3 – M4 L2A 14 Time Series Risk Model Specific Variance V2

We can also use the results of the regression to estimate a time series for the specific return. For each time period, the specific return is the residual from taking the actual minus estimated excess return of the stock. The actual return is data that we just used to input into the regression. The estimated return is calculated by using the market return and the regression estimates for the factor exposure and the intercept term. If we calculate the difference between actual and estimated returns for multiple time periods, this is an estimate for the specific return time series. The variance of the specific return can be used in the risk model. Similarly, we can also calculate the specific return of the second stock, then calculate the variance of that specific return. Note that calculating specific variance is also not a settled science. The time window chosen affects the result. This difference between actual and estimated return, which we often refer to as the residual return, is what we’re calling the specific return in this context. If you’re working in quant finance, you may hear an expression like, the returns that are not explained by the model or the returns that are not explained by the factors. Since the goal of risk factor models is to explain where the returns of assets came from by breaking them down into well-defined components or factors, anything left over that is unexplained is represented by the residual.

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