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