Mollyycolllinss Authors Macrocephalopod
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A few things that I didn't cover yesterday when I talked about equity factor models (it's a huge area and it's impossible to more than scrape the surface)
1. How do you get the exposure matrix Xt?
There are different ways to estimate it, depending on the factor. Simplest is factors like industry or country exposure where the entries can be 0/1 depending on whether the stock is in that industry/country or not.
Some exposures can be estimated by linear regression on historical data, if you already have a time series which approximates the factor returns. E.g. exposure to the market factor (beta) is estimated this way, by regressing each stock against the S&P 500 (or some other index)
This also works for "macro" factors e.g. you can estimate exposures for each stock to commodity prices, exchange rates, interest rates, GDP or inflation surprises etc by regressing stock returns against the relevant historical time series.
Finally you can have exposures which are heuristically derived from other observable data about the stock, e.g. accounting data, analyst reports, past price movements etc. In this case you find some metric which measures the factor you care about (e.g. price to earnings) and
A few people in the DMs asking about equity factor models so here's a short explainer.
— macrocephalopod (@macrocephalopod) February 2, 2021
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.
1. How do you get the exposure matrix Xt?
There are different ways to estimate it, depending on the factor. Simplest is factors like industry or country exposure where the entries can be 0/1 depending on whether the stock is in that industry/country or not.
Some exposures can be estimated by linear regression on historical data, if you already have a time series which approximates the factor returns. E.g. exposure to the market factor (beta) is estimated this way, by regressing each stock against the S&P 500 (or some other index)
This also works for "macro" factors e.g. you can estimate exposures for each stock to commodity prices, exchange rates, interest rates, GDP or inflation surprises etc by regressing stock returns against the relevant historical time series.
Finally you can have exposures which are heuristically derived from other observable data about the stock, e.g. accounting data, analyst reports, past price movements etc. In this case you find some metric which measures the factor you care about (e.g. price to earnings) and