Question

10. Assume you can invest in the risk free interest rate rf but that in order to borrow you need to pay a higher rate ſv. You can also invest in risky securities. a. Draw the investment opportunity line, and the mean-variance efficient portfolios. b. Where will highly risk averse investors invest? What about very risk tolerant investors? c. Where will be the market portfolio? (assume all securities are correctly priced).

Answer 1

The solution to part a)

In the image below, the first graph is about the investment opportunity line. We have plotted the return of the portfolios on the y-axis and the standard deviation of the portfolios on the x-axis. Point B to A represents the minimum variance portfolios and point B to C represents the efficient frontier as per the mean-variance theory, which means all the portfolios that are on efficient portfolio are similar and no portfolio is better than the other.

Efficient Portfolio Opportnity line Efficient fronte 168 Thoifference OLM Efficient "Fronter

Solution b)

A risk-averse investor desires more return for higher risk hence he will invest in Minimum variance portfolios i.e. in risk-free securities. A risk-tolerant investor will invest in risky securities on the efficient frontier.

Solution c)

Since all the securities are correctly priced, in order to find out the optimal market portfolio we will draw a risk-return indifference curve. The market portfolio (point M) will be found at the point of tangency between the efficient frontier and a risk-return indifference curve which is represented by Point M in the above image.

In order to identify the market portfolio