For anyone building and managing equity portfolios for clients, I have two pieces of advice.
1. Use a fundamental risk model.
One of the first advantages of fundamental risk models is they afford easier portfolio optimization. When you have thousands of stocks to choose from, in order to model them completely using returns you would need a covariance matrix with several million elements. As fast as modern computers have become, I still wouldn’t advise you try grinding through a 4,000,000 cell covariance matrix (which is what you need in order to model 2,000 stocks) on your laptop. By comparison, fundamental risk models entail much smaller covariance matrices since they reduce the risks among stocks to only several dozen factors.
Another advantage is how adaptable they can be. If a company sells off a significant line of business, it will take a while for a returns based risk model to reflect changes in the stock’s return pattern. Similarly, an IPO or a spin-off won’t have any return history to model for a while. Meanwhile, a fundamental risk model might be able to model the IPO, spin-off, or recapitalized stock immediately. Keep in mind that SOME companies are having such corporate actions all the time, so to the extent a returns based risk model might profile a stock without any recent corporate actions accurately, the model will still distort the profiles of all the stocks that have undergone changes.
Visit the websites of APT, Axioma, Barra, and Northfield to learn more.
With due mention to fundamental risk models out of the way, the rest of this post is meant to help investors who AREN’T using fundamental risk models such as the ones these vendors offer.
2. If you’re not using a fundamental risk model, then use Matrix Reconstructed Returns to model portfolios and indexes.
In a recent post I referred to “imaginary returns” for the purpose of calculating portfolio statistics such as Beta, sigma, and covariances and correlations.
I’ve decided a better name for these is “Matrix Reconstructed Returns.”
A Matrix Reconstructed Return is a pro-forma rebalanced return; it’s what would have been earned if the index or portfolio had been constructed in identical weights to its weights today. This is different from the historical return, unless the weights have always been rebalanced identically, such as might be the case in some equally weighted indexes.
The Matrix Reconstructed Return is computationally useful: it obviates the need to compute a covariance matrix. For portfolios or indexes containing more than a few dozen stocks, that’s a useful feature. You say Russell Reconstitution is coming up and you want to know a stock’s forecast Beta against the Russell 2000? Using only historical returns, you’ve got two choices:
1. Grind through a 4,000,000 cell covariance matrix. Again, don’t do it on a laptop, please.
2. Generate a weighted average historical return series of all the constituents at their provisional weights. This is the Matrix Reconstructed Return. Now regress your stock’s returns against the Matrix Return series – its Beta, covariance, and correlations to the Matrix Reconstructed Return are mathematically identical to what you’ll get from the covariance matrix.