# Isolating single assets standard deviation in a portfolio accounting for correlation

I am running a simple Monte Carlo analysis in Excel using mean return, standard deviation and the =NORMINV(RAND(),mean,std dev) method. I have a correlation matrix that I use to compute the portfolio variance for varying weights of 16 assets.

I would like to compute the standard deviation of a single asset after accounting for correlations with the portfolio. For example using the data in the attached picture, if I wanted to run a Monte Carlo analysis on asset 1 after accounting for the correlations with assets 2 and 3 in portfolio 1, what would me steps be? The mean return would simply be the weight of the asset in the portfolio times the assets return but what would the standard deviation of the asset be, the standard deviation of the portfolio times the weight of the asset?

• Running regression of on the single assets with the portfolios as regressors seems a more logic way for me to determine the 'corrected' standard ' deviations.
– Tim
Jan 31, 2016 at 1:00

This is given by $$\sigma(X_j;X) = \sigma(X_j)\ \rho(X_j, X)$$