Suppose there are three assets, and the first asset has volatility 18%, the second asset has volatility 16%, and the third asset has volatility 16%. Suppose also that the first two assets' returns are correlated with each other with correlation coefficient 0.7, but the third asset is not correlated with the first two assets.
Suppose the risk free rate is 2%, and the expected returns of the three assets are 7%, 4% and 5% respectively.
Now consider the efficient portfolio of risky assets, i.e. the "one fund" F. What is the weight of the first asset?
Answer should be 0.87 (87%)
What I have done so far: Using matrix notation: M(covariance matrix)* v(vector of unscaled weights) = r (mean return value)- risk free rate
Step1. I constructed M using volatilities and p given.
Step 2. subtracted mean returns - risk fee rate
Step 3. Taking inverse of M solved for v, scaled to w(weights) But as a weight of first asset I am getting 0.51 instead of 0.87. What am I doing wrong?