Mean-Variance Weights

Problem

Compute the optimal two-asset mean-variance weights with a budget constraint.

For expected returns mu1, mu2, variances var1, var2, and risk aversion gamma, return [w1, 1 - w1] with w1 = (mu1 - mu2 + gamma * var2) / (gamma * (var1 + var2)). Return [0.5, 0.5] when the denominator is zero.

Hint

Higher risk aversion tilts the allocation away from the higher-variance asset.

Test cases

case 1

in: [0.1,0.05,0.04,0.01,2]

expected: [0.7000000000000001,0.29999999999999993]

case 2

in: [0.08,0.08,0.09,0.01,3]

expected: [0.1,0.9]

case 3

in: [0.05,0.1,0.04,0.04,1]

expected: [-0.12500000000000003,1.125]

Starter codePython

def mean_variance_weights(mu1, mu2, var1, var2, gamma):
    # Returns [w1, w2]
    # Your code here
    pass

3 test cases · run your code against them in the editor