted in Exhibit 23-6 (see Overheads and 23-33). Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit 23-6 Combinations of Yield Curve Shifts
Upward Shift/Flattening/Positive Butterfly Yield Positive Butterfly Flattening Parallel Maturity Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit 23-6 Combinations of Yield Curve Shifts
Downward Shift/Steepening/Negative Butterfly Yield Parallel Steepening Negative Butterfly Maturity Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Yield Curve Strategies (p. 532) In portfolio strategies that seek to capitalize on expectations based on short-term movements in yields, the dominant source of return is the impact on the price of the securities in the portfolio. This means that the maturity of the securities in the portfolio will have an important impact on the portfolio’s return. The key point is that for short-term investment horizons, the spacing of the maturity of bonds in the portfolio will have a significant impact on the total return. In a bullet strategy, the portfolio is constructed so that the maturities of the securities in the portfolio are highly concentrated at one point on the yield curve. In a barbell strategy, the maturities of the securities in the portfolio are concentrated at two extreme maturities. In a ladder strategy the portfolio is constructed to have approximately equal amounts of each maturity. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Duration and Yield Curve Shifts Duration is a measure of the sensitivity of the price of a bond or the value of a bond portfolio to changes in market yields. A bond with a duration of 4 means that if market yields change by 100 basis points, the bond will change by approximately 4%. However, if a three-bond portfolio has a duration of 4, the statement that the portfolio’s value will change by 4% for a 100-basis-point change in yields actually should be stated as follows: The portfolio’s value will change by 4% if the yield on five-, 10-, and 20-year bonds all change by 100 basis points. That is, it is assumed that there is a parallel yield curve shift. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies The proper way to analyze any portfolio strategy is to look at its potential total return. If a manager wants to assess the outcome of a portfolio for any assumed shift in the Treasury yield curve, this should be done by calculating the potential total return if that shift actually occurs. This can be illustrated by looking at the performance of two hypothetical portfolios of Treasury securities assuming different shifts in the Treasury yield curve. The three hypothetical Treasury securities shown in Exhibit (see Overhead 23-37) are considered for inclusion in our two portfolios. For our illustration, the Treasury yield curve consists of these three Treasury securities: a short-term security (A, the five-year security), an intermediate-term security (C, the 10-year security), and a long- term security (B, the 20-year security). Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit 23-8 Three Hypothetical Treasury Securities
Bond Coupon (%) Maturity (years) Price Plus Accrued Yield to Maturity (%) Dollar Duration Convexity A 8.50 5 100 4.005 B 9.50 20 8.882 C 9.25 10 6.434 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies
Bullet portfolio: 100% bond C Barbell portfolio: 50.2% bond A and 49.8% bond B. Dollar duration of barbell portfolio = .502 (4.005) (8.882) = 6.434 Dollar convexity of barbell portfolio = .502 ( ) ( ) = Portfolio yield for barbell portfolio = .502 (8.50%) (9.50%) = 8.998% Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Cost of convexity (i.e., giving up yield to get better convexity)
Bond C, the bullet portfolio, has a yield-to-maturity of 9.25% and a Dollar Convexity of Bond (A+B)/2, the Barbell portfolio, has a yield-to-maturity of 8.998% and a Dollar Convexity of The difference in the two yields (9.25% %) is referred to the cost of convexity ( – ) of Bond (A+B)/2, the Barbell portfolio. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies Duration is just a first approximation of the change in price resulting from a change in interest rates. Convexity provides a second approximation. Dollar convexity has a meaning similar to convexity, in that it provides a second approximation to the dollar price change. For two portfolios with the same dollar duration, the greater the convexity, the better the performance of a bond or a portfolio when yields change. What is necessary to understand is that the larger the dollar convexity, the greater the dollar price change due to a portfolio’s convexity. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies Now suppose that a portfolio manager with a six-month investment horizon has a choice of investing in the bullet portfolio or the barbell portfolio. Which one should he choose? The manager knows that (1) the two portfolios have the same dollar duration, (2) the yield for the bullet portfolio is greater than that of the barbell portfolio, and (3) the dollar convexity of the barbell portfolio is greater than that of the bullet portfolio. Actually, this information is not adequate in making the decision. What is necessary is to assess the potential total return when the yield curve shifts. