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Multiplicative Risk Premiums

Published online by Cambridge University Press:  06 April 2009

Douglas D. Gregory
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Extract

The certainty-equivalent method of evaluating risky investments has been widely discussed in the literature ([2], [5], [14, p. 356], [19], [20]) and consists of applying a multiplicative factor, αt, to each period's expected cash flow, μt, to produce a certainty-equivalent flow, αtμt. The certainty-equivalent flow is then discounted with the riskless rate of interest, αtμt/(l + i)t. Although there has been much discussion of αt, researchers have not derived explicit expressions for αt, relying instead on ad hoc graphs [24, p. 328] or arguments involving mean-variance indifference curves [2] which may not even exist ([4], [12], [22], [23]). In this paper, I will (1) provide a rigorous definition of αt, (2) derive formal expressions for a for αt three special cases, (3) discuss relationships between αt and σt, the standard deviation of the period t cash flow, (4) formally derive the period t risk-adjusted discount rate, kt, from assumptions concerning the decision maker's (d. m.'s) risk preferences and cash flow distribution, and (5) apply the preceding results to a specific problem involving calculation of the risk-adjusted present value of an uncertain cash flow stream.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 13 , Issue 5 , December 1978 , pp. 947 - 963
Copyright
Copyright © School of Business Administration, University of Washington 1978

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References

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