# Factor Analysis & Factor Contribution to Risk

The purpose of factor analysis is to uncover the relationship between one dependent variable (typically a fund) and one or more explanatory variables (typically market or style indices) by using a statistical estimation method. The Stepwise regression method is a selection process that utilizes the Akaike Information Criterion (AIC for short) in order to select the factors that best explain the variance of each fund in your portfolio. Most stepwise regression methods in standard software packages either deploy a forward or a backward looking selection process.

• Forward selection: Involves starting with no variables in the model, trying out the variables one by one and including them if they are ‘statistically significant’.
• Backward elimination: Involves starting with all candidate variables, testing them one by one for statistical significance, and deleting any that are not significant.

The R² statistic measures the overall goodness of fit of the model. It shows you how much of the total variance of the fund can be accounted for by the factors. R² can take values between 0 and 1. R² value of 1 means that you have perfect fit of the model. There are no set rules for the range of R² that would be indicative of a good model. In theory, hedge funds are supposed to be uncorrelated to the market in general, so finding a good model by using market factors should be impossible. However, this theory rarely holds since for most hedge funds, you will be able to find a set of factors that adequately captures the fund profile. In general, an R² above 0.7 is considered a good fit. An R² of 0.4 – 0.7 is an adequate fit and an R² below 0.4 is a poor one. The magnitude of the R² statistics varies across hedge fund strategies. An R² of 0.38 may be considered a poor fit for a directional strategy like long/short equity. But it can be a very reasonable fit for a relative strategy like fixed income arbitrage. Factor contribution to risk gives you insight into the breakdown of risk by its systematic and specific parts. It allows you to see the exposure of the portfolio to market factors and the contribution of those factors to the risk of the portfolio. The risk measure for this section is standard deviation. In other words, the provided information is about factor contribution to portfolio volatility.

This section provides an analysis of the total risks of the portfolio broken down into two components:

• Systematic Risk – the risk attributable to those factors to which the portfolio has exposure
• Specific Risk – the risk which cannot be attributed to market factors.

The included chart graphically shows this breakdown in percent of systematic and specific risks of the portfolio as well as the breakdown of the systematic portion of risk across all factors used in the model. The percentage of specific risk is represented by the blue bar on the chart. The red bars represent the percentage contribution to portfolio risk coming from each of the factors which form the systematic portion of risk. You can also view this in data format.

Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.