# Portfolio Return Decomposition

Barra gives factor weights for a common set of factors, for each asset. Given a long-short portfolio, is there a way I can combine the individual factor weights to get the factor exposures for the overall portfolio? Ideally, I want to be able to make statements like "10% of the portfolio returns are due to Factor x".

2 concerns that I had:

1. How would I calculate the portfolio weights, as the \$value of asset i divided by the sum of the \$ values of all assets, or should I divide by the sum of the absolute \\$ values?

2. I don't think (but I could be wrong) Barra has standardized factors in the individual asset regression. Hence, even if I had a way of obtaining portfolio factor weights, would it be possible to make statements like the one I described above?

Many thanks!

• One way from ML world would be looking at the partial derivatives in the optimization process – Vitomir Jul 14 at 15:08
• Thanks @Vitomir. I thought about that, but I thought there must be an easier way given what Barra already provides, i.e. the individual asset factor weights and the factor covariance matrix. – rbm Jul 14 at 15:38
• assuming your factors are exhaustive, it's not uncommon/unreasonable to normalize factor loadings to make statements like you describe. for instance with betas of .1, .2, .6, -.1, you can assert your exposure is 10% derived from factor one, 20% from 2, 60% from 3, and 10% from 4. to do this you obviously take the only the magnitude of the negative exposures. – Chris Jul 15 at 5:00