# How to find the variance co-variance matrix for 4 assets and market returns using the CAPM?

I understand the process on excel: calculate betas, calculate covariance with $Cov(R_{i,t},R_{j,t}) = \beta_{i,m} \cdot \beta_{j,m} \cdot \sigma^2_m$

where m is the market return and i and j are assets.

I'm confused as to what the assumptions are in order to be able to do this?

Can I do this since I have market data 4 US stocks and the S&P500 meaning that I'm only considering systematic risk?

Please could someone give me the assumptions in order to use the CAPM relation to find a variance covariance matrix?

• Are you asking when you can approximate the covariance matrix this way or when this is the true covariance matrix? – BKay Jan 6 '16 at 16:58
• @Bkay to approximate – user146745 Jan 6 '16 at 16:58

It is worth mentioning that in your equation above, the diagonal entries are not exactly what you write. Instead it is: $Var(R_{i,t}) = \beta_{i,m}^2 \cdot \sigma^2_m +\sigma^2_\epsilon$ where $\sigma^2_\epsilon$ is the variance of the residual of the linear approximation equation.