Assignment Detail

MGF 696 Practical Allocation Project – MATLAB Programming – Practical Asset Allocation

Returns assumptions –

You are to assume that various asset classes have normal returns, independent in time.

Use assumptions from Mercer (posted).

Assume that returns are normally distributed.

If you use Excel, email me your covariance matrix, and I will email you back the Cholesky matrix L.

Asset classes – Use the following asset classes:

1. US Large Cap Equity

2. US Small Cap Equity (as a proxy for Venture Capital)

3. International Large Cap Equity

4. Emerging markets

5. Private Equity

6. Cash

7. US Fixed Income

8. Hedge Funds

9. Infrastructure

10. Private natural resources

Asset allocation –

1. Simulate annual normal returns for a period of 10 years. Simulate 1,000 scenarios.

2. Start with a random set of weights to each asset class. Simulate the portfolio returns.

3. Start with an initial amount (at year 0) of $1,000 mil. Calculate the compounded returns after 10 years.

4. Each year, assume a payout rule calculated as follows:

– Payout in year 0 is 4% of the fund value at year end.

– Payout in year (t+1) is the payout in year t, increased by inflation (=cash returns).

– If the payout is lower than 4% of the fund value, pay 5% of the fund’s value.

– If the payout is larger than 6% of the fund value, pay 5%.

Asset allocation –

1. After subtracting the payouts each year, calculate the downside risk of the fund from the cumulative cash rate over 10 years. Thus, for each given set of weights, you can calculate one downside risk number.

2. For each expected return x% between 5% and 11% per year, in increments of 0.5%, find the set of weights that are all >0 and that minimize the 10-year downside risk of the fund, relative to investing in cash, subject to the expected return being x%.

3. Plot the downside risk – expected return efficient frontier you got in part 2.

Asset allocation –

You now have a set of efficient portfolios.

Consider the following objectives:

– Minimize the possibility that the returns drop below -15% in a year

– Minimize the possibility that the returns will be higher than 30% in a year

– Maximize the probability that the payout hits the lower bound of 4%

– Minimize the probability to hit the 6% upper payout barrier

– Maximize the probability that the cumulative return is larger than 6% annual for all the 10 years

– Minimize inter-temporal payout volatility

Give each of these criterion a score.

Normalize scores across portfolios.

Weight these scores according to your preferences.

Create the fund’s utility function by aggregating the scores.

Calculate the utility of each efficient portfolio.

Find the portfolio that maximizes the utility function.