CH-21-22 Credit Risk Modeling – Bond Markets, Analysis and Strategies : Book Guide

This Document Contains Chapters 21 to 22 CHAPTER 21 CREDIT RISK MODELING CHAPTER SUMMARY Credit risk models are used in finance to measure, monitor, and control a portfolio’s credit risk. In fixed-income analysis they are also used in the pricing of credit risky debt instruments. Credit risk models are classified as either structural models or reduced-form models. This chapter provides the main elements of structural and reduced-form models. It also discusses structural/reduced-form hybrid models and, in particular, the incomplete information model. DIFFICULTIES IN CREDIT RISK MODELING Quantifying interest risk exposure is less complicated than modeling credit risk exposure. There are three reasons why this is so. First, credit default risk is a rare event and, as a result, the historical data needed to compute the inputs into a credit risk model (e.g., default rates and recovery rates) are considerably less in comparison to the data available for the modeling of interest rate risk. Second, it is much more difficult to draw any meaningful and possibly predictive conclusions about the probability of default because of the diversity of the corporations involved and the lack of complete information regarding corporate practices. Third, there are various causes of default by a corporate borrower that make default hard to predict. Moreover, while our focus in this chapter will be on credit risk modeling for U. S. corporations, applying these models to non-U.S. entities is complicated by the fact that default is not a universal concept. Every country has its own bankruptcy code to deal with defaults. Furthermore, there is no assurance that the administrators of the bankruptcy law will apply the law in a manner that is consistent with the bankruptcy code. Even though it may be unlikely that credit risk modeling will yield significant information, credit risk models have long been employed in the finance and insurance industries. The focus of the early models was on generating forecasts of default rates, credit ratings, and credit spreads. Since the mid-1990s, more sophisticated approaches to credit risk modeling have been proposed and made commercially available to portfolio managers. For one of these approaches that is commercially available, the theoretical foundation of the model dates back to the early 1970s. OVERVIEW OF CREDIT RISK MODELING Credit risk modeling is used to estimate the default probability, price individual corporate bonds, and measure a portfolio’s credit risk. The default probability is the likelihood that a borrower will default sometime over the life of the debt obligation. By default it is meant that the borrow fails to honor the terms of the agreement, such as the failure to make a principal or coupon payment required under the agreement, or the violation of a covenant. To estimate the default probability for one year, a credit risk model requires the following: (1) a definition of what constitutes a default event, (2) a model of investor uncertainty, and (3) how that information will evolve over time. Given a credit risk model and observed market prices for corporate bonds and/or credit derivatives, a fair value for the credit spread for an illiquid or unpriced corporate bond with a given credit rating or other credit-based characteristic can be estimated. This credit spread is referred to as the fair market credit spread. To estimate the fair market credit spread, a credit risk model requires (1) a model that estimates recovery if a default occurs, (2) a model that shows the credit spread that investors want in order to accept systematic credit risk and idiosyncratic risk, and (3) a model of the risk-free rate. CREDIT RATINGS VERSUS CREDIT RISK MODELS A long-term credit rating is a prediction of the likelihood that an issuer or issue will default and the severity of the loss. There are three reasons why one cannot simply rely on credit ratings as a forecaster of default. First, unlike default probabilities, credit ratings are discrete with a limited number of rating grades. Second, while ratings are updated very infrequently, default probabilities can be estimated on a real-time basis. Third, there is no clear maturity for a credit rating. STRUCTURAL MODELS The Black-Scholes-Merton (BSM) option pricing model and its extensions are referred to as structural models. The fundamental feature that is common to all structural models is that default can be viewed as some type of option by the equity owners on the assets of the firm, and that the option is triggered (i.e., the corporation defaults) when the value of the corporation’s assets declines below a certain default point. The outputs of structural models show how the credit risk of a corporate bond is a function of the issuer’s leverage and the volatility of the issuer’s assets. Structural models have been used by banks in making credit decisions and by bond portfolio managers. Structural models may perform well in one area of application in bond portfolio management but turn out to be useless for other applications. When considering the potential use of structural models, it is important to be aware of the underlying assumptions of the model because it is these assumptions that may limit the usefulness of a model to one or more of the six areas mentioned previously. Fundamentals of the Black-Scholes-Merton Model BSM model assumes the firm’s outstanding bond is a zero-coupon bond that matures in T years, the risk-free interest rate is constant over the bond’s life, the bond’s payment follows the principle of absolute priority if there is a default, and volatility is assumed to be constant. Extensions of the BSM model attempt to relax the more unrealistic assumptions. The BSM model includes the following variables. E(t) is the value of the corporation’s equity at time t. A(t) is the value of the corporation’s asset at time t. K is the maturity value of the zero-coupon bond issued by the corporation. At the maturity date of the zero-coupon bond, T, the value of the corporation’s equity is E(t) and the value of the corporation’s assets is A(t). Now let’s look at what can happen at the maturity date of the zero-coupon bond. There are only three possible scenarios at the maturity date of the zero-coupon bond (T): Scenario 1: A(T) > K; Scenario 2: A(T) 0; Scenario 2: E(T) = A(T) – K < 0; Scenario 1: A(T) = K. For Scenario 1, the bondholders are paid in full and stockholders get the rest. For Scenario 2, bondholders would receive less than the maturity value of the bond and take over the company. For Scenario 3, the stockholders would pay off the bondholders in full but own a corporation with zero value. If we let B(T) denote the value of the corporation’s zero-coupon bond, then its value at the maturity date can be expressed as: B(T) = A(T) – max [A(T) – K, 0]. The notation max [A(T) – K, 0] means the maximum of A(T) – K and zero. For Scenario 1, A(T) – K is positive so the maximum value is A(T) – K and the value of the bond is K is: B(T) = A(T) – [A(T) – K] = K. For Scenario 2, A(T) – K is negative and the maximum value is zero and the value of the bond is: B(T) = A(T) – 0 = A(T). For Scenario 3, the value of the bond is simply K. The term max [A(T) – K, 0] is the payoff of a call option with a strike price of K that expires at T. Since the term enters into the equation with a negative sign, this means a short position in a call option (i.e., the sale of a call option). Thus, the bondholder has a long position in the corporation’s assets and has sold a call option to the common stockholders on the corporation’s assets. The value of a corporate bond is the value of the total assets reduced by the value of the call option. The call option can be valued by using an option pricing model such as the Black-Scholes model. If we rewrite B(T) = A(T) – max [A(T) – K, 0], we have another interpretation that is useful. The equation can be rewritten as B(T) = K – max [K – A(T), 0]. The results for each of the three scenarios for this equation are the same as B(T ) = A(T ) – max [A(T ) – K, 0]. The term [K – A(T)] is the payoff of a put option at time T written on the corporation’s assets with a strike price K. Since this term enters into B(T) = K – max [K – A(T), 0] with a negative sign, it is the payoff of a short put position. One can interpret the position given by B(T) = K – max [K – A(T), 0] as a position in a risk-free bond reduced by the value of the put position that the stockholders sold to the bondholders on the corporation’s assets. To value the option using this approach to corporate bond valuation using an option pricing model, the following inputs are required: the corporation’s capital structure; the corporation’s market value; and, the volatility of the market value of the corporation. Extensions of the Black-Scholes-Merton Model Researchers have developed extensions of the BSM model by relaxing the assumptions. First, consider Assumption 1 (the corporation has only one type of bond outstanding). If the company has a series of zero-coupon bonds outstanding with different maturities, then it is quite easy for the BSM model to characterize default at different times. Another series of models have been proposed to extend the BSM model to the case where default can occur not only at maturity but at any time prior to maturity. The underlying legal principle here is that there are typically covenants in a typical bond indenture granting the bondholders the right to restructure the corporation should the value of the corporate assets fall below a given amount, referred to as a default barrier. These models are referred to as first-passage time models with the first such model being proposed by Black and Cox. With respect to Assumption 3, a constant risk-free rate, Shimko, Tejima, and van Deventer extend the BSM model to allow for stochastic interest rates. Moody’s KMV Model A number of software/consulting companies have developed credit risk models based on structural models. The two most popular models use BSM to model defaults using large databases of historical data. In the Moody’s KMV methodology, information contained in equity prices and the balance sheet of corporate bond issuers is used to extract the probability of default, which it refers to as the expected default frequency (EDF) and is the probability of defaulting within a specified time period. So, a corporation with an EDF for a one-year time period of 3% has a 3% probability of defaulting within the next 12 months. Moreover, each EDF can be associated with a credit spread curve and a credit rating. The credit rating assigned by the model based on market prices is called a market implied rating. Instead of being aggregated into rating classes, corporations are categorized in the Moody’s KMV methodology using a “distance-to-default index” measure. Advantages and Disadvantages of Structural Models From a theoretical perspective, structural models analyze default based on a reasonable assumption that it is a result of the value of the corporate issuer’s assets falling below the value of its debt. In addition to providing default probabilities, these models allow a bond portfolio manager to see how the credit risk of corporate debt is a function of the leverage and the asset volatility of the issuer. Accordingly, the impact of a new stock or bond offering that will change the capital structure of a corporation can be assessed. While superior to what was previously available, there are two concerns that have been expressed about structural models: difficult to calibrate and computationally burdensome. To calibrate a structural model to price a corporate bond requires calibration to asset volatility, asset value, face value of the corporate issuer’s debt, the default barrier (in the case of first-passage time models), and the risk-free rate. For first-passage time models, a suitable default barrier must be estimated. Because of this difficulty, it is argued that structural models are not suitable for the frequent marking to market of credit contingent securities. From a computational perspective, the pricing of a corporate zero-coupon bond is just like pricing an option on a bond. However, for coupon-bearing corporate bonds the problem becomes one of pricing a compound option, a more difficult problem. To price a subordinated bond, it is necessary to simultaneously value all of the more senior debt (bonds and loans). ESTIMATING PORTFOLIO CREDIT RISK: DEFAULT CORRELATION AND COPULAS For a portfolio of corporate bonds, there is the risk that some event that triggers the default of one of the corporate bonds in the portfolio will adversely impact another corporate bond in the portfolio, thereby increasing the probability of the default of that second corporation. A commonly used statistical concept to gauge the dependence between two variables is correlation. In credit risk management, this type of risk is referred to as default correlation. Developers of credit risk models need an estimate of the default correlations in order to assess the credit risk of a portfolio and credit derivatives. The technique used to estimate the default correlation varies. For example, Moody’s uses Monte Carlo simulation of historical data on rating transitions and defaults in its analysis. Another rating agency, Fitch Ratings, uses correlations based on equity price changes. However, there are reasons that a correlation measure is not a suitable one in the case of credit risk modeling. For example, there is asymmetrical dependence. Thus, many developers of credit risk models use different measures of dependence to understand the multivariate relationship between all of the bonds in a portfolio. The combination of individual default probabilities (or default distributions) and their dependence are known mathematically as a “copula.” What is important to understand is that by using copulas rather than simple correlations to gauge the nature of the dependency between two variables, a modeler can better handle