MANG 6222 Fixed Income Securities Analysis Bond Portfolio Management Strategies Dr. Yun Luo Learning Objectives 1. The Asset Allocation Decision 2. Variety of Bond Portfolio Strategies 3. The Use of Leverage The Asset Allocation Decision v Public pension funds have allocations of about 2/3 in equities (which includes real estate and private equity) and about 1/3 in fixed income. v Regardless of the institutional investor, there are two important decisions to be made by an investor/client: v “How much should be allocated to bonds ” v “Who should manage the funds to be allocated to bonds ” How Much Should Be Allocated To Bonds The decision as to how much to invest in the major asset classes is referred to as the asset allocation decision. The asset allocation decision must be made in light of the investor’s investment objective. For institutions such as pension funds, the investment objective is to generate sufficient cash flow from investments to satisfy pension obligations. For institutions such as banks and thrifts, funds are obtained from the issuance of certificates of deposit, short-term money market instruments, or floating-rate notes. These funds are then invested in loans and marketable securities. The objective in this case is to earn a return on invested funds that exceeds the cost of acquiring those funds. Who Should Manage the Bond Portfolio Let’s assume that an investor has made the decision to allocate a specified amount to the fixed income sector. The next decision that must be made is whether that amount will be managed by internal managers or external managers or by a combination of internal and external managers. If external managers are hired, a decision must be made as to which asset management firm (e.g. asset management firm) to engage. Who Should Manage the Bond Portfolio In practice, the term asset allocation is used in two contexts. 1） The first involves allocation of funds among major asset classes that includes bonds, equities and alternative assets. Although we have mentioned bonds and equities as the major asset classes, there is now accepted a group of assets referred to as alternative assets. For example, for the California Public Employees Retirement System (CalPERS), the actual (as of January 31, 2011) and target allocation (as of June 2009) asset allocation amongst the asset classes defined by CalPERS is shown in Exhibit 22- 1. Exhibit 22-1 Asset Allocation of CalPERS: Actual as of January 31, 2011, and Target Allocation as of June 2009 Asset Class Market Value ($ billion) Actual Allocation Target Allocation (%) Cash Equivalents 4.50 2.0% 2.0% Global Fixed Income 47.50 20.8% 20.0% AIM 32.20 14.1% 14.0% Equity 120.30 52.8% 49.0% Total Global Equities 152.50 66.9% 63.0% Real Estate Global 16.60 7.3% 10.0% Inflation Linked Global 6.80 3.0% 5.0% Total Fund* 227.90 100.0% 100.0% Source: http://www.calpers.ca.gov/index.jsp bc=/investments/assets/assetallocation.xml Who Should Manage the Bond Portfolio 2) The second way is how the funds should be allocated amongst the different sectors within that asset class after a decision has been made to invest in a specified asset class. In the case of equities, equities are classified by market capitalization and by other attributes such as growth stocks value. E.g. companies may be categorized as large-, mid-, or small-cap depending on their market capitalization. Who Should Manage the Bond Portfolio The asset allocation among the different sectors of the bond is made at two levels. 1. The first is where a client must make a decision as to allocate among each sector and 2. then if an external money manager is to be hired, deciding on the asset management and amount to be allocated to each. Portfolio Management Team q We refer to the person making the investment decisions as the “manager” or “portfolio manager.” q In practice, while there is someone who will make the ultimate decision about the composition and therefore risk exposure of a portfolio, that decision is the result of recommendations and research provided by the portfolio management team. q At the top of the investment organization chart of the investment group is the chief investment officer (CIO) who is responsible for all of the portfolios. q A chief compliance officer (CCO) monitors portfolios to make sure that the holdings comply with the fund’s investment guidelines and that there are no activities conducted by the managers of the fund that are in violation of laws or investment policies. Portfolio Management Team q An asset management firm employs analysts and traders. § The analysts are responsible for the different sectors and industries. § The traders are responsible for executing trades approved by a portfolio manager. § The analysts and traders can support all of the portfolios managed by the firm or just designated portfolios. q