The returns on n = 4 assets are described by a Gaussian (normal) random vector r ∈ Rn , having expected value r and covariance matrix Σ
The last asset corresponds to a risk-free investment. I attempt to design a portfolio mix with weights x ∈ Rn (each weight xi is non-negative, and the sum of the weights is one) so as to obtain the best possible expected return, while guaranteeing that:
(i) No single asset weighs more than 40%. (ii) The risk-free assets should not weigh more than 20%. (iii) No asset should weigh less than 5%. (iv) The probability of experiencing a return lower than q = −1% should be no larger than ε = 0.0001