Your task in this assignment is to design an asset allocation for the superannuation fund of an individual who is investing to fund his retirement. The asset classes under consideration are:
- Australian equities (large cap)
- Australian equities (mid cap)
- Australian equities (small cap)
- Cash
- Australian government bonds
- International equities
- International government bonds
- Commodities
- Australian real estate
- Gold
Your client is currently 40 years old, and hopes to retire after 25 years (i.e. when he is 65). He currently earns $120,000 per year, before tax, and he requires his superannuation fund to provide an inflation adjusted pension of $120,000 per year, for at least 25 years after he retires. His superannuation fund is currently valued at $80,000, and you may assume that he will invest 13% of his gross annual salary in the fund per year. *You may assume further that your client's salary will grow at the annual long term inflation rate of 3% per year. *An individual may make tax- free superannuation contributions of up to 13% of his gross annual salary per year.
(1) What should the value of your client's superannuation fund be when he retires in 25 years' time, in order to fund his pension? You should assume that the contents of his fund will be invested in a money market account paying the same return as an equi-weighted portfolio of cash and Australian bonds, upon retirement. You should also assume that, after retiring, your client will make monthly withdrawals from this account, at the end of each month.
(2) Based on your previous answer, determine the target monthly return on your client's superannuation fund for the next 25 years. You should assume that his salary is paid at the end of each month, at which time he makes a monthly contribution to his fund.
(3) Generate the vector of expected monthly returns for the ten asset classes considered, as well as the covariance matrix for their monthly returns.
(4) Plot the minimal variance set generated by the asset classes above, with short-sales allowed, for expected monthly returns in the range of 0%-2%.
(5) Plot the minimal variance set generated by the asset classes above, with short-sales disallowed.
(6) Assuming that the monthly returns of the asset classes are jointly normally distributed, design an asset allocation for your client that maximizes the expected monthly return of his superannuation fund, subject to the following two constraints:
- Diversification: Between 5% and 15% of the fund should be invested in each asset class.
- Maximum drawdown: The probability of a monthly loss in excess of 1% should not exceed 10%.
(7) Write an analysis of your recommended asset allocation for your client, paying special attention to the following:
- Does your recommendation allow him to fund his retirement?
- Is the portfolio you have constructed efficient, when compared with portfolios on the efficient frontier with short sales disallowed? If not, how inefficient is it, and what is the source of the inefficiency?
- Justify the diversification constraint, by comparing the holdings of your recommended asset allocation with those of nearby portfolios on the efficient frontier with short sales disallowed.
- Explain the maximum drawdown constraint in nontechnical terms. What does it mean, and how should it manifest itself in the behavior of your client's fund? What is it designed to achieve?
(8) Assuming that the monthly returns of the asset classes are jointly normally distributed, generate a random sample of 1,000 monthly returns for your recommended asset allocation. Plot a histogram of these returns, and determine whether they appear to satisfy the maximal drawdown constraint. How does the average return of the sample compare with the expected return of your asset allocation?
(9) Assuming that the monthly returns of the asset classes are jointly normally distributed, calculate the 95% confidence interval for the value of your client's superannuation fund at the time of his retirement, based on your recommended asset allocation.