Joel R. Barber

Immunization Using Principal Component Analysis

oped a useful method for classifying term structure shifts. A given shift is thought of as a vector whose elements correspond to rate changes at different maturity dates. Viewed in this manner, Fisher-Wed immunization protects a bond portfolio against a shift in the direction of a vector with all components equal. Different duration measures given in the literature are designed to protect portfolios against term structure shifts in a particular direction. Given that we do not know a priori the direction in which the term structure will shift, we are faced with the practical problem of choosing the best single direction in which to anticipate a shift. This is an important problem, because the success of an immunization strategy depends upon how well the assumed term structure model approximates reality. A more general and accurate model allows the term structure to shift in multiple directions. Under a multiple-direction model, an immunized portfolio must be protected against shifts in each fundamental (independent) direction. The problem is determining the set of fundamental directions. The only guide we have is the history of term structure movements. This article shows how principal component I

Credit Spread Changes and Equity Volatility: Evidence from Daily Data

We investigate the determinants of daily changes in credit spreads in the U.S. corporate bond market. Using a sample of liquid investment grade and high‐yield bonds, we show that both systematic bond and stock market factors as well as idiosyncratic equity market factors affect changes in the yield spread at the daily frequency. In particular, we find that increase in stock market volatility has a positive effect on changes in the spread of corporate bonds over the corresponding Treasuries beyond that captured by standard term structure variables. Our results show that there is an almost contemporaneous inverse relationship between changes in the bond yield spread and the stock return of the issuing firm.

A minimax risk strategy for portfolio immunization

Abstract This paper develops a minimax immunization strategy for an infinite factor interest rate model. The risk of a portfolio of cash flows is measured as the maximum sensitivity of the portfolio value. The objective is to choose the portfolio whose maximum sensitivity over a set of possible interest rate shocks is minimum.

A Note on Approximating Bond Price Sensitivity Using Duration and Convexity

he interest rate elasticity of the price of a bond is given by the duration (Hicks [1946]). Because the price-yield relationship is non-linear, the T duration is an accurate approximation of bond price sensitivity for small yield changes. For this reason, many researchers (Bienvag, Kaufman, and Latta [1988] and Christensen and Sorensen [1994], among others) approximate the price sensitivity with the first two terms of a Taylor series expansion of the bond price formula:

Arbitrage opportunities and immunization

It is often argued that an immunization strategy violates arbitrage-free equilibrium. Because immunization is a static concept, we contend that this argument is not valid. This paper examines the immunization strategy in a dynamic setting, and shows that global immunization is feasible for any arbitrage-free affine term structure model, including the parallel shift model. Further, we show that immunization does not violate arbitrage-free pricing because the cost of immunization over time is positive. Consequently, immunization strategies based upon commonly used duration, measures are not theoretically unsound.

Bond immunization for additive interest rate shocks

This paper explores bond immunization for additive term structure models. This class of term structures contains many models that are commonly used in the duration and immunization literature. We establish the necessary and sufficient conditions for immunization and prove the existence of a bond portfolio that satisfies the immunization condition. Based upon the immunization condition, we develop a general definition of duration that applies to any additives term structure model.

Bank failure, risk, and capital regulation

This paper examines the effect of capital regulation on bank risk. It is shown that an increase in the capital-to-asset ratio reduces the riskiness of a banks equity capital. Nevertheless, the probability of bank failure increases. The reason for this result is that the probability of bank failure depends upon both the risk and return of the asset portfolio. An increase in the capital requirement results in an optimal portfolio with a risk-return combination that has a higher probability of bank failure.

A Simple Procedure for Computing the Present Value of Non-Annual Damages

Virtually all literature concerning the present-value compensation for damages due to personal injury, wrongful death, and medical malpractice assumes that awards are based on the present value of year-end projected losses. ~ A casual survey of expert testimony reveals that the practice of assessing the present value of economic losses is also based on year-end projections. Year-end losses are the sum of losses projected to occur over a given year. For example, year-end wage losses are often based on annual salaries reported in federal income tax records or based on average yearly wages reported in the Bureau of Labor Statistics. When damages, like the loss of wages, loss of services, and future medical care, are likely to occur frequently within a year, awards based on the present value of year-end losses are inadequate. The purpose of this paper is to develop a simple formula for adjusting the conventional year-end present value to reflect losses that are equal and spaced periodically throughout the year. 2 We show that the present value of equal periodic losses is a constant adjustment to the conventional year-end present value. The constant adjustment does not depend upon the pattern of year-end losses or the projected number of years of loss.

Credit Spreads and Regime Shifts

The authors use data on a large sample of investment-grade and high-yield corporate bonds of non-financial firms to investigate the stability of the relationship between yield spreads and both Treasury term structure and market risk variables. The sample spans before, during, and after the recent financial crisis. Regression model estimates reveal a negative relationship between credit spread changes and changes in the term structure variables, as well as a significant effect of stock market conditions, bond volatility, and aggregate liquidity on spreads. Results from a Markov switching-regime model confirm the presence of two regimes and show different effects of certain spread determinants undereach regime.