What Is a Multi-Factor Model?

A multi-factor model is a financial model that employs multiple factors in its calculations to explain market phenomena and/or 澳洲幸运5官方开奖结果体彩网:equilibrium asset prices. A multi-factor model can be used to explain either an individual security or a 澳洲幸运5官方开奖结果体彩网:portfolio o𝔉f securities. It does so by comparing two or more fa𝄹ctors to analyze relationships between variables and the resulting performance.

Understanding a Multi-Factor Model

Multi-factor models are used to construct portfolios with certain characteristics, such as risk, or to track indexes. When 🦋constructing a multi-factor model, it is difficult to decide how many and which factors to include. Also, models are judged on historical numbers, which mighꦐt not accurately predict future values.

Multi-factor models a🌼lso help explain the weight of the different factors used in the models, indicating which factor has more of an impaꦐct on the price of an asset.

Multi-Factor Model Formula

Factors are compared using the fﷺollowing formula:

Ri = ai + _i(m) * Rm + _i(1) * F1 + _i(2) * F2 +...+_i(N) * FN + ei

Where:

Ri is the return of security

Rm is the market return

F(1, 2, 3 ... N) is each of the factors used

_ is the beta with respect to each factor includin♔g the🅘 market (m)

e is the error term

a is the intercept

Types of Multi-Factor Models

Multi-factor models can be divided into three categories: macroeconomic models, funda🥀mental models, and statistical models.

Macroeconomic models: Macroeconomic models compare a security's return to such factors as employment, 澳洲幸运5官方开奖结果体彩网:inflation, and interest.

Fundamental models: Fundamental models analyze the relationship between a security's return and its underlying financials, such as earnings, 澳洲幸运5官方开奖结果体彩网:market capitalization, and debt levels.

Statistical models: Statistical models are used to compare the returns of different securities based on the statistical performance of each security in and of itself. Many times, hi♌storical data is used in this type of modeling.

Construction of Multi-Factor Models

The three most commonly used models to construct a multi-factor model are a🅺 combination model, a sequential model, and an intersectional model.

Combination model: In a combination model, multiple single-factor models, which utilize a single factor to distinguish stocks, are combined to create a multi-factor model. For example, stocks may be sorted based on momentum alone in the first pass. Subsequent passes will use other factors, such as 澳洲幸运5官方开奖结果体彩网:volatility, to classify them.

Sequential model: A sequential model sorts stocks based on a single factor in a sequential manner to create a multi-f𓆉actor model. For example, stocks for a specific market capitalization may be sequentially analyzed for various factors, such as value and momentuꦏm, sequentially.

Intersectional model: In the intersectional model, stocks are sorted based on their intersections for factors. For example, stocks may be sorted and classified based on intersections in value and momentum.

Measurement of Beta

The beta of a security measures the 澳洲幸运5官方开奖结果体彩网:systematic risk of a security in rela🧜tion to the overall market. A beta of 1 indicates that the security theoretically experiences the same degree ofౠ volatility as the market and moves in tandem with the market.

A beta greater than 1 indicates the security is theoretically more volatile than the market. Conversely, a beta less than 1 indicates the security is theoretically less vola♑tile than the market.

When multꩵi-factor models are used by investment managers to assess the risk of investments, beta is an important factor that they can use.

Fama-French Three-Factor Model

One widely used multi-factor model is the Fama-French three-factor model. The Fama-French model has three factors: the size of firms, 澳洲幸运5官方开奖结果体彩网:book-to-market values, and excess returns on the market. In other words, the three factors used are SMB (small minus big), HML (high minus low), and the portfolio's return less the 澳洲幸运5官方开奖结果体彩网:risk-free rate of return.

SMB accounts for publicly traded companies with small market caps that generate higher returns, while HML accounts for 澳洲幸运5官方开奖结果体彩网:value stocks with high book-to-market ratios that generate higher returns in c🗹o🍌mparison to the market.