Factor Models

Factor models are financial models that usefactors— that can be technical, fundamental, macroeconomic or alternate to define a security’s risk and returns.

These models arelinear,as they define the securities returns to be a linear combination of factor returns weighted by the securities factor exposures.

Securities Factor Exposures

Capital Asset Pricing Model

The most popular factor model is the single factor —Capital Asset Pricing Modelor CAPM, which forms the basis of the Modern Portfolio Theory.

The CAPM, describes security’s risk as a function of it’s market exposure or marketBeta

Market Beta

The Market Beta is a measure of the systematic risk of the security. In statistics, beta is the slope of the line which is obtained by regressing the returns of stock return with that of the market return.

Multi Factor Model

The most popular model in factor literature is theFama-French 3-factor model. In their seminal paper published in the 1993 Fama & French demonstrate that 90% of an equity’s risk can be described based on the 3 factors —market sensitivity, valueandsize.

Fama-French 3-factor model

Later,momentumas a factor was added to the equation by Jagdeesh Titman in 1993,low volatilityin 2006 andqualityin 2013.

Now, with the advent ofSmart Betastrategies, any strategies returns are widely believed to be broken down into —market component, smart beta components, manager returns (or active returns)

Smart Beta strategies

MSCI Barra, the leading provider of factor indices categorises global equity factor in 8 groups and 16 factors

MSCI Structure

Many quantitative portfolio managers device strategies that follow one or more of these factor models

Maths

For a quant, the most fascinating aspect of these models is the maths! If we can identify and capture all the relevant factor exposures, these factors can fully describe a securities risk and returns!

Factor covariance matrix

where Q is the factor covariance matrix and w is the weight of the factors.

Quantitative Factor Strategies

With these models quants can focus on ~ 30 factors that they believe describe the market instead of 3000 stocks in the total market universe. Many of these factor strategies find their basis in economic theories which makes their performance predictable and implementable using financial models.