2 – M4 L2A 13 Time Series Risk Model Factor Exposure V4

To estimate the other variables, we’ll also collect a time series of data for each stock and make use of the capital asset pricing model. Remember that the capital asset pricing model assumes that the stock’s excess return above the risk-free rate can be modeled as its exposure to the market’s excess return above the risk-free rate multiplied by the market’s excess return above the risk-free rate. To make this discussion less wordy, I’ll just say market’s excess return when referring to the market excess return above the risk-free rate. I’ll also just say stock’s excess return when referring to the stock’s excess return above the risk-free rate. Also, notice that the market exposure, which is what we’ve been calling this Beta variable when discussing the CAPM, is called a factor exposure when we’re discussing factor models. The term factor exposure is a more general term that describes any factor including the market factor. We’re going to demonstrate one way to estimate factor exposures using regression. But keep in mind that factor exposure estimation is not a settled science. So, there are also other approaches to estimating a stock’s exposure to a particular factor. We’ll get a time series of the market’s excess return, a time series of the first stock’s excess return and run them through a regression. The coefficient Beta is an estimate of the first stock’s exposure to this one factor. We can do the same with a time series of the second stock’s returns and estimate the factor exposure of the second stock to this one factor.

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