Stochastic Discount Factors

The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views on possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself. Yields vary across different investment opportunities and their interrelations are difficult to explain. For the same agent, a different discounting factor has to be used for every separate valuation occasion. If, however, one is ready to accept discounting that varies randomly with the possible outcomes, and therefore accepts the concept of a stochastic discount factor, then an economically consistent theory can be developed. Asset valuation becomes a matter of randomly discounting payoffs under different states of nature and weighing them according to the agent’s probability structure. The advantages of this approach are obvious, since a single discounting mechanism suffices to describe how any asset is priced by the agent. 0. Introduction Within active and liquid financial markets, economic agents are able to make investment decisions. Capital is allocated today in exchange for some future income stream. If there is no uncertainty regarding the future payoff of an investment opportunity, the yield that will be asked on the investment will equal the risk-free interest rate prevailing for the time period covering the time of investment until the time of the payoff. However, in the presence of any payoff uncertainty when undertaking an investment venture, economic agents will typically ask for risk compensation, and thus for some investment-specific yield, which will discount the expected future payoff stream. The yields, that particular agents ask for, depend both on their statistical views on possible future outcomes, as well as their attitudes towards risk. Yields vary across different investment opportunities and their interrelations are difficult to explain. For the same agent, a different discounting factor has to be used for every separate valuation occasion. If one, however, is ready to accept discounting that varies randomly with the possible outcomes, and therefore accepts the concept of a stochastic discount factor, then a very economically consistent theory can be developed. Asset valuation becomes a matter of randomly discounting payoffs under different states of nature and weighing them according to the agent’s probability structure. The advantages of this approach are obvious, since a single discounting mechanism suffices to describe how any asset is priced by the agent. Date: January 8, 2010.