# Monte Carlo based mean variance optimization

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:

1. Produce a set of efficient portfolios with increasing volatility / return.
2. Find the minimum variance portfolio
3. Find the highest sharpe ratio portfolio.

Portfolios should be subject to the following constraints:

1. No shorting (all weights >= 0)
2. 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?

• The way you've put it, I agree that it is poorly phrased. Even if you sampled the returns with Monte Carlo, you could still pass the expected returns and covariances of that result to any portfolio optimizer. They could have meant Michaud resampling, but just saying MC-based MVO is too vague.
– John
Feb 22, 2016 at 18:31
• Thanks John. I thought perhaps the intent was to generate a traditional MVO with the provided inputs and then generate resampled MVO using f permutations on the starting inputs like this. corporate.morningstar.com/ib/documents/MethodologyDocuments/… I did ask the interviewer but was given no additional input. I've certainly done Google searches over time for some guidance but found nothing definitive. Thus I put it out here. Feb 22, 2016 at 18:38
• The resampling procedure in that paper is the same that I was thinking of. I wouldn't stress about it too much: would you really want to work for someone who can't make their interview questions clear?
– John
Feb 22, 2016 at 22:05