Knowledge that Transforms

Expectations theories of asset returns may be interpreted as stating either that risk premia are zero, or that they are constant through time. Under the former interpretation, different versions of the expectations theory of the term structure are inconsistent with one another, but I show that this does not necessarily carry over to the constant risk premium interpretation of the theory. Furthermore, I argue that differences among expectations theories are of 'second order" in a precise mathematical sense. I present an approximate linearized framework for analysis of the term structure in which these differences disappear, and I test its accuracy in practice using data from the CRSP government bond tapes.

This paper explores geometric relations, in mean-variance space, among the sample frontier, the maximum likelihood estimator, and two other estimators of the zerobeta return. It is also demonstrated that a partition of the portfolio space is determined by a family of parabolas; the zeros of each parabola are the maximum likelihood estimators associated with all portfolios on the parabola. This observation is the basis for an additional interpretation of the statistic of the Likelihood Ratio Test of portfolio efficiency without a riskless asset.

Duality theory is employed to provide necessary and sufficient conditions for portfolios on the minimum-variance frontier to have positive investment proportions in all assets. These conditions involve the feasibility of portfolios that have non-negative correlation with all assets and positive correlation with at least one. Using these results, several “qualitative” results concerning the signs of investment proportions in efficient portfolios are proved. It is argued that the conditions that ensure all-positive weights in efficient portfolios are intuitively compelling and are not unique to the CAPM. With large numbers of assets, however, the signs of weights in minimum-variance portfolios can be very sensitive to slight departures from these conditions due to, for example, sampling error.

James N. Bodurtha Jr., Integration vs. Segmentation in the Canadian Stock Market: Discussion, The Journal of Finance, Vol. 41, No. 3, Papers and Proceedings of the Forty-Fourth Annual Meeting of the America Finance Association, New York, New York, December 28-30, 1985 (Jul., 1986), pp. 614-616

This paper tests the effectiveness of techniques proposed by: Scholes-Williams; Dimson; Fowler, Rorke, and Jog; and Cohen, Hawawini, Maier, Schwartz, and Whitcomb to control for bias in beta estimates from thin trading and price adjustment delays. Each technique produces beta estimates that reduce the amount of this bias, but the amount of reduction in the best case is only 29%.