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies Exhibit 23-9 provides an analysis of the six-month total return of the two portfolios when the yield curve shifts. (See truncated version of Exhibit 23-9 in Overhead ) The numbers reported in the exhibit are the difference in the total return for the two portfolios. Specifically, the following is shown: difference in doll return = bullet portfolio’s total return – barbell portfolio’s total return Thus, a positive value means that the bullet portfolio outperformed the barbell portfolio, and a negative sign means that the barbell portfolio outperformed the bullet portfolio. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Relative Performance of Bullet Portfolio and Barbell Portfolio over a Six-Month Investment Horizon Yield Change Parallel Shift Nonparallel Shift (%) -5.000 -7.19 -10.69 -3.89 -4.750 -6.28 -9.61 -3.12 -4.500 -5.44 -8.62 -2.44 -4.250 -4.68 -7.71 -1.82 -4.000 -4.00 -6.88 -1.27 -3.750 -3.38 -6.13 -0.78 -3.500 -2.82 -0.35 … 3.750 -1.39 -1.98 -0.85 4.000 -1.57 -2.12 -1.06 4.250 -1.75 -2.27 4.500 -1.93 -2.43 -1.48 4.750 -2.58 -1.70 5.000 -2.31 -2.75 -1.92 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies Let’s focus on the second column of Exhibit 23-9, which is labeled “parallel shift.” This is the relative total return of the two portfolios over the six-month investment horizon assuming that the yield curve shifts in a parallel fashion. In this case parallel movement of the yield curve means that the yields for the short-term bond (A), the intermediate-term bond (C), and the long-term bond (B) change by the same number of basis points, shown in the “yield change” column of the table. Which portfolio is the better investment alternative if the yield curve shifts in a parallel fashion and the investment horizon is six months? The answer depends on the amount by which yields change. Notice that when yields change by less than 100 basis points, the bullet portfolio outperforms the barbell portfolio. The reverse is true if yields change by more than 100 basis points. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Analyzing Expected Yield Curve Strategies This illustration makes two key points. First, even if the yield curve shifts in a parallel fashion, two portfolios with the same dollar duration will not give the same performance. The reason is that the two portfolios do not have the same dollar convexity. The second point is that although with all other things equal it is better to have more convexity than less, the market charges for convexity in the form of a higher price or a lower yield. But the benefit of the greater convexity depends on how much yields change. As can be seen from the second column of Exhibit 23-9, if market yields change by less than 100 basis points (up or down), the bullet portfolio, which has less convexity, will provide a better total return. (The truncated version of Exhibit 23-9 was in Overhead ) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Approximating the Exposure of a Portfolio’s Yield Curve Risk A portfolio and a benchmark have key rate durations. The extent to which the profile of the key rate durations of a portfolio differs from that of its benchmark helps identify the difference in yield curve risk exposure. Complex Strategies A study by Fabozzi, Martinelli, and Priaulet finds evidence of the predictability in the time-varying shape of the U.S. term structure of interest rates using a more advanced econometric model. Variables such as default spread, equity volatility, and short-term and forward rates are used to predict changes in the slope of the yield curve and (to a lesser extent) changes in its curvature. Systematic trading strategies based on butterfly swaps reveal that the evidence of predictability in the shape of the yield curve is both statistically and economically significant. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Yield Spread Strategies Yield spread strategies involve positioning a portfolio to capitalize on expected changes in yield spreads between sectors of the bond market. Swapping (or exchanging) one bond for another when the manager believes that the prevailing yield spread between the two bonds in the market is out of line with their historical yield spread, and that the yield spread will realign by the end of the investment horizon, are called intermarket spread swaps. Credit or quality spreads change because of expected changes in economic prospects. Credit spreads between Treasury and non-Treasury issues widen in a declining or contracting economy and narrow during economic expansion. Spreads attributable to differences in callable and noncallable bonds and differences in coupons of callable bonds will change as a result of expected changes in (1) the direction of the change in interest rates, and (2) interest-rate volatility. