macrocephalopod

A few people in the DMs asking about equity factor models so here's a short explainer. Let's make it a concrete problem -- you are the risk manager at a big multi-manager hedge fund with ~100 sub-PMs each of whom has a portfolio of 10-50 stocks, long and short.

You want to understand exactly what risks are being taken so that you can hedge the undesired risks and keep the ones you are likely to get paid for. To do this you want to understand how well each stock can be used as a hedge for any other stock in the portfolio, i.e. you want

the covariance matrix, a 2000 x 2000 matrix which tells you, for every pair of stocks A and B, how much is B likely to move if A moves by 1%? Estimating the covariance matrix from historical data is a hopeless problem (for boring linear algebra reasons) so instead you use

a factor model. The idea is that the return of every stock can be modeled as depending linearly on a number of *factors* which are generic, possibly unobservable drivers of returns. Simple examples of factors are the overall stock market, sectors, country or currency exposure.

You also have accounting-based factors, like price-to-earnings (expensive stocks tend to move together), return-on-assets (high margin companies move together), debt-to-equity ratio (leveraged companies move together) etc.

There can be purely price-based factors, e.g. a slightly surprising fact is that "momentum" names move together, i.e. stocks that have gone up in the last year often move together, and inversely to stocks that went down in the last year.

Or you can get more esoteric, e.g. a factor representing all stocks that have recently been upgraded by analysts, or a factor representing stocks that are highly shorted.