the modeling of extreme events. REDUCED-FORM MODELS Reduced-form models were introduced in the mid 1990s. The major difference between reduced-form models and structural models is how default is treated. As with all economic models, structural and reduced-form models are merely an abstract simplified mathematical representation of relationships between economic variables. In structural models, default is endogenous; in reduced-form models it is exogenous. As it turns out, specifying defaults exogenously, as is done in reduced-form models, greatly simplifies credit risk modeling because it ignores the constraint of defining what causes default and simply looks at the default event itself. The key elements in reduced-form models are: (1) the default-time, (2) recovery rate process, and (3) risk-free interest rate. The modeling of when a default occurs and the recovery process, if the issuer defaults, is how the reduced-form models that have been proposed differ. Accurately modeling the bankruptcy recovery process is not simple. Recognition must be given to the trade-off between analytic tractability and practical applicability. Based on restrictive assumptions about the dynamics of the default and recovery processes, a closed-form solution to reduced-form models has been derived by their proposers. The theoretical framework for reduced-form models is the Poisson process, which is a simple stochastic process. Poisson Process A Poisson process is one of the most important classes of stochastic processes. To understand the Poisson process, we begin with a sequence, which counts the number of some defined event occurring from an initial point in time. We denote the value of this counter at time t as Nt. That is Nt = number of occurrences in the interval 0 to t. Nt will increase by 1 for every occurrence of an event, and these increases are referred to as “increments.” The probability of an event occurring from one integer to the next over a small time interval dt is given by Probability [Nt+dt + Nt–1 = 1] = λdt where the parameter λ is called the intensity parameter of the Poisson process. In reduced-form models, the event in a Poisson process is defined as a default. The intensity parameter in reduced-form models is called the default intensity and is a key parameter in the model. In the context of a reduced-form model, the default intensity at time t can be thought of in terms of a probability. The Jarrow-Turnbull Model The Jarrow-Turnbull model is a simple model of default and recovery. It assumes that no matter when default occurs, the recovery payment is paid at the maturity date. By making the assumption that the recovery payment is made at maturity, Jarrow and Turnbull assume away any dependency between the bond price and the conditional default probability. The Duffie-Singleton Model The model proposed by Duffie and Singleton (1) allows the recovery payment to occur at any time and (2) restricts the amount of recovery to be a fixed fraction of the non-default bond price at the time of default. Advantages and Disadvantages of Reduced-Form Models Because the default probabilities and recovery rates are exogenously specified in the model, one can use a series of risky zero-coupon bonds to calibrate out a default probability curve and hence a credit spread curve. The ability to quickly calibrate to the market so that traders can assess relative prices and construct arbitrage trading strategies is the major reason why reduced-form models are strongly favored by practitioners involved in the credit derivatives market. A criticism of reduced-form models is precisely the advantage cited by its proponents: It does not explain the economic reasoning behind default because it treats default as an exogenous event. INCOMPLETE INFORMATION MODELS In both structural and reduced-form models, no consideration is given to the fact that the information that investors use may be imperfect. In structural models, for example, firm value is based on the market evaluating correctly the value of the corporation. Incomplete information models take into account imperfect information reported in financial statements. Giesecke and Goldberg propose a structural/reduced form hybrid model based on incomplete information. Their model, which is used by MSCI Barra, is a first-passage time model wherein it is assumed that investors do not know the default barrier. The approach allows a portfolio manager or credit analyst to include their view on the financial well-being of a company in calibrating the model to market data. KEY POINTS • Credit risk models are used to measure, monitor, and control a portfolio’s credit risk as well as to price credit risky debt instruments. • Credit risk models are classified as either structural models or reduced-form models. • Options theory provides the underlying theory for all structural models. • The basic idea underlying structural models is that a company defaults on its debt if the value of its assets falls below a certain default point and that the value of a corporate bond can be modeled as an option on these assets. With this insight, researchers were able to apply the same principles used for option pricing to the valuation of corporate bonds using the issuer’s stock price and balance sheet data. • The Black-Scholes-Merton structural model is based on some simplifying assumptions. There have been several modifications and extensions to this model. • Reduced-form models do not look into the microeconomic factors of a company. Rather, they model directly the default probability or transition risk. • The theoretical framework for reduced-form models is the Poisson process. • The two most notable reduced-form models are the Jarrow-Turnbull and Duffie-Singleton models. • Both structural models and reduced-form models assume that the information reported by the issuing corporations is accurate. However, corporate bankruptcies that have been attributable to fraud and opaque/inaccurate financial accounting data have made practitioners aware that when modeling credit risk, there must be consideration of the possibility that information is imperfect. This has led to the development of incomplete information models. • The Giesecke and Goldberg model combines the structural and reduced-form models but incorporates incomplete information. ANSWERS TO QUESTIONS FOR CHAPTER 21 (Questions are in bold print followed by answers.) 1. Why is credit risk modeling more difficult than interest rate modeling? There are three reasons that can be cited for why credit risk modeling is more difficult than interest rate modeling. First, credit default risk is a rare event and, as a result, the historical data needed to compute the inputs into a credit risk model (e.g., default rates and recovery rates) are considerably less in comparison to the data available for the modeling of interest rate risk where, for example, historical U. S. Treasury prices are available on a daily basis for many decades. Second, even with the default data that are available, it is much more difficult to draw any meaningful and possibly predictive conclusions about the probability of default because of the diversity of the corporations involved (in terms of industry sector, size, and leverage) and the lack of complete information regarding corporate practices. Three, there are various causes of default by a corporate borrower—ranging from microeconomic factors (such as poor management) to macroeconomic factors (such as high interest rates and recession)—that make default hard to predict. 2. A corporate bond portfolio manager was overhead asking: “Why do I need a credit risk model. I can get information about the probability of default from credit ratings?” How would you respond to this portfolio manager? There are reasons for why one would want to use a credit risk model instead of simply relying on the probability of default from credit ratings. First, ratings are discrete with a limited number of rating grades. In contrast, default probabilities are continuous and range from 0% to 100%. Second, while ratings are updated very infrequently, default probabilities can be estimated on a real-time basis. Van Deventer provides an example of the downgrade of Merck (from AAA to AA-) in 2004. The downgrade came three weeks after the withdrawal of a major drug that significantly impacted Merck’s stock price. Finally, there is no clear maturity for a credit rating. While there is a separate short- and long-term credit rating, credit risk models provide a default probability by maturity (i.e., a term structure of default probabilities). This provides insight into the default probabilities for different phases of the business cycle. 3. What is a common feature of all structural models? The common feature for all structural models (e.g., the BSM model and its extensions) is that default can be viewed as some type of option by the equity owners on the assets of the firm, and that the option is triggered (i.e., the corporation defaults) when the value of the corporation’s assets declines below a certain default point. The application of option pricing theory avoids the use of a risk premium and tries to use other marketable securities to price the option. The use of option pricing theory provides an improvement over traditional methods for valuing corporate bonds. The outputs of structural models show how the credit risk of a corporate bond is a function of the issuer’s leverage and the volatility of the issuer’s assets. The output of these models also provides information about how to hedge the default risk, which was not obtainable from traditional methods. 4. Give two interpretations of the value of a bond from an option’s perspective. First, the value of a bond can be viewed as a long position in the corporation’s assets and the sell of a call option to the common stockholders on the corporation’s assets. This implies that the value of a corporate bond is the value of the total assets reduced by the value of the call option. Second, the value of a bond can be viewed as a position in a risk-free bond reduced by the value of the put position that the stockholders sold to the bondholders on the firm’s assets. To value the option using this approach to corporate bond valuation, the following inputs are needed: the firm’s capital structure; the firm’s market value (typically derived from its stock price); and, the volatility of the firm’s market value (typically derived from the volatility of the stock’s price). 5. Explain how the Black-Scholes-Merton model has been extended to allow for multiple bond issues in a corporation’s debt structure. The question is asking us how the BSM model is extended if we relax Assumption 1 (which supposes that the corporation has only one type of bond outstanding). If there are multiple bond issues in a corporation’s debt structure (e.g., a series of zero-coupon bonds outstanding with different maturities given the zero bond assumption), then it is quite easy for the BSM model to be extended to characterize default at different times. Geske demonstrated how this is done by using a “compound option” model. A compound option is an option on another option. The main point of the Geske model is that defaults can be described as a series of contingent events and that later defaults are contingent upon whether there was no prior default. Based on this notion, layers of contingent defaults build up a series of sequential compound options, one linking to the other. 6. Explain how the Black-Scholes-Merton model has been extended to overcome the assumption that default can only occur at maturity. The question is asking us how the BSM model is extended if we relax Assumption 2 (which supposes that the bond outstanding is a zero-coupon bond that matures in T years.). Thus, we want to extend the BSM model to the case where default can occur not only at maturity but at any time prior to maturity. The underlying legal principle to extend the BSM model for this situation is that there are typically covenants in a typical bond indenture granting the bondholders the right to restructure the corporation should the value of the corporate assets fall below a given amount, referred to as a default barrier. Thus what in needed are models that utilize this notion of a default barrier. Such models that do so are referred to as first-passage time models with the first such model being proposed by Black and Cox. In all of these models, a threshold is defined (default barrier) and default occurs when a corporation’s asset value crosses that threshold. Default is viewed as a form of barrier option. A barrier option is a path dependent option. For such options, both the payoff of the option and the survival of the option to the stated expiration date depend on whether the price of the underlying asset reaches a specified level over the life of the option. 7. How can structural models be used by bond portfolio managers? In making credit decisions, structural models have been used bond portfolio managers (and other entities such as banks for that matter) in one or more of the following ways: to estimate a corporate bond’s default risk; to predict rating changes (with particular interest in downgrades); to forecast changes in corporate bond credit spreads; to identify relative value opportunities within the corporate bond market; to identify relative value opportunities for a firm with several issues; and, to evaluate the sensitivity of corporate bond credit spreads to equity prices. In assessing the merits of structural models, these potential uses must be kept in mind. Structural models may perform well in one area of application in bond portfolio management but turn out to be useless for other applications. When considering the potential use of structural models, it is important to be aware of the underlying assumptions of the model because it is these assumptions that may limit the usefulness of a model. 