QUESTION ONE
This question concerns efficient portfolios and Markowitz Diversification.

a. Discuss how a given investor chooses an optimal portfolio. Is this choice of portfolio always a diversified portfolio, or could it be a single asset? Explain your answer.
[5 marks]

b. Compared with an investor who can only invest in risky assets, (i) describe and (ii) graph how the return-to-variability ratio can be improved for this investor, assume that the investor can invest in a portfolio of risky stocks and can lend or borrow at the risk-free rate.
[10 + 10 marks]

c. When a risk-free rate is available (i) explain and (ii) graph how two investors with different risk aversion levels will choose the same portfolio of risky assets but will invest different proportions of their entire wealth in this portfolio.
[10 + 5 marks]

d. Suppose M is the tangent portfolio of risky assets (tangent to the line which intercepts the risk-free rate, Rf) with an expected return of 12% and a standard deviation of 20%. Assume the risk-free rate is 4%. Suppose investor A invests 30% of the wealth in the M and 70% in the risk-free asset and suppose investor B invests 110% of the wealth in the M and borrows 10% at the risk-free rate. Calculate the expected returns and standard deviations
for these two investors.