A large firm may also employ an economist or an economic staff that would support all portfolios managed by the firm. q At the individual portfolio level there is either a lead or senior portfolio manager or co-managers. q It is the lead manager or co-managers who will make the decision regarding the portfolio’s interest rate exposure and the allocation of the fund’s assets among the countries, sectors and industries. Variety of Bond Portfolio Strategies q The bond portfolio strategy selected by an investor or client depends on the investment objectives and policy guidelines. q In general, bond portfolio strategies can be categorized into the following three groups: 1) bond benchmark-based strategies, 2) absolute return strategies, and 3) liability-driven strategies. Bond Benchmark-Based Strategies § There is a wide range of bond portfolio management strategies for an investor or client who has selected a bond index as a benchmark. § Traditional bond benchmark-based strategies can be classified as: 1) pure bond index matching; 2) enhanced indexing: matching primary risk factors; 3) enhanced indexing: minor risk-factor mismatches; 4) active management: larger risk-factor mismatches; and 5) active management: full-blown active. Bond Benchmark-Based Strategies These strategies are categorized based on how much the portfolio manager departs from the primary risk factors. Basically, one can view a benchmark (bond index) as a package of risk factors. The classification of a strategy into one of the categories above depends on the degree to which a portfolio manager is allowed to depart from the quantity of risk in the benchmark. It is not only important to understand what the risk factors are, but also how to quantify them. The Primary Risk Factors The primary risk factors can be divided into two general types: 1) systematic risk factors and 2) non-systematic risk factors. Systematic risk factors are forces that affect all securities in a certain category in the benchmark. Non-systematic risk factors are the risks that are not attributable to the systematic risk factors. – Non-systematic factor risks are classified as non- systematic risks associated with a particular issuer, issuer-specific risk, and those associated with a particular issue, issue-specific risk. The Primary Risk Factors (cont.) Systematic risk factors, in turn, are divided into two categories: term structure risk factors and non-term structure risk factors. 1) Term structure risk factors are risks associated with changes in the shape of the term structure. 2) Non-term structure risk factors include sector risk, credit risk and optionality risk. § Sector risk is the risk associated with exposure to the sectors of the benchmark. § Credit risk, also referred to as quality risk, is the risk associated with exposure to the credit rating of the securities in the benchmark. § Optionality risk is the risk associated with an adverse impact on the embedded options of the securities in the benchmark. Absolute Return Strategies § In an absolute return strategy, the portfolio manager seeks to earn a positive return over some time frame irrespective of market conditions. § Few restrictions are placed on the exposure to the primary risk factors. § Absolute return strategies are typically pursued by hedge fund managers using leverage. § Other absolute return managers set as their target as earning a return from 150 to 400 basis points per annum over the return on cash and hence such strategies are referred to as cash-based absolute return strategies. § A bond portfolio strategy that calls for structuring a portfolio to satisfy future liabilities is called a liability- driven strategy. § When the portfolio is constructed so as to generate sufficient funds to satisfy a single future liability regardless of the course of future interest rates, a strategy known as immunization is often used. § When the portfolio is designed to 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. Liability-Driven Strategies Top-Down Versus Bottom-Up Portfolio Construction and Management q There are two general approaches to construction and management of a bond portfolio: top-down and bottom- up. q In the top-down approach, a bond portfolio manager looks at the major macro drivers of bond returns (hence this approach is also referred to as a macro approach) and obtains a view (forecast) about these drivers in the form of a macroeconomic forecast. q Among the major variables considered in obtaining a macroeconomic forecast are monetary policy, fiscal policy, tax policy, political developments, regulatory matters, exchange-rate movements, trade policy, demographic trends, and credit market conditions. q Given the amount of the portfolio’s funds to be allocated to each sector of the bond market, the manager must then decide how much