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:

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 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.