Gerald O. Bierwag

Designing an immunized portfolio: Is M-squared the key?

Abstract The theoretical and empirical properties of M -squared, a measure of cash flow dispersion used in designing duration-hedged portfolios, are examined. Contrary to prior research, minimizing M -squared is not independent of the stochastic process and the minimum M -squared portfolio is a ‘bullet’ only under a specific, convexity condition derived in the paper. Using a data base of default-free, Government of Canada bonds to set up minimum M -squared, duration-matching portfolios, we find that the convexity property does not hold in general and that minimum M -squared portfolios fail to hedge as effectively as portfolios including a bond maturing on the horizon date.

Duration and Bond Portfolio Analysis: An Overview

In recent years, academicians and practitioners have been using the concept of duration more frequently in the analysis of debt securities. Although the use of duration has greatly expanded our insights into the behavior of bond prices and bond risk, it has given rise to a considerable degree of confusion and misunderstanding. The purpose of this review paper is twofold: (1) to clarify the record on what duration is and is not and what it can do and cannot do, and (2) to discuss the appropriate uses of duration in the analysis of security portfolios.

Immunization Strategies for Funding Multiple Liabilities

A number of recent papers have shown that it is possible for an investor to immunize a portfolio of default and option-free coupon bonds so that the return realized over a given planning period will never be less than that promised at the time the bonds were purchased. In this way, a future fixed dollar liability may be discharged with certainty by acquiring an asset portfolio with a market value equal to the present value of the liability and setting its appropriate duration equal to the time remaining to the date of discharge. However, most investors have more than one liability to discharge. In his seminal article in 1952, F. M. Redington showed that a stream of liabilities may be immunized if an asset portfolio having the same present value as the liabilities is selected so that:1. its duration is equal to the duration of the liabilities; and2. “the spread of the value of asset-proceeds about the mean term (duration) should be greater than the spread of the value of the liability†([16], p. 191).

Duration gaps with futures and swaps for managing interest rate risk at depository institutions

Duration gaps for depository institutions are derived for economic net worth, economic net income, and book value interest income. The duration gaps previously constructed for on-balance sheet accounts are expanded to off-balance sheet accounts, including futures contracts and swap agreements. These expanded duration gaps are indicators of the sensitivity of the market value of net worth and income measures to interest rate fluctuations. Managers of depository institutions can establish these duration gaps as targets and can utilize futures markets and swap agreements to affect the target values. The developments in this article are based on a single factor model of interest rate movements, but the results can be extended.

The Ho-Lee Binomial Stochastic Process and Duration

GERALD 0. BIERWAG is the Ryder Systems professor of finance at Florida International University in Miami. stochastic interest rate processes are usehl for valuing a variety of interest rate-conclaims. Two leading binomial interest rate used by practitioners are those devised by Ho and Lee [1986] and by Black, Derman, and Toy [1988, 19891. Kalotay, Willrams, and Fabozzi (KWF) [1993] describe the elements of the latter model. In these models, duration can be calculated as the percentage change in a security’s price per unit shift in an interest rate structure, ceteris paribus. KWF call this the “effective duration,” computed as the percentage change in a security’s price resulting from an upward or downward unit shift of the entire binomial interest rate lattice. It is a simulated duration analogous to that devised as the option-adjusted spread. Although “effective duration’’ may be a very useful indicator of the interest rate volatility of a security, it has some deficiencies. This duration is not equal to the maturity of a zero-coupon bond, and it consequently can be used neither as an immunizing duration in the traditional sense nor as a precise hedging duration. Nor is there any assurance that all portfolios having the same duration wdl have the same returns. There is, however, a measure of duration embedded in the Ho-Lee binomial model that provides a one-to-one correspondence with the returns on interest rate-sensitive securities. Indeed, this duration measure even appears as a parameter in the Ho-Lee development, although it has never been recognized as a duration measure. It is possible in the Ho-Lee model to define a specific duration (or set of durations) for virtually all portfolios of interest rate-sensitive securities. The oneperiod return on any portfolio of securities can be

Bond Portfolio Strategy Simulations: A Critique

In recent years, a number of studies have been published evaluating alternative bond portfolio strategies. These studies basically simulate risk-return characteristics for a variety of strategies designed for use by financial institutions. Typical strategies considered include portfolios of bonds that have laddered or barbell (dumbbell) maturity structures. In laddered strategies, bonds are spaced evenly among a number of consecutive maturities, while in barbell strategies, bonds are concentrated in short and long maturities. The results of these studies tend to differ and conflict. For example, in a recent article in this journal, Fogler, Groves, and Richardson (FGR) conclude that “dumbbell portfolio strategies are not as efficient as indicated by previous analyses.†Among the previous studies to which they refer is one by Watson, who concluded that “portfolios split between a spaced group of short maturity bonds and a longer investment security†(barbell portfolios) are most efficient. Similar results are reported by Wolf and by Bradley and Crane.

Pricing Eurodollar futures options with the Ho and Lee and Black, Derman, and Toy models: An empirical comparison

This article compares empirically the Ho and Lee (1986) and Black, Derman, and Toy (1990) discrete‐time debt option pricing models in the pricing of Eurodollar futures options over the period from March 1997 through February 1998 using daily data. The results indicate that both models performed well. The average absolute pricing errors over the sample period were less than one tick (0.01) in every case. The Black, Derman, and Toy model slightly outperformed the Ho and Lee model in the pricing of in‐the‐money call options and out‐of‐the‐money put options over the period studied.

Durations for portfolios of bonds priced on different term structures

Abstract This paper develops the duration of a portfolio of bonds that trade on different term structures because of, say, differences in credit quality. Such portfolios are widely held by investors. In contrast to the duration of a portfolio of bonds priced on the same term structure, the duration of a portfolio of bonds priced on different term structures is shown to be a function of the future values of the composite securities at the portfolio duration date rather than their present values. Portfolio duration expressions for such portfolios are derived for alternative assumptions about the stochastic process driving movements in interest rates across securities. It is also shown that portfolio durations based on present-value weights are a special case of those based on future-value weights.

Interest rate effects of commercial bank underwriting of municipal revenue bonds: Additional evidence *

This study analyzed data for municipal revenue bond issues sold in 1979 to identify the impact of commercial bank eligibility on the interest cost to the issuing state or local government. The empirical evidence developed suggests that commercial bank eligibility had no statistically significant effect on the interest cost of municipal revenue bonds sold competitively or by neogotiation, when other factors explaining the interest cost are taken into account properly. Nor did bank eligibility increase the power of the model to explain the interest cost of the bono issues. The theoretical and empirical weaknesses of some earlier studies that report opposite findings are analyzed.

Duration as a measure of basis risk: The wrong answer at low cost — Rejoinder

ultekin and Rogalski (G-R) claim in their 8 note that “business people-are wasting a lot of time and effort implementing duration-based analysis, especially analysis derived using DI [Macaulay] .” The authors basically reiterate arguments made in the Journal of Business [1984]. Despite this claim, duration analysis has continued to increase in popularity among practitioners to the point where our 1983 statement, cited by G-R, that ”duration promises to become as widely used [for bonds] as beta is for equities” is almost a reality (Kaufman [ 19831). Moreover, a recent survey article in the Journal of Economic Literature by Professors Gerald Faulhaber and William Bauinol [ 19881 cites duration along with portfolio selection, beta, and option pricing as prime examples of ”economists’ contribution to financial practice”