Multiplicative Risk Premiums

Abstract

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, α t , to each period's expected cash flow, μ t , to produce a certainty-equivalent flow, α t μ t . The certainty-equivalent flow is then discounted with the riskless rate of interest, α t μ t /(l + i) t . Although there has been much discussion of α t , researchers have not derived explicit expressions for α t , 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 α t , (2) derive formal expressions for a for α t three special cases, (3) discuss relationships between α t and σ t , the standard deviation of the period t cash flow, (4) formally derive the period t risk-adjusted discount rate, k t , 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.