Answer the following questions on the Markowitz portfolio theory.

1. a Define efficient frontier. (3 marks)

2. b Given that there are only two risky assets in the market, according to the Markowitz portfolio theory, what value of the correlation between these two risky assets will provide the highest diversification effect when a portfolio of these two assets is constructed? Please explain. (3 marks)

3. c Following on from part (b), does a correlation of zero provide a diversification effect to a portfolio of two risky assets? Please explain. (3 marks)

4. d Suppose you are considering an investment in two risky assets. The following table summarizes the risk and return characteristics of the above two risky assets.

Security

Asset E Asset D

Expected return

20% 8%

Standard deviation

15% 10%

The correlation of rates of return between the two risky assets is 0.2.

Using the above information, determine the expected return and standard deviation of the optimal risky portfolio consisting of the two

risky assets. Show your calculations.

(15 marks)

5. e Given that a risk-free asset with a return of 2% is available, what is the Sharpe ratio of the optimal risky portfolio in part (d)? Show your calculations. (4 marks)

6. f Suppose a risk-free asset with a return of 2% is available and assume that the optimal market portfolio is with an expected return of 10% and a standard deviation of 8%.

   If a risk-averse investor can only accept a risk of a standard deviation of 5%, what would be the expected return of the optimal portfolio invested in by this investor? What is the portion of risk-free asset in this optimal portfolio? Show your calculations.

   (12 marks)