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 rate-of-return on non-marketable assets held by individual i, and let
be the vector of covariances with the rates-of-return on marketable assets. The individual maximisation problem then becomes:
Differentiating with respect to x and setting the derivative equal to zero gives:
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 non-marketable 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 non-marketable assets.
Aggregating individual demand and imposing the market clearing condition, gives:
where φ is the ratio of the total value of non-marketable 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 non-marketable assets.