Multivariate Normal Distribution in Excel

[reasonfa]

Hey,

I have a portfolio of 20 stocks over a time period of 15 years. I calculated the mean returns and the covariance matrix. Now I want to perform a Monte Carlo simulation based on a multivariate normal distribution with the same parameters. I downloaded the “real statistics resource pack” for excel to actually generate these randomly generated returns for the 20 stocks over the time period. Based on the newly generated returns I again calculate the mean returns and the covariance matrix.

The problem is:
The covariance matrix based on the random sample has a lot of minus values compared to the original covariance matrix where there is not one minus value. Moreover, the new covariance matrix is way smaller than the original covariance matrix.

Is that normal? Because my efficient frontier optimization would not plot almost in the same area of the original sample. The standard deviation is too small.

 

[joeu2004]

I downloaded the "real statistics resource pack" for excel to actually generate these randomly generated returns for the 20 stocks over the time period. Based on the newly generated returns I again calculate the mean returns and the covariance matrix. The problem is: The covariance matrix based on the random sample has a lot of minus values compared to the original covariance matrix where there is not one minus value. Moreover, the new covariance matrix is way smaller than the original covariance matrix. Is that normal?

IMHO, you would have to direct your question to real-statistics.com, who provided the add-on that you are using. This is a question about their add-on, not about your Excel usage.

That aside, I'm very interested in the work that you are doing. If you would not mind sharing, please upload an Excel file -- probably one without the real-statistics add-on -- to a file-sharing website, and post a pubic/shared link to it in a response here. I'd like to take a look at it, for my own edification.

As to your question about the results.... In my experience, yes, Monte Carlo sims can yield wildly different results compared to historical data, especially if you are looking at a sim of only one timeline. I don't know anything about what the real-statisics add-on is doing.