8. Answer each of the below questions. (a) Explain expected default frequency. The default probability is the likelihood that a borrower will default sometime over the life of the debt obligation. By default it is meant that the borrow fails to honor the terms of the agreement, such as the failure to make a principal or coupon payment required under the agreement, or the violation of a covenant. It is common in practice to look at the default over the next one year. The default probability is sometimes referred to as an expected default frequency. To estimate the default probability for one year, a credit risk model requires the following: (1) a definition of what constitutes a default event, (2) a model of investor uncertainty, and (3) how that information will evolve over time. In the Moody’s KMV methodology, information contained in equity prices and the balance sheet of corporate bond issuers is used to extract the probability of default, which it refers to as the expected default frequency (EDF) and is the probability of defaulting within a specified time period. So, a corporation with an EDF for a one-year time period of 3% has a 3% probability of defaulting within the next 12 months. The EDF is specific to a corporation, as any default of any security is legally applicable to all securities of the issuer. (b) Explain market implied rating. Each firm’s expected default frequency (as discussed in the previous question) can be associated with a credit spread curve and a credit rating. The credit rating assigned based on market prices is called a market implied rating. (c) Explain distance-to-default index measure. A distance-to-default index measure is used in Moody’s KMV methodology to compute a firm’s expected default frequency (EDF). A distance to default index is calculated as the number of standard deviations between the mean distribution of the asset value and debt value. More details are given below. Instead of being aggregated into rating classes, corporations are categorized in the Moody’s KMV methodology using a “distance-to-default index” measure. There are three steps involved in computing a firm’s EDF in the Moody’s KMV methodology. First, the market value and volatility of a firm’s assets need to be estimated. Second, using option pricing theory applied to the valuation of corporate bonds, the distance-to-default index measure is computed. Finally, the distance-to-default index measure is combined with a large dataset of actual default rates to compute the probability of default. This last step is the major advantage of the model and what also sets it most apart from the BSM approach. 9. How does the treatment of default in structural models and reduced-form models differ? In structural models, default is endogenously determined within the economic model as its value depends on other variables in the model. In contrast, in reduced-form models default is exogenously determined being independent of other variables in the model. As it turns out, specifying defaults exogenously, as is done in reduced-form models, greatly simplifies credit risk modeling because it ignores the constraint of defining what causes default and simply looks at the default event itself. Pricing of corporate bonds with different maturities can be seen as independent, unlike structural models where defaults of longer maturity corporate bonds of an issuer are contingent on defaults of shorter-maturity corporate bonds of that same issuer. As with all economic models, structural and reduced-form models are merely an abstract simplified mathematical representation of relationships between economic variables. 10. How do the Jarrow-Turnbull and Duffie-Singleton reduced-form models differ? The Jarrow-Turnbull reduced-form model assumes that the recovery payment can occur only at maturity (rather than when default actually occurs) and the recovery amount can fluctuate randomly over time. On the contrary, the model offered by Duffie and Singleton permits the recovery payment to occur at any time and restricts the amount of recovery to be a fixed fraction of the non-default bond price at the time of default. More details are given below. The assumption that the recovery payment can occur only at maturity rather than when default actually occurs (or soon after) in the Jarrow-Turnbull model so that a closed-form solution can be derived is not realistic. This is one of two major drawbacks of that model. The second drawback is that the recovery amount can fluctuate randomly over time. The recovery amount fluctuates because it depends on the corporation’s liquidation value at the time of default. As a result, it is possible to have scenarios for the Jarrow-Turnbull model wherein the recovery payment may exceed the price of the bond at the time of default because the recovery rate is an exogenously specified percentage of the risk-free bonds. In contrast, the model proposed by Duffie and Singleton (1) allows the recovery payment to occur at any time and (2) restricts the amount of recovery to be a fixed fraction of the non-default bond price at the time of default. Because of this second assumption, the Duffie-Singleton model is referred to as a fractional recovery model or fractional recovery of predefault market value model. The rationale for this assumption is as a corporate bond’s credit quality deteriorates, its price falls. At the time of default, the recovery price will be some fraction of the final price that prevailed prior to default, and, as a result, one does not encounter the shortcoming of the Jarrow-Turnbull model that price can be greater than the price prior to default. 11. How does the Jarrow-Turnbull-Lando model differ from the basic Jarrow-Turnbull model? The Jarrow-Turnbull model is a straightforward model of default and recovery. It assumes that no matter when default occurs, the recovery payment is paid at the maturity date. By making the supposition that the recovery payment is made at maturity, Jarrow and Turnbull assume away any dependency between the bond price and the conditional default probability. The basic Jarrow-Turnbull model has been extended by Jarrow, Lando, and Turnbull to include different credit ratings rather than of just two states (default and survival). That is, instead of a single state for default (and survival), there can be a number of probabilities, each for the probability of moving from one credit rating to another credit rating. This is done by supplying the probabilities for these rating movements where the probabilities can be obtained from the rating transition tables published periodically by the rating agencies. Thus, such an extended reduced-form model deals with migration risk of credit ratings rather than default risk. 12. Answer the below questions. (a) How is an event defined in the Poisson process? In the Poisson process, an event is defined as a default. (b) What is meant by the intensity parameter in the Poisson process? The intensity parameter (given by λ in the Poisson process) refers to the probability of default over a small time period. More specifically, default intensity at time t is the conditional probability of default per unit time given that the corporation has not previously defaulted. 13. Answer the below questions. (a) What is the meaning of the default intensity parameter in a reduced-form model? In reduced-form models, the event in a Poisson process is defined as a default where the parameter (λ) is called the intensity parameter of the Poisson process. Another name for the intensity parameter, λ, is the default intensity and it is a key parameter in the model. The default intensity at time t can be thought of in terms of a probability. More specifically, it is the conditional probability of default per unit time given that the corporation has not previously defaulted. Consequently, the Poisson process basically describes the near-term default risk of a corporation. (b) What are the various ways that the default intensity parameter can be modeled in a reduced-form model? The intensity parameter in reduced-form model can be modeled in one of three ways. The first is simply as a deterministic or constant value that is independent of time t. The second way is to specify the intensity parameter as a deterministic function of time t. Finally, the intensity function can be modeled as a random variable that depends on some exogenously specified state variables. 14. What is meant by default correlation? For a portfolio of corporate bonds, there is the risk that some event that triggers the default of one of the corporate bonds in the portfolio will adversely impact another corporate bond in the portfolio, thereby increasing the probability of the default of that second corporation. A commonly used statistical concept to gauge the dependence between two variables is correlation. In credit risk management, this type of risk is referred to as default correlation. One would expect that for corporate issuers in the same industry sector, default correlation is high. 15. What is the drawback of the default correlation measure and what alternative measure is used in measuring portfolio credit risk? The drawback of the default correlation measure found in structural models relates to asymmetrical dependence among firms in regards to defaulting. Alternative models developed to measure portfolio risk treat default as an exogenous variable so that one does not have to depend on default being determined by other variables. These alternative models are reduced-form models. More details on the drawback of the default correlation measure are given below (details on reduced-form models were discussed in previous questions). While correlation quantifies the dependence between two variables, it should be noted that correlation is often incorrectly used to mean any notion of dependence between two variables. However, correlation is only one of several measures in statistics used to quantify a dependence structure, and there are reasons this measure is not a suitable one in the case of credit risk modeling. One reason is that the independence of two random variables implies a correlation that is equal to zero. However, conversely, a correlation of zero does not imply independence. To see the relevance for credit risk management, suppose that there are numerous potential suppliers of a particular part to the automotive industry. Assume that ABC Company is one such supplying firm. From the perspective of the ABC Company, defaults of firms in the automotive industry are likely to have severe adverse economic consequence, potentially leading to its bankruptcy. Hence, from the perspective of an investor in ABC Company’s bond, there is high default risk between ABC Company and the automotive industry. However, from the holder of the corporate bonds of companies in the automotive industry, the default of ABC Company is highly unlikely to have any impact on these companies. Thus, from the perspective of the automotive industry, the impact on default risk is likely to be zero. Because of this asymmetrical dependence and other drawbacks of correlation as a measure of risk, many developers of credit risk models use different measures of dependence to understand the multivariate relationship between all of the bonds in a portfolio. The combination of individual default probabilities (or default distributions) and their dependence are known mathematically as a “copula.” What is important to understand is that by using copulas rather than simple correlations to gauge the nature of the dependency between two variables, a modeler can better handle the modeling of extreme events. 16. What is the motivation for the development of incomplete information credit risk models. The motivation for the development of incomplete information credit risk models is the belief that both structural and reduced-form models suffer from using incorrect information in their models. Not only that but the information used can even be manipulated by corporations. More details are provided below. In both structural and reduced-form models, no consideration is given to the fact that the information that investors use may be imperfect. In structural models, for example, firm value is based on the market evaluating correctly the value of the corporation. This could be due to off-balance sheet derivatives, lease financing, pension obligations, etc., all being based on generally accepted accounting principles but not reflecting a true economic state. Moreover, corporate scandals such as that of Enron, Tyco, WorldCom, and Parmalat are constant reminders that the financial information provided by corporations may be far from reflecting their true economic condition. For example, in first-passage time models, as explained earlier, a default barrier is required. Using the information by Enron, Tyco, and WorldCom would have resulted in misleading default barriers. Incomplete information models take into account imperfect information reported in financial statements. While incomplete information models were proffered by several researchers, Giesecke and Goldberg propose a structural/reduced form hybrid model based on incomplete information. Their model, which is used by MSCI Barra, is a first-passage time model wherein it is assumed that investors do not know the default barrier. The approach allows a portfolio manager or credit analyst to include their view on the financial well-being of a company in calibrating the model to market data. 17. Why is the calibration of a credit risk model to the market important in fixed income trading? While superior to what was previously available, there are two concerns that have been expressed about structural models: difficult to calibrate and computationally burdensome. Calibration is a necessary first step in fixed income trading because it allows traders to clearly see relative prices and hence be able to construct arbitrage trading strategies. To calibrate a structural model to price a corporate bond requires calibration to asset volatility, asset value, face value of the corporate issuer’s debt, the default barrier (in the case of first-passage time models), and the risk-free rate. While some of these values required for calibration can be estimated from market data (e.g., using Treasuries to estimate the risk-free rate), many are not observable or easy to obtain. The value of a corporation is estimated from stock prices for publicly traded corporations. Determining the face value of the corporation’s debt may seem simple; however, in complex capital structures involving multiple bond issues, bank debt, guarantees on debt issues by others, pension liabilities, leasing obligations, and any interest rate derivatives that the issuer may be exposed to, it is not simple. For first-passage time models, a suitable default barrier must be estimated. Because of this difficulty, it is argued that structural models are not suitable for the frequent marking to market of credit contingent securities. CHAPTER 22 BOND PORTFOLIO MANAGEMENT STRATEGIES CHAPTER SUMMARY In this chapter we look at bond portfolio strategies where the benchmark by which a manager is evaluated is a bond index. Before we discuss bond portfolio management strategies in this chapter, we begin with a discussion of the asset allocation decision in two contexts: allocation of funds among asset classes in the capital markets and allocating funds within the bond market. We also preface our coverage of bond portfolio management strategies with a description of a bond portfolio management team. THE ASSET ALLOCATION DECISION 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. Regardless of the institutional investor, there are two important decisions to be made by an investor/client: (1) “How much should be allocated to bonds?” and (2) “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 life insurance companies, the basic objective is to satisfy obligations stipulated in insurance policies and generate a profit. 