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Importance of Dollar Duration Weighting of Yield Spread Strategies (p. 539) Par Value Price Modified Duration Bond X 100 80 5 Bond Y 90 4 Market Value Modified Duration of 1% 10 million 8 million 400,000 (400,000/4%) * (9/10) 400,000/4% Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Individual Security Selection Strategies There are several active strategies that money managers pursue to identify mispriced securities The most common strategy identifies an issue as undervalued because either its yield is higher than that of comparably rated issues, or its yield is expected to decline (and price therefore rise) because credit analysis indicates that its rating will improve. A swap in which a money manager exchanges one bond for another bond that is similar in terms of coupon, maturity, and credit quality, but offers a higher yield, is called a substitution swap. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Strategies for Asset Allocation within Bond Sectors The ability to outperform a benchmark index will depend on the how the manager allocates funds within a bond sector relative to the composition of the benchmark index. Exhibit (see Overhead 23-48) shows a one-year rating transition matrix (table) based on a Moody’s study for the period 1970–1993. Exhibit (see Overhead 23-49) shows the expected incremental return estimates for a portfolio consisting of only three-year Aa-rated bonds. Exhibit (see Overhead 23-50) shows expected incremental returns over Treasuries assuming the rating transition matrix given in Exhibit and assuming that the horizon spreads are the same as the initial spreads. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit 23-10 One-Year Rating Transition Probabilities (%)
Aaa Aa A Baa Ba Bb C or D Total 91.90 7.38 0.72 0.00 100.00 1.13 91.26 7.09 0.31 0.21 0.10 2.56 91.20 5.33 0.61 0.20 5.36 87.94 5.46 0.82 Source: From Leland E. Crabbe, “A Framework for Corporate Bond Strategy,” Journal of Fixed Income, June 1995, p. 16. Reprinted by permission of Institutional Investor. 23-51 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Expected Incremental Return Estimates for Three-Year Aa-Rated Bonds over a One-Year Horizon Initial Spread Horizon Rating Return over Treasuries (bp) X Transition Probability (%) = Contribution to Incremental Return (bp) 30 Aaa 25 38 1.13 0.43 Aa 91.26 27.38 A 35 21 7.09 1.49 Baa 60 –24 0.31 –0.07 Ba 130 –147 0.21 –0.31 Portfolio Incremental Return over Treasuries = 28.90 Source: From Leland E. Crabbe, “A Framework for Corporate Bond Strategy,” Journal of Fixed Income, June 1995, p. 17. Reprinted by permission of Institutional Investor. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Exhibit Expected Incremental Returns over Treasuries When Rating Transitions Match Historical Experience (One-Year Horizon, bp) Initial Spread Incremental Return Aaa 25 24.2 30 28.4 Aa 28.9 35 31.4 A 31.1 45 37.3 Baa 60 46.3 70 39.9 31.7 34.6 40 30.3 55 34.8 37.9 75 42.7 85 21.9 115 27.4 Source: From Leland E. Crabbe, “A Framework for Corporate Bond Strategy,” Journal of Fixed Income, June 1995, p. 18. Reprinted by permission of Institutional Investor. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

The Use of Leverage If permitted by investment guidelines a manager may use leverage in an attempt to enhance portfolio returns. A portfolio manager can create leverage by borrowing funds in order to acquire a position in the market that is greater than if only cash were invested. The funds available to invest without borrowing are referred to as the “equity.” A portfolio that does not contain any leverage is called an unlevered portfolio. A levered portfolio is a portfolio in which a manager has created leverage. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

The Use of Leverage (continued)
Motivation for Leverage The basic principle in using leverage is that a manager wants to earn a return on the borrowed funds that is greater than the cost of the borrowed funds. The return from borrowing funds is produced from a higher income and/or greater price appreciation relative to a scenario in which no funds are borrowed. The return from investing the funds comes from two sources. interest income change in the value of the security (or securities) at the end of the borrowing period There are some managers who use leverage in the hopes of benefiting primarily from price changes. Small price changes will be magnified by using leveraging. For example, if a manager expects interest rates to fall, the manager can borrow funds to increase price exposure to the market. Effectively, the manager is increasing the duration of the portfolio. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Motivation for Leverage The risk associated with borrowing funds is that the security (or securities) in which the borrowed funds are invested may earn less than the cost of the borrowed funds due to failure to generate interest income plus capital appreciation as expected when the funds were borrowed. Leveraging is a necessity for depository institutions (such as banks and savings and loan associations) because the spread over the cost of borrowed funds is typically small. The magnitude of the borrowing (i.e., the degree of leverage) is what produces an acceptable return for the institution. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Duration of a Leveraged Portfolio In general, the procedure for calculating the duration of a portfolio that uses leverage is as follows: Step 1: Calculate the duration of the levered portfolio. Step 2: Determine the dollar duration of the portfolio of the levered portfolio for a change in interest rates. Step 3: Compute the ratio of the dollar duration of the levered portfolio to the value of the initial unlevered portfolio (i.e., initial equity). Step 4: The duration of the unlevered portfolio is then found as follows: (ratio computed in Step 3) x [100/(rate change in Step 2 in bps)] x 100 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Duration of a Leveraged Portfolio Suppose that the initial value of the un-levered portfolio is $100 million and the leveraged portfolio is $400 million ($100 million equity plus $300 million borrowed): Step 1: Calculate & find the duration of the levered portfolio: 3. Step 2: If the duration of the levered portfolio is 3, then the dollar duration for a 50-basis-point change in interest rates is: 3 x 0.5% x 400 millions, or 6 millions. Step 3: The ratio of the dollar duration for a 50-basis-point change in interest rates to the $100 million initial market value of the un-levered portfolio is 0.06 ($6 million divided by $100 million). Step 4: The duration of the un-levered portfolio is then found as follows: (0.06) x [100/(50)] x 100, or 12. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

How to Create Leverage Via the Repo Market A manager can create leverage in one of two ways. One way is through the use of derivative instruments. The second way is to borrow funds via a collateralized loan arrangement. A repurchase agreement is the sale of a security with a commitment by the seller to buy the same security back from the purchaser at a specified price at a designated future date. The price at which the seller must subsequently repurchase the security for is called the repurchase price, and the date that the security must be repurchased is called the repurchase date. There is a good deal of Wall Street jargon describing repo transactions. To understand it, remember that one party is lending money and accepting a security as collateral for the loan; the other party is borrowing money and providing collateral.. Despite the fact that there may be high-quality collateral underlying a repo transaction, both parties to the transaction are exposed to credit risk. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Dollar interest on a repo transaction
Dollar interest = (dollar amount borrowed) x (repo rate) x repo term / 360 For example, at a repo rate of 6.5% and a repo term of one day (overnight), the dollar interest is $1,805 as shown below: $9,998,195 x x 1/360 = $1,805 The advantage to the dealer of using the repo market for borrowing on a short-term basis is that the rate is lower than the cost of bank financing. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

How to Create Leverage Via the Repo Market Repos should be carefully structured to reduce credit risk exposure. The amount lent should be less than the market value of the security used as collateral, thereby providing the lender with some cushion should the market value of the security decline. The amount by which the market value of the security used as collateral exceeds the value of the loan is called repo margin or simply margin. There is not one repo rate. The rate varies from transaction to transaction depending on a variety of factors: quality of collateral, term of the repo, delivery requirement, availability of collateral, and the prevailing federal funds rate. The more difficult it is to obtain the collateral, the lower the repo rate. To understand why this is so, remember that the borrower (or equivalently the seller of the collateral) has a security that lenders of cash want, for whatever reason. Such collateral is referred to as hot or special collateral. Collateral that does not have this characteristic is referred to as general collateral. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Chapter 23 Active Bond Portfolio Management Strategies

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Chapter 23 Active Bond Portfolio Management Strategies

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