to allocate to each industry within a sector. § In the case of bond portfolio manager who is entitled to invest in both U.S. and non-U.S. bonds, the first decision is the allocation among countries, then sectors within a country, and then industries. Top-Down Versus Bottom-Up Portfolio Construction and Management (Cont.) q The bottom-up approach to active bond portfolio management focuses on the micro analysis of individual bond issues, sectors, and industries. § The primary research tools used in this form of investing is credit analysis, industry analysis, and relative value analysis. § To control the portfolios risk, risk modeling is used. Top-Down Versus Bottom-Up Portfolio Construction and Management (Cont.) q Types of Shifts in the 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. § A nonparallel shift in the yield curve indicates that the yield for maturities does not change by the same number of basis points. § Historically, two types of nonparallel yield curve shifts have been observed: a twist in the slope of the yield curve and a change in the humpedness of the yield curve. Active/Passive Portfolio Strategies – Yield curve strategies q Impact on Historical Returns § In practice, the slope of the yield curve is measured by the spread between some long-term Treasury yield and some short-term Treasury yield. § 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. Yield curve strategies q Frank Jones analyzed the types of yield curve shifts that occurred between 1979 and 1990. q He found that the three types of yield curve shifts are not independent, with the two most common types of yield curve shifts being q a downward shift in the yield curve combined with a steepening of the yield curve. q an upward shift in the yield curve combined with a flattening of the yield curve. q These two types of shifts in the yield curve are depicted in Exhibit 22-3. Yield curve strategies empirical evidence (Jones 1991) In portfolio strategies that seek to capitalize on expectations based on short-term movements in yields. This means that the maturity of the securities in the portfolio will have an important impact on the portfolio’s return. For example: the total return over a one-year investment horizon for a portfolio consisting of securities all maturing in 30 years will be sensitive to how the yield curve shifts because one year from now the value of the portfolio will depend on the yield offered on 29-year securities. Yield curve strategies q 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. There are three yield curve strategies q 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. q In a barbell strategy, the maturities of the securities in the portfolio are concentrated at two extreme maturities. q In a ladder strategy the portfolio is constructed to have approximately equal amounts of each maturity. Yield curve strategies Yield curve strategies Example Question Two portfolios with a market value of $1000 million. The bonds in both portfolios are trading at par value. The dollar duration of the two portfolios is the same. Issue Years to Maturity Par Value (in millions) Bonds Included in Portfolio I A 4.0 $240 B 5.0 $260 C 40.0 $300 D 41.0 $200 Bonds Included in Portfolio II E 19.4 $400 F 20.0 $460 G 20.2 $ 140 Which portfolio can be characterized as a bullet portfolio Which portfolio can be characterized as a barbell portfolio Answer Question Which portfolio can be characterized as a bullet portfolio 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. Thus, Portfolio II can be characterized as a bullet portfolio because the maturities of its securities are concentrated around one maturity (twenty years). Which portfolio can be characterized as a barbell portfolio In a barbell strategy, the maturities of the securities included in the portfolio are concentrated at two extreme maturities. Thus, Portfolio I can be characterized as a barbell portfolio because the maturities of its securities are concentrated at two extreme maturities (four years and forty years). 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. 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. Exhibit 22-5 Three Hypothetical Treasury Securities Bond Coupon (%) Maturity (years) Price Plus Accrued Yield to Maturity (%) Dollar Duration Dollar Convexity A 8.50 5 100 8.50 4.005 19.8164 B 9.50 20 100 9.50 8.882 124.1702 C 9.25 10 100 9.25 6.434 55.4506 The three hypothetical Treasury securities shown in Exhibit 22- 5 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). Analyzing Expected Yield Curve Strategies Consider the following two yield curve strategies: a bullet strategy and a barbell strategy. We will label the portfolios created based on these two strategies as the “bullet portfolio” and the “barbell portfolio” and they comprise the following: Bullet portfolio: 100% bond C Barbell portfolio: 50.2% bond A and 49.8% bond B Analyzing Expected Yield Curve Strategies The dollar duration for the bullet portfolio per 100-basis- point change in yield is 6.434. For the barbell portfolio, the dollar duration is just the weighted average of the dollar duration of the two bonds: dollar duration of barbell portfolio = 0.502(4.005) +0.498(8.882) = 6.434 The dollar duration of the barbell portfolio is the same as that of the bullet portfolio. 