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 to engage. In practice, the term asset allocation is used in two contexts. The first involves allocation of funds among major asset classes that includes bonds, equities and alternative assets. 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. The asset allocation among the different sectors of the bond is made at two levels. The first is where a client must make a decision as to allocate among each sector and 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 We refer to the person making the investment decisions as the “manager” or “portfolio manager.” The composition and therefore risk exposure of a portfolio is the result of recommendations and research provided by the portfolio management team. 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. 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 federal and state securities laws or investment policies. 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. A large firm may also employ an economist or an economic staff that would support all portfolios managed by the firm. At the individual portfolio level there is either a lead or senior portfolio manager or co-managers. 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. SPECTRUM OF BOND PORTFOLIO STRATEGIES The bond portfolio strategy selected by an investor or client depends on the investment objectives and policy guidelines. 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. These strategies range from low risk strategies at the top to high risk-tolerance strategies at the bottom of the above list. It is not only important to understand what the risk factors are, but also how to quantify them. With the first three strategies above, a portfolio manager is not permitted to deviate from the benchmark’s duration. The last two strategies are active bond portfolio management strategies. They differ to the extent with which they allow mismatches relative to the benchmark. It is important to note that even if a manager pursues an active strategy, the manager may still elect to have a duration equal to that of the benchmark (i.e., pursue a duration-matching strategy). Portfolio managers often pursue what is referred to as a core/satellite strategy. Basically, this strategy involves building a blended portfolio using an indexed and active strategy. The core component is a low-risk portfolio constructed using one of the indexing strategies. The satellite component is constructed using an active strategy with a benchmark that is specialized rather than a broad liquid bond market index. 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. Liability-Driven 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. BOND INDEXES Typically, bond portfolio managers are given a mandate that involves their performance evaluation relative to a bond index. The wide range of bond market indexes available can be classified as broad-based market indexes and specialized market indexes. Why have broker/dealer firms developed and aggressively marketed their bond indexes? Enhancing the firm’s image is only a minor reason. The key motivation lies in the potential profit that the firm will make by executing trades to set up an indexed portfolio and rebalance it. The broad-based U.S. bond market indexes most commonly used by institutional investors are the Barclays Capital U.S. Aggregate Bond Index. The index is a market-value weighted index. The pricing of the securities in each index are either trader priced or model priced. Each index is broken into sectors. Understanding the eligibility requirements for inclusion in a bond index is important. Active bond portfolio strategies often attempt to outperform an index by buying non-eligible or non-index securities. THE PRIMARY RISK FACTORS Primary risk factors in bond indexes are those risk factors that a portfolio manager can match or mismatch when constructing a portfolio. A portfolio manager will only intentionally mismatch if the belief is that the manager has information that strongly suggests there is a benefit that is expected to result from mismatching. The primary risk factors can be divided into two general types: systematic risk factors and 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. 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. 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. 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. TOP-DOWN VERSUS BOTTOM-UP PORTFOLIO CONSTRUCTION AND MANAGEMENT There are two general approaches to construction and management of a bond portfolio: top-down and bottom-up. Typically, a portfolio blends the elements of both approaches in junction with certain considerations and constraints in constructing a portfolio. 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. 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. 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. 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 portfolio’s risk, risk modeling is used. ACTIVE PORTFOLIO STRATEGIES Armed with an understanding of the primary risk factors for a benchmark we now discuss various active portfolio strategies that are typically employed by managers. 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. We emphasize the use of the total return framework for evaluating active strategies rather than the blind pursuit of a strategy based merely on general statements. 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. Yield Curve Strategies 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. Types of Shifts in the Yield Curve and Impact on Historical Returns 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 humped ness 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 humped Ness of the yield curve, is referred to as a butterfly shift. Yield Curve Strategies 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. 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. 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, a greater convexity implies a better bond portfolio performance 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. Suppose that a portfolio manager with a six-month investment horizon has a choice of investing in a bullet portfolio or a barbell portfolio. Further suppose that 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. Which portfolio should he choose? Actually, the portfolio manager does not have enough information to make an adequate decision. What is necessary is to assess the potential total return when the yield curve shifts. 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. 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. 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. 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. 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 Spreads 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. Yield spreads between Treasury and federal agency securities will vary depending on investor expectations about the prospects that an implicit government guarantee will be honored. Spreads between Callable and Noncallable Securities 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. An expected drop in the level of interest rates will widen the yield spread between callable bonds and noncallable bonds as the prospects that the issuer will exercise the call option increase. Importance of Dollar Duration Weighting of Yield Spread Strategies What is critical in assessing yield spread strategies is to compare positions that have the same dollar duration. To understand why, consider two bonds, X and Y that are being considered as alternative investments in a strategy other than one based on anticipating interest-rate movements. The amount of each bond in the strategy should be such that they will both have the same dollar duration. 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 (i) its yield is higher than that of comparably rated issues, or (ii) 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. 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. The incremental return over Treasuries depends on the initial spread, the change in the spread, and the probability of a rating change. For all rating sectors and maturity sectors, expected incremental returns are less than the initial spread. 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. 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. The first is the interest income and the second is the 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. Thus 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. 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 × × 100. 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. Repurchase Agreement 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 to borrow the money. Credit Risks Despite the fact that there may be high-quality collateral underlying a repo transaction, both parties to the transaction are exposed to credit risk. 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. Determinants of the Repo Rate 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. KEY POINTS • The asset allocation decision is the decision made to determine how much should be allocated amongst the major asset classes and is made in the light of the investment objective. • Once the asset allocation decision is made, the client must decide whether to use only internal managers, use only external managers, or use a combination of internal and external managers. • The term asset allocation is also used after a decision has been made to invest in a specified asset class to indicate how funds should be allocated amongst the different sectors within that asset class. • In general, there are three categories of bond portfolio strategies: bond benchmark-based strategies, absolute return strategies, and liability-driven strategies. • Bond benchmark-based strategies include indexing type strategies (pure bond index matching enhanced indexing with matching of primary risk factors, and enhanced indexing with minor risk-factor mismatches) and active management type strategies (with larger risk-factor mismatches and full-blown active). • With a core/satellite strategy there is a blending of an indexed strategy (to create a low-risk core portfolio) and an active strategy (to create a specialized higher risk-tolerant satellite portfolio). • The wide range of bond market indexes available can be classified as broad-based market indexes and specialized market indexes. • The primary risk factors affecting a portfolio are divided into systematic risk factors and nonsystematic risk factors. In turn, each of these risk factors is further decomposed. Systematic risk factors are divided into term structure risk factors and non-term structure risk factors. Examples of non-term structure risk factors are sector risk, credit risk, and optionality risk. Non-systematic risk factors are classified as issuer-specific risk and issue-specific risk. • Active bond portfolio strategies seek to capitalize on expectations about changes in factors that will affect the price and therefore the performance of an issue over some investment horizon. • The total return framework should be used to assess how changes in these factors will affect the performance of a strategy over some investment horizon. • Leveraging involves creating an exposure to a market in excess of the exposure that can be obtained without borrowing funds. The objective is to earn a return in excess of the cost of the borrowed funds. The risk is that the manager will earn a return less than the cost of the borrowed funds. The return on the borrowed funds is realized from the interest earned plus the change in the value of the securities acquired. The duration of a portfolio is magnified by leveraging a portfolio. • The most common way in which a manager can borrow funds is via a repurchase agreement. This is a collateralized loan arrangement in which a party borrows funds. It is called a reverse repo agreement when a party lends funds. There is credit risk in a repo agreement, and there are mechanisms for mitigating this risk. ANSWERS TO QUESTIONS FOR CHAPTER 22 (Questions are in bold print followed by answers.) 