Question

Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance

Answer 1

One can easily identify the optimal risky as the point of intersection between the efficient portfolio and the risk free rate.

Below this point of tangency , lies all the portfolios between the risk free rate and the efficient portfolio which are consisting of combinations of the market portfolio and the risk free rate. Above this point of tangency, lies all the portfolios between the risk free rate and the efficient portfolios, which  consists of the optimum risky portfolio purchased on margin.

Thus, the separation theorem separates the investing and financing decisions. That is, all investors will invest in the same optimal risky portfolio, and adjust the risk level of the portfolio by either lending (investing in U.S. Treasuries, i.e., lending to the U.S.government) or borrowing (buying risky securities on margin).