1. Asset Classes 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 0.00%5.00%10.00%15.00%20.00%25.00%30.00% Expected Risk (standard deviation) Private Equity Hedge Funds Real Estate Intl Stocks US Stocks Bonds Expected Return Adapted from Will McLean’s 2/6/09 lecture http://users.iems.northwestern.edu/~armbruster/2009iems326/NUendowment.ppt

2. Math r i = expected return of asset class i C(i,j) = matrix of covariances x i = % allocation to asset class i Expected return = x T r Variance of return = x T C x

3. Optimization max x expected return s.t. standard deviation <= 10% max x x T r s.t. x T Cx <= (10%) 2 1 T x = 1