1. Why might the investment objective of a portfolio manager of a life insurance company be different from that of a mutual fund manager? The first step in the investment management process is setting investment objectives. The investment objective will vary by type of financial institution. The objectives of a life insurance company and a mutual fund company are different with a life insurance company generally focusing more on safer fixed income investments that are needed to match its liabilities. More details are given below. For institutions such as life insurance companies, the basic objective is to satisfy obligations stipulated in insurance policies and generate a known profit. Most insurance products guarantee a dollar payment or a stream of dollar payments at some time in the future. The premium that the life insurance company charges a policyholder for one of its products will depend on the interest rate that the company can earn on its investments. To realize a profit, the life insurance company must earn a higher return on the premium it invests than the implicit (or explicit) interest rate it has guaranteed policyholders. For investment institutions such as mutual funds, the investment objectives will be set forth in a prospectus. With the exception of mutual funds that have a specified termination date (called target term trusts), there are no specific liabilities that must be met. Typically, the fund establishes a target payout even though it has no liabilities that guarantee dollar payments. 2. Explain how it can be possible for a portfolio manager to outperform a benchmark but still fail to meet the investment objective of a client. An index or benchmark may produce low or even negative returns over a period of time. Thus, even if a manager outperforms the benchmark, the objectives of a particular fund (such as meeting required liabilities) may not be met. As discussed below, there are ways managers can overcome this problem. Portfolio strategies can be classified as either active strategies or passive strategies. Passive strategies involve minimal expectational input. One popular type of passive strategy is indexing, whose objective is to replicate the performance of a predetermined index or benchmark. Although indexing may be a reasonable strategy for an institution that does not have a future liability stream to be satisfied, consider the circumstances in which pension funds operate. If a pension fund indexes its portfolio, the fund’s return will be roughly the same as the index return. Yet the index may not provide a return that is sufficient to satisfy the fund’s obligations. Consequently, for some institutions, such as pension funds and life insurance companies, structured portfolio strategies such as immunization or dedication may be more appropriate to achieve investment objectives. Within the context of these strategies, an active or enhanced return strategy may be followed. 3. The following two quotes are from the website for the FTIF Franklin High Yield Fund dated December 31, 2009 (http://www.franklintempleton.com.es/pdf/funds/fdata/0825_ksp_es.pdf): a. “Portfolio risk is controlled primarily through our extensive bottom-up, fundamental analysis process, as well as through security and industry diversification.” What does this mean? The statement refers to how FTIF Franklin High Yield Fund seeks to contain portfolio risk, which is to say how it seeks to lower the probability that individual investments in its portfolio will fall in value. It has chosen a bottom-up approach that involves a basic process using various forms of diversification to control market or systematic risk. More details are given below. A major risk factor is the exposure of a benchmark or portfolio to changes in the level of interest rates. This risk can be controlled by using an indexing strategy. An enhanced indexing strategy involves matching primary risk factors. The primary risk factors can be divided into two general types: systematic risk factors and nonsystematic risk factors. Systematic risk factors are forces that affect all securities in a certain category in the benchmark. Nonsystematic risk factors are the risks that are not attributable to the systematic risk factors. 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. 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. At the macro level, these sectors include Treasury, agencies, corporates, residential agency mortgage-backed securities, commercial mortgage-backed securities, and asset-backed securities. Each of these sectors is divided further. For example, the corporate sector (called the credit sector) is divided into financial institutions, industrials, transportations, and utilities. In turn, each of these subsectors is further divided. The financial institutions subsector, for example, is broken down into the following: banking, brokerage, financial companies, insurance, and other. 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. This includes embedded options in callable and put able corporate bonds, MBS, and ABS. 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. There are two general approaches to construction and management of a bond portfolio to over risk factors: top-down and bottom-up. Typically, portfolio managers do not use a pure top-down or bottom-up approach but instead blend the elements of both in junction with certain considerations and constraints in constructing a portfolio. FTIF Franklin High Yield Fund uses a bottom-up approach, which is an approach to active bond portfolio management focusing 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 portfolio’s risk, risk modeling is used. b. “The overall volatility of the product (i.e., standard deviation) and tracking error versus its benchmark and peer group is monitored and projected from a top-down quantitative approach.” What is meant by a top down approach? (In the next chapter, the quantitative approach and tracking error will be discussed.) There are two general approaches to construction and management of a bond portfolio to over risk factors: top-down and bottom-up. Typically, portfolio managers do not use a pure top-down or bottom-up approach but instead blend the elements of both in junction with certain considerations and constraints in constructing a portfolio. In general, a top-down approach (also known as step-wise design) is essentially the breaking down of a system to gain insight into its compositional sub-systems. In a top-down approach an overview of the system is formulated, specifying but not detailing any first-level subsystems. Each subsystem is then refined in yet greater detail, sometimes in many additional subsystem levels, until the entire specification is reduced to base elements. More details are given below as applied to managing a portfolio of funds. 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. 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. For a portfolio manager who is managing a global bond portfolio, a macro forecast is required for all country markets. Based on this assessment and forecast, the manager decides on how much of the portfolio’s funds to allocate among the different sectors of the bond market and how much to cash equivalents (i.e., money market instruments). 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. A manager who follows a top-down approach often relies on an analysis of the bond market to identify those countries (if permitted), sectors, and industries that will benefit the most on a relative basis from the anticipated economic forecast. Once the amount to be allocated to each country, sector, and industry is made, the manager then looks for the individual bonds to include in the portfolio. The top-down approach looks at changes in several macroeconomic factors to assess the expected excess return (anticipated performance over risk-free return) on securities and portfolios. The portfolio allocation amongst countries, sectors, and industries is altered as macroeconomic conditions change. 4. Answer the below questions. a. What is the essential ingredient in all active portfolio strategies? 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. In the case of active equity strategies, this may include forecasts of future earnings, dividends, or price/earnings ratios. In the case of active bond management, this may involve forecasts of future interest rates, future interest-rate volatility, or future yield spreads. Active portfolio strategies involving foreign securities will require forecasts of future exchange rates. b. Those portfolio managers who follow an indexing strategy are said to be “index huggers.” Why? An “index hugger” refers to a managed mutual fund that tends to perform much like a benchmark index. Thus, any portfolio managing using an index strategy can be called an index hugger. The majority of actively managed funds are expected to outperform the so-called average performance produced by passively managed index funds. Investors pay fund investment managers higher fees to do better than index funds, although managers often fail to outperform the index. A high R-squared factor, a mutual fund risk analysis measure, between 85 and 100 indicates that a managed fund's performance patterns are in line with the fund's benchmark index. If this is the case, investors may be better off investing in the index itself, which has lower portfolio turnover and lower expense ratio features. Thus, being an “index hugger” may be advantageous. 5. Explain whether you agree or disagree with the following statement: “All duration-matching strategies are indexing strategies.” One would disagree with the above statement because a portfolio manager following an indexing strategy can be ordered not to deviate from the benchmark’s duration. Thus, the manager could not achieve a desired duration match. For example, even when minor mismatches in the primary risk factors are permitted in an enhanced indexing strategy, the mismatch may not occur with respect to duration. To illustrate further, suppose that the benchmark index has a duration of 5. Then a portfolio manager pursuing an indexing strategy is not permitted to construct a portfolio whose duration differs from 5. More details are given below. A duration-matching strategy refers to a method of assembling a bond portfolio so that the duration of the portfolio equals the duration of the investor's liability stream. Duration is the number of years until the investor receive the present value of all income from a bond (including interest and principal), and is used to gauge a bond's sensitivity to interest rate changes. A duration matching strategy is intended to reduce the portfolio's sensitivity to interest rates in order to reduce the risk of loss to the holder. Whereas a duration-matching strategy actively matches the duration of the assets to the duration of the liabilities, an indexing strategy is a passive strategy, which tries to follows the weight age of an index on a daily basis. It is usually taken up with the idea of not underperforming the index, without actively handling the same aggressively. A pure bond index strategy may match that of some index that the investor may have chosen as a benchmark. Only if the matching to the index is made to achieve a certain duration can we say that the duration-matching strategy coincides with an indexing strategy. 6. The investment objective of the Threadneedle bond fund is “To outperform the benchmark by 3% per annum (gross of fees) over an 18-24 month period” What type of fund is this? This fund is an actively managed fund. A bond fund that seeks to outperform a benchmark is following an active bond portfolio strategy. The ability to outperform a benchmark index will depend on how the manager allocates funds within a bond sector relative to the composition of the benchmark index. 7. Answer the below questions. (a) What is meant by systematic risk factors? Risk factors affecting an index can be classified into two types: systematic risk factors and nonsystematic risk factors. Systematic risk factors are forces that affect all securities in a certain category in the benchmark index. Nonsystematic risk factors are classified as risks associated with a particular issuer, issuer-specific risk, and those associated with a particular issue, issue-specific risk. (b) What is the difference between term structure and non-term structure risk factors? Systematic risk factors can be 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. 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. 