| Research on the probability distribution of returns on risky investments over short differencing intervals has suffered from at least two serious defects. First, virtually all research in this area has been directed at univariate models, e.g., such models as the stable paretian, Student t, lognormal-normal, and compound events. Second, research on the market model has not kept pace with return distribution research; the linear market model has remained unchanged since its inception. The analysis presented here, cast in a mean-variance (M-V) framework, is a step toward eliminating these defects.;The function and role of a return distribution is argued to include provision of implications for the relevant measure of security risk (as provided by M-V theory), as well as data description and conformity with a utility function. The paper's major premise is that a generalization of what has been commonly known as the logistic distribution can best fulfill this role. Intuitive support for the logistic model is argued, and its important properties are developed. Economic interpretations are provided, and several implications of the model are explored. Implications for the relevant measure of security risk are investigated in some detail, and a wide range of future research is suggested. A major conclusion is that, under the logistic hypothesis, a stock's risk measure is a function of the level of return on the market portfolio; a related result is that subjective belief about next period's return on the market portfolio can affect an investor's portfolio selection. |