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. Although we did not discuss dollar convexity, it 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. Analyzing Expected Yield Curve Strategies The dollar convexity of the bullet portfolio is 55.4506. The dollar convexity for the barbell portfolio is a weighted average of the dollar convexity of the two bonds. That is, dollar convexity of barbell portfolio = 0.502(19.8164) + 0.498(124.1702) = 71.7846 Therefore, the dollar convexity of the barbell portfolio is greater than that of the bullet portfolio. Analyzing Expected Yield Curve Strategies Similarly, the yield for the two portfolios is not the same. The yield for the bullet portfolio is simply the yield to maturity of bond C, 9.25%. The traditional yield calculation for the barbell portfolio, which is found by taking a weighted average of the yield to maturity of the two bonds included in the portfolio, is 8.998%: Portfolio yield for barbell portfolio = 0.502(8.50%) + 0.498(9.50%) = 8.998% This approach suggests that the yield of the bullet portfolio is 25.2 basis points greater than that of the barbell portfolio (9.25% – 8.998%). Analyzing Expected Yield Curve Strategies Although both portfolios have the same dollar duration, the yield of the bullet portfolio is greater than the yield of the barbell portfolio. However, the dollar convexity of the barbell portfolio is greater than that of the bullet portfolio. The difference in the two yields is sometimes referred to as the cost of convexity (i.e., giving up yield to get better convexity). 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. Exhibit 22-6 Six-Month Investment Horizon bullet portfolio’s total return – barbell portfolio’s total return Yield Change Parallel Shift (a) Nonparallel Shift (b) Nonparallel Shift (c) 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 5.44 0.35 … … … … 3.750 1.39 1.98 0.85 4.000 1.57 2.12 1.06 4.250 1.75 2.27 1.27 4.500 1.93 2.43 1.48 4.750 2.12 2.58 1.70 5.000 2.31 2.75 1.92 (b) Change in yield for bond C. Nonparallel shift as follows (flattening of yield curve): yield change bond A = yield change bond C + 25 basis points yield change bond B = yield change bond C – 25 basis points (c) Change in yield for bond C. Nonparallel shift as follows (steepening of yield curve): yield change bond A = yield change bond C – 25 basis points yield change bond B = yield change bond C + 25 basis points Analyzing Expected Yield Curve Strategies Let’s focus on the second column which is labeled “parallel shift.” 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. 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. Analyzing Expected Yield Curve Strategies Now let’s look at what happens if the yield curve does not shift in a parallel fashion. Specifically, the first nonparallel shift column assumes that if the yield on bond C (the intermediate-term bond) changes by the amount shown in the first column, bond A (the short-term bond) will change by the same amount + 25 basis points, bond B (the long-term bond) will change by the same amount shown in the first column – 25 basis points. The spread between the long-term yield (yield on bond B) and the short-term yield (yield on Bond A), the spread has decreased by 50 basis points =》 flattening of the yield curve The barbell outperforms the bullet (always negative) Analyzing Expected Yield Curve Strategies In the last column, the nonparallel shift assumes that for a change in bond C’s yield, The yield on bond A will change by the same amount – 25 basis points, The bond B will change by the same amount + 25 points Thus, the spread between the long-term yield and the short-term yield has increased by 50 basis points, and the yield curve has steepened In this case, the bullet portfolio outperforms the barbell portfolio as long as the yield on bond C does not rise by more than 250 basis points or fall by more than 325 basis points. Analyzing Expected Yield Curve Strategies The key point here is that looking at measures such as yield (yield to maturity or some type of portfolio yield measure), duration, or convexity tells us little about performance over some investment horizon, because performance depends on the magnitude of the change in yields and how the yield curve shifts. Therefore, when a manager wants to position a portfolio based on expectations as to how he might