8. The following is reproduced from the Prospectus of the T. Rowe Price Institutional Core Plus Fund dated October 1, 2010: “Principal Investment Strategies: The fund intends to invest at least 65% of its net assets in a “core” portfolio of investment-grade, U.S. dollar-denominated fixed income securities which may include, but are not limited to, debt securities of the U.S. government and its agencies, corporate bonds, mortgages, and asset-backed securities. Normally, the fund will also maintain a “plus” portion of its portfolio in other sectors of the bond market, including high yield, non-U.S. dollar-denominated, and emerging market securities, to seek additional value. Under normal conditions, the fund expects to maintain an effective duration within +/–20% of the Barclays Capital U.S. Aggregate Bond Index. As of July 31, 2010, the effective duration of this index was 4.05; however, it will change over time. The fund, in the aggregate, will seek to maintain a weighted average credit rating of A- or better, based on the weighted average credit quality of the fund’s portfolio securities. Individual bond investments in the core portfolio will be investment grade, with a minimum credit quality of BBB-. Ratings will be as determined, at the time of purchase, by at least one nationally recognized statistical rating organization (NRSRO) or, if not so rated, a comparable rating by T. Rowe Price. If a security is split-rated (i.e., one rating below investment grade and one at or above investment grade), the higher rating will be used. The plus portion of the fund’s portfolio may consist of below investment-grade (junk) bonds of U.S. and other developed country companies (not to exceed 20% of net assets), below investment-grade emerging market fixed income securities (not to exceed 10% of net assets), non-U.S. dollar-denominated securities (not to exceed 20% of net assets), and convertible and preferred securities (not to exceed 10% of net assets), as well as other investments. The fund may hold non-U.S. currencies without holding any bonds or other securities denominated in those currencies. The fund may continue to hold an investment in its core portfolio that is downgraded to below investment grade after purchase. If such rating downgrades cause high yield exposure to exceed 20% of net assets or below investment-grade emerging market securities to exceed 10% of net assets, the fund will reduce exposure within a reasonable period of time. In keeping with the fund’s objective, it may also use futures, options, and swaps. The fund may sell holdings for a variety of reasons, such as to adjust the portfolio’s average maturity, duration, or credit quality or to shift assets into and out of higher yielding or lower yielding securities or different sectors.” Discuss in detail the strategy of this fund. This fund is following a core strategy. With a core/satellite strategy there is a blending of an indexed strategy (to create a low-risk core portfolio) and an active strategy (to create a specialized higher risk tolerant satellite portfolio). Basically, this strategy involves building a blended portfolio using an indexed and active strategy. The core component is a low-risk portfolio constructed using one of the indexing strategies. The benchmark for the core portfolio is broad liquid bond market index and the core component provides broad market exposure that has basically the same primary risk factor exposure as the benchmark. The satellite component is constructed using an active strategy with a benchmark that is specialized rather than a broad liquid bond market index. It is this component of the portfolio where the manager makes bets (i.e., takes views) on the primary risk factors. The core component provides broad market exposure and therefore captures systematic market risk or what is commonly referred to as a “beta.” In contrast, an active return (commonly referred to as “alpha”) is sought in the actively managed satellite portfolio. The advantage cited for the core strategy is that it provides a cost-efficient means for controlling portfolio risk relative to a benchmark. This relative risk is referred to as tracking error. A core strategy can have a "satellite" portion, that comprises holdings that the advisor expects will add alpha, the financial term for returns exceeding systematic. If the entire allotment of the satellite portion is not deemed worthy of inclusion, that portion will either be reallocated across "core" positions or in a “satellite holder,” which a position that mirrors some aspect of the core. This satellite allocation may be implemented into 100% equity allocations and/or allocations that blend with fixed-income or non-equity positions. 9. What are the limitations of using duration and convexity measures in active portfolio strategies? Recall that duration is just a first approximation of the change in price resulting from a change in interest rates while convexity provides a second approximation. Below we discuss the limitation involved in using the measures of duration and convexity to estimate how portfolio values will be affected when interest rates change. 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. As duration is a measure of interest-rate sensitivity, this involves increasing a portfolio’s duration if interest rates are expected to fall and reducing duration if interest rates are expected to rise. For those managers whose benchmark is a bond index, this means increasing the portfolio duration relative to the benchmark index if interest rates are expected to fall and reducing it if interest rates are expected to rise. There are several limitations to achieve a change in a portfolio’s duration. First, the client may limit the degree to which the duration of the managed portfolio is permitted to diverge from that of the benchmark index. Second, research does not support the notion that an active strategy can profit from the ability to forecast the direction of future interest rates. The academic literature argues that interest rates cannot be forecasted so that risk-adjusted excess returns can be realized consistently. It is doubtful whether betting on future interest rates will provide a consistently superior return. Another limitation concerns a portfolio with assets with varying maturities. The assumption made when using duration as a measure of how the value of a portfolio will change if market yields change is that the yield on all maturities will change by the same number of basis points. The key point is that two portfolios with the same duration may perform quite differently when the yield curve shifts. An additional limitation is that knowing duration and convexity is not always enough to insure that an active strategy will succeed even if managers are correct in their assessment about changes in interest rates. For example, suppose that a portfolio manager has a choice of investing in the bullet portfolio or the barbell portfolio. Which one should be chosen if the manager knows the following? First, the manager knows that the two portfolios have the same dollar duration. Second, the manager knows the yield for the bullet portfolio is greater than that of the barbell portfolio. Third, the manager knows the dollar convexity of the barbell portfolio is greater than that of the bullet portfolio. However, even all of this information is not adequate in making the decision. This is because the decision depends not just on the direction of the interest rate change but on the amount by which yields change. Also, 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. However, even the benefit of the greater convexity depends on how much yields change. In closing, 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 reveals 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 the yield curve will shift, it is imperative to perform total return analysis. For example, in a steepening yield curve environment, it is often stated that a bullet portfolio would be better than a barbell portfolio. However, it is not always the case that a bullet portfolio would outperform a barbell portfolio. Whether the bullet portfolio outperforms the barbell depends on how much the yield curve steepens. 10. Below are two portfolios with a market value of $500 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 2.0 $120 B 2.5 $130 C 20.0 $150 D 20.5 $100 Bonds Included in Portfolio II E 9.7 $200 F 10.0 $230 G 10.2 $ 70 Answer the below questions. (a) 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 (ten years). (b) 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 (two years and twenty years). (c) The two portfolios have the same dollar duration; explain whether their performance will be the same if interest rates change. Even if the yield curve shifts in a parallel fashion due to changes in interest rates, two portfolios with the same dollar duration will not give the same performance if they have differences in dollar convexity. 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 illustration in the second column of Exhibit 22-9, 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 that the barbell portfolio. The last two columns Exhibit 22-9 illustrate the relative performance of a bullet portfolio and a barbell portfolio for a nonparallel shift of the yield curve. Specifically, the first nonparallel shift column assumes that if the yield on the bullet portfolio (consisting of the intermediate-term bond) changes by the amount shown in the first column, the short-term bond in the barbell portfolio will change by the same amount plus 25 basis points, whereas the long-term bond in the barbell portfolio will change by the same amount shown in the first column less 25 basis points. Measuring the steepness of the yield curve as the spread between the long-term yield and the short-term yield, the spread has decreased by 50 basis points. Such a nonparallel shift means a flattening of the yield curve. As can be seen in the exhibit, for this assumed yield curve shift, the barbell outperforms the bullet. In the last column of Exhibit 22-9, the nonparallel shift assumes that for a change in the intermediate bond’s yield, the yield on the short-term will change by the same amount less 25 basis points, whereas that on the long-term bond will change by the same amount plus 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 the intermediate bond does not rise by more than 250 basis points or fall by more than 325 basis points. (d) If they will not perform the same, how would you go about determining which would perform best assuming that you have a six-month investment horizon? To determine which portfolio would have the superior performance, we would want to look at the total return for the six-month investment horizon given expectations about change in yields and how the yield curve will shift. More details are given below. It is important to note that measures such as yield (yield to maturity or some type of portfolio yield measure), duration, or convexity tell 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 imperative to perform total return analysis. For example, in a steepening yield curve environment, it is often stated that a bullet portfolio with the same duration as a barbell portfolio would perform better that the barbell portfolio. However, as can be seen from Exhibit 22-9, it is not the case that a bullet portfolio would outperform a barbell portfolio. Whether the bullet portfolio outperforms the barbell depends on how much the yield curve steepens. An analysis similar to that in Exhibit 22-9 based on total return for different degrees of steepening of the yield curve clearly demonstrates to a manager whether a particular yield curve strategy will be superior to another. The same analysis can be performed to assess the potential outcome of a ladder strategy. 11. Answer the below questions. (a) Explain why you agree or disagree with the following statement: “It is always better to have a portfolio with more convexity than one with less convexity.” It is not always better to have a portfolio with more convexity than one with less convexity. This is illustrated if one examines the portfolios associated with Exhibit 22-9. 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 22-9, 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. (b) Explain why you agree or disagree with the following statement: “A bullet portfolio will always outperform a barbell portfolio with the same dollar duration if the yield curve steepens.” One would disagree with the statement that a bullet portfolio will always outperform a barbell portfolio with the same dollar duration if the yield curve steepens.” This is because the performance of a bullet portfolio compared to a barbell portfolio depends on how much the yield curve steepens. More details are given below. To answer this question let us turn again to the illustration in Exhibit 22-9. First, we can look at what happens if the yield curve does not shift in a parallel fashion. The last two columns of Exhibit 22-9 demonstrate the relative performance of the bullet and barbell portfolios for a nonparallel shift of the yield curve. 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 plus 25 basis points, whereas bond B (the long-term bond) will change by the same amount shown in the first column less 25 basis points. Measuring the steepness of the yield curve as 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. Such a nonparallel shift means a flattening of the yield curve. As can be seen in Exhibit 22-9, for this assumed yield curve shift, the barbell outperforms the bullet. 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 less 25 basis points, whereas that on bond B will change by the same amount plus 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. 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 reveals 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 imperative to perform total return analysis. For example, in a steepening yield curve environment, it is often stated that a bullet portfolio would be better than a barbell portfolio. As can be seen from Exhibit 22-9, it is not the case that a bullet portfolio would outperform a barbell portfolio. Whether the bullet portfolio outperforms the barbell depends on how much the yield curve steepens. An analysis similar to that in Exhibit 22-9 based on total return for different degrees of steepening of the yield curve clearly demonstrates to a manager whether a particular yield curve strategy will be superior to another. 