The returns on n = 4 assets are described by a Gaussian (Normal) random vector r
Question:
The returns on n = 4 assets are described by a Gaussian (Normal) random vector r ∈ Rn, having the following expected value ˆr and covariance matrix ∑:
The last (fourth) asset corresponds to a risk-free investment. An investor wants to design a portfolio mix with weights x ∈ Rn (each weight xi is nonnegative, and the sum of the weights is one) so to obtain the best possible expected return r̂ T x, while guaranteeing that:
(i) No single asset weights more than 40%;
(ii) The risk-free assets should not weight more than 20%;
(iii) No asset should weight less than 5%;
(iv) The probability of experiencing a return lower than q = –3% should be no larger than ϵ = 10–4. What is the maximal achievable expected return, under the above constraints?
Step by Step Answer:
Optimization Models
ISBN: 9781107050877
1st Edition
Authors: Giuseppe C. Calafiore, Laurent El Ghaoui