The Sharpe ratio, on the other hand, examines the ratio of the excess return on an asset to its standard deviation (or risk). That is, is the Sharpe ratio.
For pricing, recall that the one period return (ignoring dividends) is , where P is the asset's market price and the subscripts index time. Thus, according to the CAPM, and substituting for ri:
What's interesting here is that the asset's beta and the market excess return together price the asset. If the asset has a beta of zero (indicating that it doesn't covary with the market), then P0 is simply the discounted (at the risk-free rate) value of the payoff P1.
The payoff, P1 is usually not known with certainty. As such, it is a random variable that is state dependent. We are interested in its expected value E(P1). It is reasonable to think that the expected future price is a function of the stream of cash flows, or dividends, if we are thinking about a share of stock. Thus, we can write a simple dividend discount model as:
More importantly, we can show how the CAPM extends interpretation of the discount rate used in the DDM of Chapter 4. There, the pricing model discounted expected future cash flows at a constant rate, r:
The capital asset pricing model produces a logically consistent result but uses a more meaningful discounting function—we replace r with .