Abstract--Investment Horizon and the Functional Form of the Capital Asset Pricing Model: An Empirical Investigation

Abstract

This paper derives a generalized Capital Asset Pricing Model (CAPM) to allow the investment horizon to be explicitly introduced into the risk-return relationship of capital asset pricing. It is shown that the systematic risk estimated from this generalized CAPM includes finite systematic risk, Jensen systematic risk, and Cheng–Deets (CD) systematic risk as a special case. From the relationship among the finite horizon type CAPM, the Jensen instantaneous type CAPM, and the generalized CAPM, it is found that the investment horizon problem can be treated as a functional form problem which is similar to determining whether a Cobb-Douglas type or a CES type production function is appropriate in estimating a production relationship. As the rates of return on security and market rates of return are log normally distributed, it is shown that Jensen instantaneous systematic risk is identical to CD instantaneous systematic risk. Under this circumstance, it also is shown that the finite systematic risk is approximately equal to the instantaneous systematic risk times an adjustment factor.