# Matlab multivariate normal distribution parameters (mvnrnd)

I need to use the mvnrnd function in matlab to generate random monthly returns for a set of assets. However, I am a bit confused about how to use this function to do it since it asks me MU and SIGMA values. How should I pick these values ?

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Parameters of multinormal distribution $\mu$ and $\Sigma$ related to expectation and covariance matrix of the multinormal random vector. Specifically $\mathsf{E}(X_i) = \mu_i$ and $\mathsf{Cov}(X_i,X_j) = \Sigma_{i,j}$. You would choose these parameters depending on the problem you are solving – Sasha Feb 22 '12 at 13:25
What do you mean by negative values? The mean is negative, i.e. you have negative returns? Please provide more details. – user13655 Feb 22 '12 at 17:57
After I get the random values and average them I use portopt to find optimal weights for a range of expected returns. When using portopt, if I specify the expected returns I want in a vector using rMin + i * ( (rMax - rMin) / 9 ) where i<=0<=9, from time to time I get something like: "One or more requested returns are less than the return -0.003414 of the least risky portfolio." However, if dont specify anything there is no error. I thought its because of the negative returns from mvnrnd but then couldn't really figure out why.. – Cemre Feb 22 '12 at 18:25

Well, yes. If a security has declined in price over the period you're looking at, you would expect to see negative values for $\mu$. Why is this a problem when finding optimal portfolios? – Chris Taylor Feb 22 '12 at 18:24