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’.

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

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.

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.

Are standard structural models able to explain credit spreads on corporate bonds? In contrast to much of the literature, we find that the Black-Cox model matches the level of investment-grade spreads well. Model spreads for speculative-grade debt are too low, and we find that bond illiquidity contributes to this underpricing. Our analysis makes use of a new approach for calibrating the model to historical default rates that leads to more precise estimates of investment-grade default probabilities. Received October 25, 2016; editorial decision January 12, 2018 by Editor Andrew Karolyi.

Stephen M. Schaefer, Eduardo S. Schwartz, A Two-Factor Model of the Term Structure: An Approximate Analytical Solution, The Journal of Financial and Quantitative Analysis, Vol. 19, No. 4 (Dec., 1984), pp. 413-424

We identify a new and important property of affine term structure models: at long maturities, the slope of the term structure of risk premia becomes “almost observable”. Exploiting this property by fitting models to long-maturity data dramatically improves the precision of estimates of risk premia and expected short rates across the term structure. In a Monte Carlo experiment we show that using rates with maturities up to 25 years, rather than 10 years as is standard in the literature, reduces the standard deviation of estimation errors in risk premia, expected short rates and term premia by over 70%. Applying this approach to US Treasury data, we find that variation in expected short rates accounts for a much larger share of variation in yields (and variation in term premia a correspondingly smaller fraction) than in the widely used estimates reported by the Federal Reserve. Accounting for time-variation in yield volatility is key to successful extraction of the risk premium information in long rates. Our approach therefore departs from much of the empirical literature in two important respects: it incorporates long-maturity yields and allows for time-varying yield volatility, whereas most existing studies ignore long-term yields and rely on constant volatility models.