Knowledge that Transforms

The Sharpe model of capital asset pricing under conditions of risk has received wide theoretical acclaim and empirical support. This paper presents an econometric study of the model with the following objectives: (a) to show the effect of measuring the model's independent variables incorrectly; (b) to derive and use a new procedure for empirically testing the adequacy of the model as it is currently formulated.

Until very recently, in most work on normative models for capital investment planning, it has been assumed that availability of capital is unconstrained; i.e., that money may be freely borrowed or lent at a single market rate of interest, and that no other constraints affect the proper choice of available productive investment projects to be undertaken. Since practical situations almost universally do involve such constraints, the traditional theories have, for the most part, been an unsatisfactory guide to achievement of optimal capital investment behavior in the real world.

The objectives of this paper are to derive the relationship of the geometric mean of a distribution of positive values to the conventional first four moments — arithmetic mean, variance, absolute skewness, and absolute kurtosis — and to empirically evaluate certain approximations involving these four moments for estimating the geometric means of monthly and annual holding period returns for individual stocks and for portfolios. The geometric mean is shown to be positively related to the arithmetic mean and absolute skewness and negatively related to variance and absolute kurtosis. In the case of a normal distribution a very good approximation to the geometric mean is revealed to be a function of just the arithmetic mean and variance. Additionally, empirical evidence indicates that even though a number of the monthly and annual distributions deviate significantly from normality, the approximation involving only the mean and variance produces quite accurate estimates of the geometric means of these distributions.

The question “What's in a bond rating?” has been asked at least since 1909 when such ratings were started in the United States. Informed persons who answer this question typically admit that ratings depend in part on readily available statistics on a firm's operations and financial condition. Examples of such statistics are earnings coverage, leverage ratios, and profit rates.

John Lintner, The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets, The Journal of Financial and Quantitative Analysis, Vol. 4, No. 4 (Dec., 1969), pp. 347-400