Practical Asset Allocation

MGF 696 Project 2

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:

US Large Cap Equity

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

International Large Cap Equity

Emerging markets

Private Equity

Cash

US Fixed Income

Hedge Funds

Infrastructure

Private natural resources

Asset allocation

Simulate annual normal returns for a period of 10

years. Simulate 1,000 scenarios.

Start with a random set of weights to each asset

class. Simulate the portfolio returns.

Start with an initial amount (at year 0) of $1,000 mil.

Calculate the compounded returns after 10 years.

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

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.

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%.

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