12. What is a laddered portfolio? A ladder portfolio is constructed to have approximately equal amounts of each maturity. So, for example, a portfolio might have equal amounts of securities with one year to maturity, two years to maturity, and so on. 13. A portfolio manager owns $5 million par value of bond ABC. The bond is trading at 70 and has a modified duration of 6. The portfolio manager is considering swapping out of bond ABC and into bond XYZ. The price of this bond is 85 and it has a modified duration of 3.5. Answer the below questions. (a) What is the dollar duration of bond ABC per 100-basis-point change in yield? The price of bond ABC is 70 with a modified duration of 6, and bond XYZ has a price of 85 with a modified duration of 3.5. Because modified duration is the approximate percentage change per 100-basis-point change in yield, a 100-basis-point change in yield for bond ABC would change its price by about 6%. Based on a price of 70, its price will change by about 0.06(70) = $4.2 per $70 of market value. Thus, for bond ABC, its dollar duration for a 100-basis-point change in yield is $4.2 per $70 of market value. Similarly, for bond XYZ, its dollar duration for a 100-basis-point change in yield per $85 of market value can be determined. In this case it is 0.035(85) = $2.975. So if bonds ABC and XYZ are being considered as alternative investments in a strategy other than one based on anticipating interest-rate movements, the amount of each bond in the strategy should be such that they will both have the same dollar duration. (b) What is the dollar duration for the $5 million position of bond ABC? For our problem, a portfolio manager owns $5 million of par value of bond ABC, which has a market value of (70 / 100) $5M = $3.5 million. The dollar duration of bond ABC per 100-basis-point change in yield for the $3.5 million market value is 0.06 ($3.5 million) = $210,000. (c) How much in market value of bond XYZ should be purchased so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC? Mathematically, this problem can be expressed as follows: Let $DABC = dollar duration per 100-basis-point change in yield for bond ABC for the market value of bond ABC held; MDXYZ = modified duration for bond XYZ; and, MVXYZ = market value of bond XYZ needed to obtain the same dollar duration as bond ABC. The following equation sets the dollar duration for bond ABC equal to the dollar duration for bond XYZ: $DABC = MVXYZ. Solving for MVXYZ yields: MVXYZ = . Dividing by the price per $1 of par value of bond XYZ gives the par value of XYZ that has an approximately equivalent dollar duration as bond ABC. In our illustration, $DABC is $210,000 and MDXYZ is 3.5; then MVXYZ = = $6,000,000. Thus, the market value of bond XYZ that should be purchased (so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC) will be $6,000,000. (d) How much in par value of bond XYZ should be purchased so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC? The market value of bond XYZ is 85 per $100 of par value, so the price per $1 of par value is 0.85. Dividing MVXYZ (which is $6 million) by 0.85 indicates that the par value of bond XYZ that should be purchased. We have: = $7.0588235 million or about $7,058,824. 14. Explain why in implementing a yield spread strategy it is necessary to keep the dollar duration constant. When comparing positions that have the same dollar duration, it is critical to assess yield spread strategies. Failure to adjust a portfolio repositioning based on some expected change in yield spread so as to hold the dollar duration the same means that the outcome of the portfolio will be affected not only by the expected change in the yield spread but also by a change in the yield level. Thus a manager would be making a conscious yield spread bet and possibly an undesired bet on the level of interest rates. 15. The excerpt that follows is taken from an article titled “Smith Plans to Shorten,” which appeared in the January 27, 1992, issue of Bond Week, p. 6: “When the economy begins to rebound and interest rates start to move up, Smith Affiliated Capital will swap 30-year Treasuries for 10-year Treasuries and those with average remaining lives of nine years, according to Bob Smith, Executive V.P. The New York firm doesn’t expect this to occur until the end of this year or early next, however, and sees the yield on the 30-year Treasury first falling below 7%. Any new cash that comes in now will be put into 30-year Treasuries, Smith added.” What type of portfolio strategy is Smith Affiliated Capital pursuing? Smith appears to be following an interest-rate expectation strategy. A 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. As duration is a measure of interest-rate sensitivity, this involves increasing a portfolio’s duration if interest rates are expected to fall and reducing duration if interest rates are expected to rise. For those managers whose benchmark is a bond index, this means increasing the portfolio duration relative to the benchmark index if interest rates are expected to fall and reducing it if interest rates are expected to rise. The degree to which the duration of the managed portfolio is permitted to diverge from that of the benchmark index may be limited by the client. If we can assume the remaining maturities or the same, it appears that Smith is following a substitution swap strategy. 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. This swap depends on a capital market imperfection. Such situations sometimes exist in the bond market owing to temporary market imbalances and the fragmented nature of the non-Treasury bond market. The risk the money manager faces in making a substitution swap is that the bond purchased may not be truly identical to the bond for which it is exchanged. Moreover, typically, bonds will have similar but not identical maturities and coupon. This could lead to differences in the convexity of the two bonds, and any yield spread may reflect the cost of convexity. 16. The following excerpt is taken from an article titled “MERUS to Boost Corporates,” which appeared in the January 27, 1992, issue of Bond Week, p.6: MERUS Capital Management will increase the allocation to corporates in its $790 million long investment-grade fixed-income portfolio by $39.5 million over the next six months to a year, according to George Wood, managing director. MERUS will add corporates rated single A or higher in the expectation that spreads will tighten as the economy recovers and that some credits may be upgraded. What types of active portfolio strategies is MERUS Capital Management pursuing? MERUS is increasing corporates in it long investment-grade fixed-income portfolio in the next months to one year. They are focusing upon investment-grade securities because they expect the spread will tighten and some issues will be given higher ratings thus increasing their value. Consequently, now is the time to lock in a higher spread as well as investing in investment-grade securities that will be strengthened by a robust economy. Given the above, MERUS is employing a yield spread strategy that involves 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. MERUS is also using a credit spread strategy. 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 (which is MERUS’s case). The economic rationale is that in a declining or contracting economy, corporations experience a decline in revenue and reduced cash flow, making it difficult for corporate issuers to service their contractual debt obligations. To induce investors to hold non-Treasury securities of lower-quality issuers, the yield spread relative to Treasury securities must widen. The converse is that during economic expansion and brisk economic activity, revenue and cash flow pick up, increasing the likelihood that corporate issuers will have the capacity to service their contractual debt obligations. Yield spreads between Treasury and federal agency securities will vary depending on investor expectations about the prospects that an implicit government guarantee will be honored. 17. This excerpt comes from an article titled “Eagle Eyes High-Coupon Callable Corporates” in the January 20, 1992, issue of Bond Week, p. 7: “If the bond market rallies further, Eagle Asset Management may take profits, trading $8 million of seven-to 10-year Treasuries for high-coupon single-A industrials that are callable in two to four years according to Joseph Blanton, Senior V.P. He thinks a further rally is unlikely, however. Eagle has already sold seven-to 10-year Treasuries to buy $25 million of high-coupon, single-A nonbank financial credits. It made the move to cut the duration of its $160 million fixed income portfolio from 3.7 to 2.5 years, substantially lower than the 3.3-year duration of its bogey . . . because it thinks the bond rally has run its course. . . . Blanton said he likes single-A industrials and financials with 9 1/210% coupons because these are selling at wide spreads of about 100150 basis points off Treasuries.” What types of active portfolio strategies are being pursued by Eagle Asset Management? Blanton may take profits by trading seven-to 10-year Treasuries for high-coupon single-A industrials that are callable in two to four years because the market rally will fade. This means Blanton believes the spread will stop decreasing and may even increase making these securities less desirable. By buying callable bonds, it is implied that interest rates may increase. Blanton has already sold some seven-to 10 year Treasuries to buy high-coupon single-A nonbank financial credits implying that he further believes interest rates will increase. In anticipation of interest rates increasing, Blanton has cut the duration of his portfolio so as not to be stuck with long-term investments in securities paying low coupon rates relative to market yields. Finally, Blanton has shifted from Treasuries to industrial and financials where the spread are believed to be relatively high. From the above, Blanton appears to be following a strategy to capitalize on differences in spreads between callable and noncallable securities. For example, Blanton has bought some callable securities. 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 (i) the direction of the change in interest rates, and (ii) interest-rate volatility. An expected drop in the level of interest rates will widen the yield spread between callable bonds and noncallable bonds as the prospects that the issuer will exercise the call option increase. The reverse is true: The yield spread narrows if interest rates are expected to rise. Next, Blanton is also involved in a credit spread strategy. For example, Blanton has already sold seven-to 10-year Treasuries to buy $25 million of high-coupon, single-A nonbank financial credits. 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. Additionally, Blanton is engaged in a strategy that involves changing his portfolio’s duration. 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. As duration is a measure of interest-rate sensitivity, this involves increasing a portfolio’s duration if interest rates are expected to fall and reducing duration if interest rates are expected to rise. For those managers whose benchmark is a bond index, this means increasing the portfolio duration relative to the benchmark index if interest rates are expected to fall and reducing it if interest rates are expected to rise. The degree to which the duration of the managed portfolio is permitted to diverge from that of the benchmark index may be limited by the client. 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. Further, it appears that Blanton is following is a yield spread strategy. Blanton is involved in positioning a portfolio to capitalize on expected changes in yield spreads between sectors of the bond market. For example, the excerpt states: “Blanton said he likes single-A industrials and financials with 9 1/210% coupons because these are selling at wide spreads of about 100150 basis points off Treasuries.” 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. 18. The following excerpt is taken from an article titled “W.R. Lazard Buys Triple Bs,” which appeared in the November 18, 1991, issue of Bond Week, p. 7: “W.R. Lazard & Co. is buying some corporate bonds rated triple B that it believes will be upgraded and some single A’s that the market perceives as risky but Lazard does not, according to William Schultz, V.P. The firm, which generally buys corporates rated single A or higher, is making the move to pick up yield, Schultz said.” What types of active portfolio strategies are being followed by W.R. Lazard & Co.? Schultz wants to capitalize on what he believes are underpriced bonds rated triple B’s and single A’s. Thus, Schultz appears to be using a credit spread strategy. 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. To induce investors to hold non-Treasury securities of lower-quality issuers, the yield spread relative to Treasury securities must widen. Schultz wants to earn a higher spread for issues that are below AA because he thinks these spreads will be reduced. Schultz’s strategy can also be viewed as a yield spread strategy which involves differences in yields within the corporate sectors. 19. In an article titled “Signet to Add Pass-Throughs,” which appeared in the October 14, 1991, issue of Bond Week. p. 5, it was reported that Christian Goetz, assistant vice president of Signet Asset Management, “expects current coupons to outperform premium pass-throughs as the Fed lowers rates because mortgage holders will refinance premium mortgages.” If Goetz pursues a strategy based on this, what type of active strategy is it? Goetz appears to be pursuing an active strategy that relies on forecasts of future interest-rate levels. Future interest rates, for instance, affect the value of options embedded in callable bonds and the value of prepayment options embedded in mortgage-backed securities. Callable corporate and municipal bonds with coupon rates above the expected future interest rate will underperform relative to noncallable bonds or low-coupon bonds. This is because of the negative convexity feature of callable bonds. Goetz is also concerned with an active strategy used in the mortgage-backed securities market. This strategy involves identifying individual issues of pass-throughs, CMO classes, or stripped MBS that are mispriced, given the assumed prepayment speed to price the security. Another active strategy commonly used in the mortgage-backed securities market is to create a package of securities that will have a better return profile for a wide range of interest-rate and yield curve scenarios than similar duration securities available in the market. Because of the fragmented nature of the mortgage-backed securities market and the complexity of the structures, such opportunities are not unusual. 