# Factor Analysis

Regression and time series attribution models in the Windham Portfolio Advisor

Factor analysis is a powerful technique that can identify and measure common sources of risk and return for managers, asset classes, and portfolios. Each factor represents an underlying exposure to the market. Factor analysis goes beyond the asset allocation to identify the underlying exposures to specific sources of risk and return. Factor analysis can be used in a variety of applications including

Explaining differences in returns across a universe of financial assets

Forecasting the expected value of asset returns

Explaining systematic variations and co-movements in returns

Stress testing asset class returns

Evaluating managers' exposure to risk factors

## Regression Models

Regression can be used to describe the relationship between an investment vehicle and a risk factor or group of factors. The Windham Portfolio Advisor allows for the use of Single, Multi, and Stepwise regression analysis to identify the factor sensitivities of a portfolio.

### Single Factor Model

The single factor Capital Asset Pricing Model (CAPM) is an early example of a single-factor regression model. CAPM specifies that an asset’s expected return in excess of the risk free rate is proportional to the asset’s sensitivity to systematic risk (non-diversifiable risk of the market). The sensitivity term is commonly referred to as beta (or factor loading). A single-factor model assesses the return sensitivity of each vehicle against an individual factor, and repeats the exercise for each factor. The single-factor regression provides the best descriptor of the exposure of the manager to a specific risk factor in isolation.

### Multi-Factor Model

### Stepwise Multi-Factor Model

## Analysis Types

The Windham Portfolio Advisor provides three approaches to review risk factors across portfolios.

### Factor Loadings

Factor loadings (sensitivities) show us the sensitivity of an investment vehicle to each factor. The regression coefficients are also known as factor loadings.

### Risk Decomposition

The Windham Portfolio Advisor separates the variance of each time series into that which can be explained by beta exposures to the factors and that which cannot be explained by the factor model (residual). The “Residual” is the percentage of variance not explained by the multi-factor model. We calculate the risk decomposition from the weighted averages of the managers’ multi-factor loadings and the factors’ standard deviations and correlations.

### Return Decomposition

The software separates the return of each time series into that which can be explained by beta exposures to the factors and returns that cannot be explained by factor exposures (intercept).

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