I was asked this question in an interview some years ago. It struck me as a poorly formed question. I thought I would put it out there to the community to see if I just simply missed something.
Problem Statement For n assets, you are given expected returns (ER), variances (V) and covariances. Your task is to write Monte Carlo based mean variance optimization that will:
- Produce a set of efficient portfolios with increasing volatility / return.
- Find the minimum variance portfolio
- Find the highest sharpe ratio portfolio.
Portfolios should be subject to the following constraints:
- No shorting (all weights >= 0)
- No leverage (sum of all weights = 100%).
Why I think this is poorly stated problem I understand MVO and MC. The only context I have seen MC in a MVO concept is where MC is utilized to make random draws from a chosen distribution to arrive at an ER and Covariance Matrix. Those however are given here.
If I am wrong here then what is the MC random draws in this case - the asset weights?