Stephen M. Schaefer, Taxation and Bond Market Equilibrium in a World of Uncertain Future Interest Rates: Comment, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 5 (Dec., 1981), pp. 773-777

Stephen M. Schaefer, Discussion: Analyzing Convertible Bonds, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 4, Proceedings of 15th Annual Conference of the Western Finance Association, June 19-21, 1980, San Diego, California (Nov., 1980), pp. 931-932

This paper develops a new methods for measuring tax effects in bond markets and presents empirical results for British Government Securities. The basic idea is to construct a least cost portfolio which, for investors in a given tax bracket, dominates a given bond. A portfolio is said to dominate a bond if it provides cash flows which are at least as great in every period, and has a lower price. In effect our method calculates an upper bound on the value of a bond to investors in a given tax bracket. The results demonstrate (i) the existence of clientele effects and (ii) the absence of an ‘effective tax rate’.

It has been said [2, 4, 5, 6, 7, and 8], and it seems to be widely accepted, that the geometric mean of the price relatives of a group of securities can be interpreted as the return which would have been earned on a portfolio of those securities, managed continuously over time to maintain an equal money investment in each security. This is a theoretical concept which could not be implemented literally by a portfolio manager, but it can still be treated rigorously in a mathematical sense. In a recent paper in this journal Rothstein [8] defined continuous reallocation as the limiting case of a policy which does have an operational definition. He showed that the index corresponding to a policy of the equalization of dollar investments approaches the geometrically averaged index as its limiting value. We shall argue that this interpretation of the geometric mean is a misleading one, since it depends upon assumptions which imply serious market inefficiencies.

Stephen M. Schaefer, Conditional Predictions of Bond Prices and Returns: Discussion, The Journal of Finance, Vol. 35, No. 2, Papers and Proceedings Thirty-Eighth Annual Meeting American Finance Association, Atlanta, Georgia, December 28-30, 1979 (May, 1980), pp. 417-419

Abstract Value-at-risk methods which employ a linear (“delta only”) approximation to the relation between instrument values and the underlying risk factors are unlikely to be robust when applied to portfolios containing non-linear contracts such as options. The most widely used alternative to the delta-only approach involves revaluing each contract for a large number of simulated values of the underlying factors. In this paper we explore an alternative approach which uses a quadratic approximation to the relation between asset values and the risk factors. This method (i) is likely to be better adapted than the linear method to the problem of assessing risk in portfolios containing non-linear assets, (ii) is less computationally intensive than simulation using full-revaluation and (iii) in common with the delta-only method, operates at the level of portfolio characteristics (deltas and gammas) rather than individual instruments.

Richard Brealey, Stephen Schaefer, Term Structure with Uncertain Inflation, The Journal of Finance, Vol. 32, No. 2, Papers and Proceedings of the Thirty-Fifth Annual Meeting of the American Finance Association, Atlantic City, New Jersey, September 16-18, 1976 (May, 1977), pp. 277-289

This paper estimates real term structures from cross-sections of British government index-linked (‘realrd) bond prices. The Cox, Ingersoll, and Ross (1985) model is then fitted to the same data; the model closely approximates the shapes of the directly-estimated term structures. In contrast to similar studies of the nominal term structure, the long-term zero-coupon yield is quite stable, as the CIR model predicts, and in common with previous studies, the level of implied short rate volatility corresponds well with time series estimates. The other parameters, however, are often highly correlated and intertemporal parameter stability is rejected.

We investigate how the dynamics of corporate debt policy affect the pricing of corporate bonds. We find empirically that debt issuance has a significant stochastic component that is imperfectly correlated with shocks to asset value. As a consequence, the volatility of leverage is significantly higher than asset volatility over short horizons. At long horizons, the relation between leverage and asset volatility is reversed due to mean reversion in leverage. We incorporate these stochastic debt dynamics into structural models of credit risk, both standard diffusion models as well as newer models with stochastic volatility and jumps. Including stochastic debt gives more accurate predictions of credit spreads in both the cross-section and the time series.