Mayers [1972; 1973; 1976] and Brito [1977; 1978] have examined the effect of nonmarketable assets, such as human capital, on the CAPM. Let and be the expectation and the variance, respectively, of the rateofreturn on nonmarketable assets held by individual i, and let be the vector of covariances with the ratesofreturn on marketable assets. The individual maximisation problem then becomes:
Differentiating with respect to x and setting the derivative equal to zero gives:
where
is the vector of coefficients from the regression of the return on the individual's nonmarketable assets, and the marketable security returns.
Equation (5.10) shows that separation no longer holds with nonmarketable assets. This reflects the ability of investors to take hedging positions in the market, in order to eliminate as much as possible of the risk exposure in holding nonmarketable assets.
Aggregating individual demand and imposing the market clearing condition, gives:
where φ is the ratio of the total value of nonmarketable assets, to the total value of marketable assets and is the vector of covariances between the returns of marketable assets and the total return on nonmarketable assets.
