Eliezer Z. Prisman

Duration measures for specific term structure estimations and applications to bond portfolio immunization

Abstract This paper explores duration measures which are induced by a polynomial approximation to the stochastic process that governs the term structure. The paper reaches two main conclusions: (1) Complete immunization is possible only by holding a zero coupon bond if the polynomial is of a degree which is not less than two. Hence, for such polynomials, measures of immunization risk should be used to construct portfolios so as to minimize these risks. (2) The paper derives risk measures based on the polynomial stochastic process. It explores their connection to the Fong– Vasicek risk measure. This measure is a particular case of the risk measures developed here and is shown not to measure risk effectively for some stochastic processes.

A general model of the banking firm under conditions of monopoly, uncertainty, and recourse

Abstract We develop a stochastic programming model of the monopolistic competition banking firm. It assumes the bank faces a downward-sloping loan demand curve and is a price taker in securities markets. Uncertainty and liquidity requirements are incorporated. Bank decisions are made within a two-stage framework where realized disturbances that violate constraints can be rectified ex post at a cost. The results are: (1) Optimal loan and deposit rates are positive functions of the recourse penalty. (2) Asset/liability decisions are interdependent and elastically supplied deposits lower the loan rate. (3) The effect of uncertainty depends upon the penalty rate level.

Immunization as a maxmin strategy: A new look

The purpose of this paper is to broaden the analysis of immunization when it is viewed as amaxmin strategy. Several results are demonstrated which provide a new interpretation of maxmin strategy by using a more general theory of Lagrangians. We clarify the exact assumptions required for the duration strategy and the maxmin strategy to be equivalent in a world with taxes. It is shown that in a world with taxes the immunization strategy requires the portfolio to satisfy a constraint about the bond to be included, in addition to the duration constraint.

Conjugacy in quasi-convex programming

This paper develops a symmetric conjugate relation for quasi-convex functions. The concept of an evenly quasi-convex function is introduced and it is shown that this is the required property for a duality framework in quasi-convex programming.

Immunization in Markets with Tax-Clientele Effects: Evidence from the Canadian Market

Empirical immunization studies have considered the efficacy of immunization strategies, in which the durations of assets and of liabilities are equated , against a strategy involving maturity matching. However, all these studies have ignored tax effects. In the presence of tax-clientele effects , immunization requires that the portfolio consists only of bonds that are correctly priced for a particular clientele. Testing for these effects, therefore, requires the identification of the correctly priced bonds for the investors in the clientele. However, since bond prices contain noise, determining these bonds is still an unresolved problem. Consequently, an empirical test of the magnitude of the error caused by ignoring taxes may be an impossible task in some markets, and indeed has never been conducted. The Canadian bond market provides perfect laboratory conditions for such a test. Tax-clientele effects are present in the Canadian market, and among the clienteles is a representative clientele. This paper examines the tax effects on immunization strategies. The results show that the error caused by ignoring tax effects is not negligible, and practitioners should use immunization with reference to tax effects.

A Unified Approach to Term Structure Estimation: A Methodology for Estimating the Term Structure in a Market with Frictions

This paper develops a methodology for term structure estimation from a no-arbitrage condition in markets with frictions. The methodology unifies existing estimation procedures, such as the regression and linear programming approaches, and substantially broadens the class of useful estimation techniques. The estimators derived in this way are capable of reflecting actual market conditions, such as the asymmetry in the tax treatment of long and short positions and the higher financial cost of establishing a short position. The methodology is derived by applying the conjugate duality theory of mathematical programming.

Optimal bond trading and the tax-timing option in Canada

Abstract The goal of this paper is to determine whether the tax-timing option effect documented in the U.S. bond market exists outside the U.S. Examining Canadian tax rules suggests that the tax option effect is simpler and less valuable than in the U.S. This view is supported by simulations in the spirit of Constantinides and Ingersoll (1984) as well as by empirical tests conducted on bond triplets following Jordan and Jordan (1991).

Arbitrage, Clientele Effects, and the Term Structure of Interest Rates

This paper derives a new and intuitive estimation procedure for the term structure under potential tax arbitrage. No a priori assumptions regarding the equality of the prices and present values of bonds are made. The data are employed to determine whether this equality holds, and an appropriate estimator is thereby endogenously derived. The suggested estimator is based on the optimizing behavior of an investor in a market with frictions, and emerges directly from the solution of the dual of the no-arbitrage optimization problem. In addition, the proposed estimator benefits from being both theoretically sound and straightforward to apply.

Tests for tax-clientele and tax-option effects in U.S. treasury bonds

Abstract In markets with taxes the deviations of the price of a bond from its present value may be due to tax clientele and tax option effects. Detecting these effects is complicated by noise in bond prices. Previous empirical research has lacked a theory of how tax effects will influence the deviations in the presence of noise. This paper develops such a theory and demonstrates a methodology for detecting tax effects. In empirical tests the tax option effect comes through most clearly, but the existence of tax clienteles cannot be ruled out.

A duality approach to minimax results for quasi-saddle functions in finite dimensions

In this paper we show how saddle point theorems for a quasiconvex—quasiconcave function can be derived from duality theory. A symmetric duality framework that provides the machinery for deriving saddle point theorems is presented. Generating the theorems,via the framework, provides a deeper understanding of assumptions employed in existing theorems which do not utilize duality theory.