1. Calculate the estimated expected return and standard deviation of the returns on the following investment portfolios. **Show your working.**

(10%)

2. Calculate the utility scores of two investors who currently hold all their wealth in Portfolio P. Investor 1 has a coefficient of risk aversion of 4: investor 2 has a coefficient of risk aversion of 8. Interpret these utility scores. **Show your working.**

(15%)

3. Sketch indifference curves for these two investors onto one set of axes. Use the utility scores you calculated in part b). Mark Portfolio P onto your diagram. Explain how the relative convexity of the curves is related to the risk aversion of the investors. **Show your working.**

(15%)

4. Assume that portfolio Q is now made available to these investors. Calculate their utility scores from this portfolio. Mark the portfolio onto your diagram. Based on the calculated utility scores, and on your diagram, explain which of the two portfolios each investor would prefer. If the two investors have the same preference, explain why this is the case. If the two investors differ in their preferences, explain why this is the case.**Show your working.**

(15%)

5. A third investor would be indifferent between portfolios P and Q. Calculate the coefficient of risk aversion of this third investor, based on this observation. Add the indifference curve of the third investor to the diagram, based on the utility score she would derive from either of these two portfolios.**Show your working.**

(15%)

6. Now form an investment portfolio R, which is an equally weighted combination of P and Q. Calculate the expected return and standard deviation of portfolio R. Evaluate portfolio R from the point of view of each of your three investors. Interpret your answer.**Show your working.**

(15%)

7. Identify and explain three limitations of your analysis.

(15%