Multi-factor Models of Asset or Portfolio Returns

Regression-based factor models are used to forecast the expected return and the risk of a portfolio. The expected return on each asset in the portfolio is approximated as a weighted sum of the expected returns to several market risk factors. The weights are called factor sensitivities or, more specifically, factor betas and are estimated by regression. If the portfolio includes broad market indices, industry factors, style factors (e.g., value, growth, momentum, size), economic factors (e.g., interest rates, inflation) or statistical factors (e.g., principal components). By inputting scenarios and stress tests on the expected returns and the volatilities and correlations of these risk factors, the factor model representation allows the portfolio manager to examine expected returns under different market scenarios.(ref Alexander, C. (2008). Market Risk Analysis II - Practical Financial Econometric. Vol 2.)

The Multi-factor Model is constructed to take into account atleast 38 factors.

The output from the model includes basic ex-ante tracking error calc, systematic and specific risk attribution of assets i.e., assets marginal contributions to risk (MCTR) and assets conditional contributions to risk (CCTR). It also includes these contributions at a factor level and drills down to asset holdings in the portfolio.

The model also outputs the systematic risk, specific risk and total risk of the portfolio based on active weights.

The Model also does exposure analysis where it compares the portfolio and index exposure to the different factors, to understand if the portfolio is taking more risk or not.

The model is uses three types of regression models, the Multi-linear regression model (MLR), the Principal Component regression (PCR) and the Partial Least Squares regression (PLSR).