20. The following excerpt comes from an article titled “Securities Counselors Eyes Cutting Duration” in the February 17, 1992, issue of Bond Week, p. 5: “Securities Counselors of Iowa will shorten the 5.3 year duration on its $250 million fixed-income portfolio once it is convinced interest rates are moving up and the economy is improving … It will shorten by holding in cash equivalents the proceeds from the sale of an undetermined amount of 10-year Treasuries and adding a small amount of high-grade electric utility bonds that have short-maturities if their spreads widen out at least 100 basis points … The portfolio is currently allocated with 85% to Treasuries and 15% to agencies. It has not held corporate bonds since 1985, when it perceived as risky the onslaught of hostile corporate takeovers …” Answer the below questions. (a) Why would Securities Counselors want to shorten duration if it believes that interest rates will rise? Securities Counselors is planning for the possibility that interest rates will increase. The plan involves shortening its duration so that it can be in a position to reinvest funds in longer term investments. This is because a short duration implies investments will be maturing and thus these funds will be available to buy securities with a higher coupon rate if interest rates do increase. (b) How does the purchase of cash equivalents and short-maturity high-grade utilities accomplish the goal of shortening the duration? Cash equivalents and short-maturity high-grades utilities are very liquid and thus by nature will mature quickly. Ceteris paribus, these investments involve very short durations. (c) What risk is Securities Counselors indicating in the last sentence of the excerpt that it is seeking to avoid by not buying corporate bonds? A hostile takeover can involve retiring holdings making the duration very short. The risk is the unexpected nature of the takeover that would cause a portfolio manager to rearrange their portfolio and perhaps have to invest in securities that do not pay as high a rate of return. 21. The next excerpt is taken from an article titled “Wood Struthers to Add High-Grade Corporates,” which appeared in the February 17, 1992, issue of Bond Week, p. 5: Wood Struthers & Winthrop is poised to add a wide range of high-grade corporates to its $600 million fixed-income portfolio … It will increase its 25% corporate allocation to about 30% after the economy shows signs of improving …It will sell Treasuries and agencies of undetermined maturities to make the purchase … Its duration is 4 1/25 years and is not expected to change significantly … Comment on this portfolio strategy. As the economy improves, there will be less risk. This implies that corporate fixed-income investments may be upgraded. The upgrade will increase the value of these securities. If Wood Struthers & Winthrop (WS&W) increases its corporate allocation it will be in a position to increase its value due to price appreciation. By selling Treasuries and agencies, WS&W will be increasing its coupon payments and thus its value due to interest payments. In conclusion, WS&W will be a position to profit through both price appreciation and increase fixed payments. This risk inherent whenever shifting away from Treasuries to corporates is the greater probability of not receiving principal and interest payments in full. 22. Explain how a rating transition matrix can be used as a starting point in assessing how a manager may want to allocate funds to the different credit sectors of the corporate bond market. A rating transition matrix can be a starting point because it provides a framework for how the credit quality for different sectors of the corporate bond market has changed historically. While the historical rating transition matrix is a useful starting point since it represents an average over a period of time, a manager must modify the matrix based on expectations of upgrades and downgrades given current and anticipated economic conditions. 23. What is the risk associated with the use of leverage? 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. 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 risk associated with leverage (or borrowing funds) is that the 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. Generally speaking borrowed funds create a legal responsibility on the part of the borrower and can lead to default if not paid back in a timely fashion. 24. Suppose that the initial value of an unlevered portfolio of Treasury securities is $200 million and the duration is 7. Suppose further that the manager can borrow $800 million and invest it in the identical Treasury securities so that the levered portfolio has a value of $1 billion. What is the duration of this levered portfolio? The portfolio has a market value of $200 million and the manager invests the proceeds in a bond with a duration of 7. 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 (7 / 100)$200 = $14 million. For this unlevered fund, the duration of the portfolio is 7. Suppose now that the manager of this portfolio borrows an additional $800 million. This means that the levered fund will have $200 + $800 = $1 billion to invest, consisting of $200 million that the manager has available before borrowing (i.e., the equity) and $800 million borrowed. All of the funds are invested in a bond with a duration of 7. Now let’s look at what happens if interest rates change by 100 basis points. The levered portfolio’s value will change by (7 / 100)($1 billion) = $70 million. This means that on an investment of $200 million, the portfolio’s value changes by $70 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. Thus, the duration for the portfolio is $70 million per $200 million or $35 per each $100 rendering a duration of 35 because a duration of 35 will change the portfolio’s equity value of $200 million by 35% or $70 million for a 100-basis-point change in rates. 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 × × 100. To illustrate the procedure for our problem, the initial value of the unlevered portfolio is $200 million and the leveraged portfolio is $200 million equity plus $800 million borrowed = $1 billion. Step 1: We are given that the duration of the levered portfolio is 7. Step 2: Let’s use a 50 basis point change in interest rates to compute the dollar duration. If the duration of the levered portfolio is 7, then the dollar duration for a 50-basis-point change in interest rates is 7(0.05)($1 billion) = $350 million (7 times 0.5% = 3.5% change for a 50-basis-point move times $1 billion). Step 3: The ratio of the dollar duration for a 50-basis-point change in interest rates to the $200 million initial market value of the unlevered portfolio is $350 million / $200 million = 1.75. Step 4: The duration of the unlevered portfolio is: ratio computed in Step 3 × × 100 = 1.75 × × 100 = 350. 25. Suppose a manager wants to borrow $50 million of a Treasury security that it plans to purchase and hold for 20 days. The manager can enter into a reverse repo agreement with a dealer firm that would provide financing at a 4.2% repo rate and a 2% margin requirement. What is the dollar interest cost that the manager will have to pay for the borrowed funds? With a reverse repo, the dealer agrees to buy the securities and sell them back later. The dollar interest for $50 million in borrowed funds is given by: dollar interest = (dollar amount borrowed)(repo rate) . Inserting in our values, we get: dollar interest = ($50,000,000)(0.042) = $116,666.67. However, if the firm cannot borrow $50 million because of a margin requirement, then we have to adjust for the margin requirement. 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. With a 2% margin requirement, the dollar amount borrowed will be adjusted by dividing by (1 + margin). Thus, we have: dollar amount borrowed = collateral / (1 + margin) = $50 million / (1 + margin) = $50 million / 1.02 = $49,019,607.84. We see that the collateral of $50 million exceeds the amount of the loan by 2%. For example, (1.02)$49,019,607.84 = $50 million. For a repo margin requirement and dollar amount borrowed of $49,019,607,84, the dollar interest is now: dollar interest = $49,019,607.84(0.042) = $114,379.08. 26. Two trustees of a pension fund are discussing repurchase agreements. Trustee A told Trustee B that she feels it is a safe short-term investment for the fund. Trustee B told Trustee A that repurchase agreements are highly speculative vehicles because they are leveraged instruments. You’ve been called in by the trustees to clarify the investment characteristics of repurchase agreements. What would you say to the trustees? First, one could define a repurchase agreement or repo by stating that a repo 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. One could emphasize that a repo is a collateralized loan, where the collateral is the security sold and subsequently repurchased. From the customer’s perspective, one could positively point out that the repo market offers an attractive yield on a short-term secured transaction that is highly liquid. One could then add that although Treasury securities are often used as the collateral, the collateral in a repo is not limited to government securities. Money market instruments, federal agency securities, and mortgage-backed securities are also used. In some specialized markets, whole loans are used as collateral. Thus, the safety of the repo is a function of the riskiness of the collateral which is generally speaking secure. One would next discuss the credit risk by stating that despite the fact that there may be high-quality collateral underlying a repo transaction, both parties to the transaction are exposed to credit risk. For example, assuming a government security is involved, if the dealer cannot repurchase the government securities, the customer may keep the collateral. If interest rates on government securities increase subsequent to the repo transaction, however, the market value of the government securities will decline, and the customer will own securities with a market value less than the amount it lent to the dealer. If the market value of the security rises instead, the dealer will be concerned with the return of the collateral, which then has a market value higher than the loan. Finally, one might point out that repos can 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. Another practice to limit credit risk is to mark the collateral to market on a regular basis. Marking a position to market means recording the value of a position at its market value. When market value changes by a certain percentage, the repo position is adjusted accordingly. 27. Suppose that a manager buys an adjustable-rate pass-through security backed by Freddie Mac or Fannie Mae, two government-sponsored enterprises. Suppose that the coupon rate is reset monthly based on the following coupon formula: one-month LIBOR + 80 basis points with a cap of 9% (i.e., maximum coupon rate of 9%). Suppose that the manager can use these securities in a repo transaction in which (1) a repo margin of 5% is required, (2) the term of the repo is one month, and (3) the repo rate is one-month LIBOR plus 10 basis points. Also assume that the manager wishes to invest $1 million of his client’s funds in these securities. The manager can purchase $20 million in par value of these securities because only $1 million is required. The amount borrowed would be $19 million. Thus the manager realizes a spread of 70 basis points on the $19 million borrowed because LIBOR plus 80 basis points is earned in interest each month (coupon rate) and LIBOR plus 10 basis points is paid each month (repo rate). What are the risks associated with this strategy? The return earned must be commensurate with the risk undertaken to determine if the strategy is viable. First, there is a cap on the adjustable-rate pass-through security that may cause problems and negate the current spread of 70 basis points. Second, there is a credit risk involved for both parties in repo transaction. For example, if the dealer cannot repurchase the securities, the customer may keep the collateral. If interest rates on the securities increase subsequent to the repo transaction, however, the market value of the securities will decline, and the customer will own securities with a market value less than the amount it lent to the dealer. If the market value of the security rises instead, the dealer will be concerned with the return of the collateral, which then has a market value higher than the loan. Also, another risk factor in structuring a repo is delivery of the collateral to the lender. The most obvious procedure is for the borrower to deliver the collateral to the lender or to the lender’s clearing agent. In such instances, the collateral is said to be “delivered out.” At the end of the repo term, the lender returns the collateral to the borrower in exchange for the principal and interest payment. This procedure may be too expensive, though, particularly for short-term repos, because of costs associated with delivering the collateral. The cost of delivery would be factored into the transaction by a lower repo rate that the borrower would be willing to pay. The risk of the lender not taking possession of the collateral is that the borrower may sell the security or use the same security as collateral for a repo with another party. 28. Why is there credit risk in a repo transaction? Despite the fact that there may be high-quality collateral underlying a repo transaction, both parties to the transaction are exposed to credit risk. Why does credit risk occur in a repo transaction? To answer this question, consider the example in the text in which the dealer uses $10 million of government securities as collateral to borrow. If the dealer cannot repurchase the government securities, the customer may keep the collateral; if interest rates on government securities increase subsequent to the repo transaction, however, the market value of the government securities will decline, and the customer will own securities with a market value less than the amount it lent to the dealer. If the market value of the security rises instead, the dealer will be concerned with the return of the collateral, which then has a market value higher than the loan. Solution Manual for Bond Markets, Analysis and Strategies Frank J. Fabozzi 9780132743549, 9780133796773