## Prices And The Capm

Up to now we have discussed equilibrium in terms of rate of return. In the introduction to this chapter we mentioned that the CAPM could be used to describe equilibrium in terms of either return or prices. The latter is of importance in certain situations, for example, the pricing of new assets. It is very easy to move from the equilibrium relationship in terms of rates of return to one expressed in terms of prices. All that is involved is a little algebra.

Let us define

Pi as the present price of asset i.

PM as the present price of the market portfolio (all assets).

7. as the dollar value of the asset one period hence. It is market value plus any dividends. Ym as the dollar value of the market portfolio one period hence including dividends, cov(YjYM) as the covariance between Yi and YM. vss(Y^) as the variance in YM. rFas{\ +Rf). The return on asset i is

Substituting this value for A. in Equation (13.6) and rearranging yields

Ending value - Beginning value Beginning value

In symbols,

Similarly,

Substituting these expressions into Equation (13.3) yields

y. KYyM Fm

Similarly,