expect the yield curve to shift, it is important to perform total return analysis. The Use of Leverage q If permitted by investment guidelines a manager may use leverage in an attempt to enhance portfolio returns. q 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. q For example, a manager may have cash to invest in the bond market of $50 million but wants an exposure of $200 million. The Use of Leverage q The funds available to invest without borrowing are referred to as the “equity.” q A portfolio that does not contain any leverage is called an unlevered portfolio. q A levered portfolio is a portfolio in which a manager has created 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. If a manager can invest $50 million earning 5% for a year but can borrow funds at a cost of 4.5% for a year, then the manager can generate for the year 50 basis points in income over its funding cost. By borrowing greater amounts, the manager can magnify the 50 basis points. This is a benefit of leveraging. Motivation for Leverage The return from investing the funds comes from two sources. i. interest income ii. 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. Motivation for Leverage § The risk associated with borrowing funds： § Cost of the borrowed funds > Borrowed funds are invested may earn § Due to failure to generate interest income plus capital appreciation as expected when the funds were borrowed. Motivation for Leverage Motivation for Leverage Leveraging is a necessity for depository institutions Depository institutions refers to 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. 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: Duration of a Leveraged Portfolio Suppose that a portfolio Market value: $100 million Duration:3 This means that the manager would expect that for a 100- basis-point change in interest rates The portfolio’s value would change by approximately $3 million. For this unlevered fund, the duration of the portfolio is 3. Duration of a Leveraged Portfolio Suppose now that the manager of this portfolio: Borrow an additional $300 million. This means that the levered fund will have $400 million to invest consisting of $100 million that the manager has available before borrowing (i.e., the equity) and $300 million borrowed. All of the funds are invested in a bond with a duration of 3. Now let’s look at what happens if interest rates change by 100 basis points. The levered portfolio’s value will change Duration of a Leveraged Portfolio All of the funds are invested in a bond with a duration of 3. If interest rates change by 100 basis points. The levered portfolio’s value will change by $12 million (3% times $400 million). This means that on an investment of $100 million, the portfolio’s value changes by $12 million. The proper way to measure the portfolio’s duration is relative to the unlevered amount or equity because the manager is concerned with the risk exposure relative to equity Duration of a Leveraged Portfolio Step 1: Calculate the duration of the levered portfolio. Assume that calculation of the duration of the levered portfolio finds that the duration is 3. Step 2: Determine the dollar duration of the portfolio of the levered portfolio for a change in interest rates. Let’s use a 50-basis-point change in interest rates to compute the dollar duration. If the duration of the levered portfolio is 3, then the dollar duration for a 50-basis-point change in interest rates is $6 million (1.5% (3*0 change for a 50-basis-point move times $400 million). Duration of a Leveraged Portfolio 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). The ratio of the dollar duration for a 50-basis-point change in interest rates to the $100 million initial market value of the unlevered portfolio is 0.06 ($6 million divided by $100 million). Step 4: The duration of the unlevered portfolio is then found as follows: Duration of a Leveraged Portfolio Step 4: The duration of the unlevered portfolio is then found as follows: If interest rates change by 100 basis points. This means that on an investment of $100 million, the portfolio’s value changes by $12 million. The proper way to measure the portfolio’s duration is relative to the unlevered amount or equity because the manager is concerned with the risk exposure relative to equity Previous Lecture Tutorial Question The YTM on 1-year zeros is currently 7%; the YTM on 2-year zeros is 8%. The treasury plans to issue a 2-year maturity coupon bond, paying coupon once per year with a coupon rate of 9%. The face value of the bond is $100. a. At what price will the bond sell b. What will the YTM on the bond be c. If the expectation theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year d. Recalculate your answer to c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1%. Previous Lecture Tutorial Question
