Multi-Factor Analysis
The “Multi-Factor“ tab, found on the analysis tab on the right side of the application, allows you to use the same factors from the Factor Analysis tab in a multivariate regression. There are three modes:
- Manual: Choose factors manually from the drop-down list. When you have selected all the factors, click Calculate to see the regression results.
- N Best Factors: The application will use a stepwise regression. At each step it will select the factor that maximizes R2.
- Max Adjusted R2: Adding an additional factor will always increase R2. Adjusted R2 includes a penalty for each additional factor. This method will continue to add factors until adjusted R2 is maximized.
For N Best Factors and Max Adjusted R2, there is a “Correlation Cut-Off(%)” parameter. To avoid issues with multicollinearity, at each step, the application will exclude factors that are more correlated than this to the factors that have already been chosen.
The attribution table includes four values for each factor
Beta Exp(%): Indicates the portfolio’s sensitivity to the factor. If a portfolio has a beta exposure of 50% to a factor and the factor undergoes a 4% return, then we would expect the portfolio’s profit to be 50% x 4% = 2% higher than it would be otherwise.
t-Stat: The Student’s t Statistic of the beta exposure
Factor σ(%): Indicates how much additional P&L we would expect from a one standard deviation move in the factor. It may be equally risky for a portfolio to have a high beta to a low volatility factor, as it is to have a low beta to a high volatility factor. From a risk perspective, what we really care about is the product of the beta exposure and the volatility of the factor. This is what "Factor σ(%)" represents. For this calculation we use the one-day standard deviation of the factor.
Risk Attribution: This is the share of the variance that is attributed to each factor and the idiosyncratic risk (the risk not explained by the factors). The sum of the risk attribution values equals 100%.