## Act2 28ctM

Summarizing these results, the trade-off between the incremental risk premium and incremental risk, referred to as the marginal price of risk, is given by the ratio

and equals one-half the market price of risk of equation 9.5.

Now suppose that, instead, investors were to invest the increment 8 in GM stock, also financed by borrowing at the risk-free rate. The increase in mean excess return is

This portfolio has a weight of 1.0 in the market, 8 in GM, and —8 in the risk-free asset. Its variance is 12ctM + 82ctgm + [2 X 1 X 8 X Cov(rGM,rM)].

The increase in variance therefore includes the variance of the incremental position in GM plus twice its covariance with the market:

Dropping the negligible term involving 82, the marginal price of risk of GM is

In equilibrium, the marginal price of risk of GM stock must equal that of the market portfolio. Otherwise, if the marginal price of risk of GM is greater than the market's, investors can increase their portfolio reward for bearing risk by increasing the weight of GM in their portfolio. Until the price of GM stock rises relative to the market, investors will keep buying GM stock. The process will continue until stock prices adjust so that marginal price of risk of GM equals that of the market. The same process, in reverse, will equalize marginal prices of risk when GM's initial marginal price of risk is less than that of the market portfolio. Equating the marginal price of risk of GM's stock to that of the market results in a relationship between the risk premium of GM and that of the market:

2Cov(rGM, M 2ctM

To determine the fair risk premium of GM stock, we rearrange slightly to obtain rv \ Cov(rGM, rM) r y-'/ \ H m ^

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