Multi-Factor Model

A multi-factor model in Finance combines several correlated factors or elements to explain the market equilibrium and asset returns. This method aims to help investors understand and forecast stock price fluctuations and the factors that influence those changes. It is also used to compute the return rates.

Investors use this model to make structured and logical investment decisions. Additionally, businesses can use this model to formulate marketing strategies that would lead to the company’s growth and higher return rates. Furthermore, this method can help an investor identify the various sources that pose a risk to the company, which would help minimize losses.

• The multi-factor model is a financial model that combines numerous factors to explain the market equilibrium and stock price fluctuations. Additionally, these models can also help determine asset returns and forecast any market changes.
• There are different models: Fama-French Three-Factor Model, Cahart Four-Factor Model, Fama-French Five-Factor Model, and Arbitrage Pricing Theory. However, the Fama-French Three-Factor Model is the most popular and widely used.
• These model types include Statistical Factor Models, Fundamental Factor Models, and, Macroeconomic Factor Models.

The multi-factor model in Finance is a model that utilizes a combination of various components and factors to explain asset returns and market equilibrium. In addition to it, investors use this model to build portfolios with specific attributes like asset risks or to monitor indexes. However, understanding what factors should be considered while formulating this model type is challenging. Furthermore, these models are based on historical numbers, so forecasted future values may not always be accurate. 

Additionally, this model aids in determining the various factors’ weights that these models comprise, which helps to identify which factors impact the asset price to what extent. There are different models, and they are as follows:

• Fama-French Three-Factor Model
• Cahart Four-Factor Model
• Fama-French Five-Factor Model
• Arbitrage Pricing Theory (APT)

These model types are as follows:

• Statistical Factor Models: Various statistical methods are employed on the historical data returns in this model type. Then they are used for explaining the covariances in numbers.
• Fundamental Factor Models: In this model type, the securities or company’s attributes are the factors that explain the fluctuations in stock prices. These factors include financial leverage, market capitalization, and price-to-earnings ratio.
• Macroeconomic Factor Models: In these models, the factors associated with surprises in macroeconomic variables are used to explain the asset class returns. The surprise or additional return can be calculated by subtracting the forecasted value from the actual value.

Let us understand the concept with the following examples:

Example #1

Suppose Mr. Ross is examining the stock of Apex Ltd. based on two factors: the unexpected percent change in interest rates and the unexpected percent change in GDP (Gross Domestic Product). Accordingly, he has gathered the following data for his study:

The expected return for Apex Ltd. = 15%

GDP factor beta = 2

Interest rate factor beta = 3

Expected growth in GDP = 4%

Expected growth in interest rates = 2%

Therefore,

According to the multi-factor model formula, Apex Ltd.’s return rate is:

Ri=E(Ri)+βi1F1+βi2F2

=15+ (2×4) + (3×2) =15 + 8 + 6 = 29%

This is a multi-factor model example.

Example #2

Suppose Green is an analyst at Dream Zone Company, a research firm. She has to calculate the returns received by Dream Zone Company. Green has gathered the following data for calculating the return:

Dream Zone Company’s anticipated return = 5%

Expected GDP growth rate = 5%

Expected Inflation rate = 2%

GDP factor-beta = 2

Inflation factor-beta = 1

Risk-free rate = 3%

However, the actual GDP growth rate is 4%, and the actual inflation rate is 3% 

Therefore,

According to the multi-factor model formula, Dream Zone company’s return

 =0.05 + 2(0.04 – 0.05) + 1(0.03 – 0.02) = 0.05 + 2(- 0.01) + 1(0.01) = 0.05 – 0.02 + 0.01 = 0.04

4%

This is a multi-factor model example.

The advantages of the multi-factor model are as follows:

• It helps to identify the reason for fluctuations in the dependent variables and determine the factors that cause those changes. When investors identify and interpret the cause-and-effect relationship, they can systematically forecast and control these changes.
• These models can help investors make logical investment decisions and achieve higher returns due to increased predicting capabilities. Investors can also use these models to generate algorithms for automated trading. However, traders must use automated trading only when the risks are low, as it may not effectively minimize significant losses.
• One of the advantages of the multi-factor model for businesses is that they can form expansion and marketing strategies based on these models. It will help them formulate a plan to attain high profit and track the outcomes closely. Furthermore, these models will aid them in regulating the company’s aims and objectives.

 The differences are as follows:

• Multi-Factor Model: This model considers several factors to calculate and explain the market equilibrium and change in stock prices. It combines the uncertainty resulting from numerous sources to illustrate the asset prices. Furthermore, this model can determine the required return rate of individual stocks and the market portfolio.

• CAPM: The Capital Asset Pricing Model (CAPM) model considers only one factor, the market factor, to regulate the required return. It recognizes the threats from only one source: covariance with the market portfolio. However, the market factor comprises smaller factors like the business cycle, inflation, and interest rates.

• Single Factor Model: This model is related to the CAPM. It elucidates that traders must consider two essential things: risk and time value. A stock’s risk is determined by a risk measure that compares asset returns to market returns. A risk-free rate identifies the return’s time value part. 

This has been a guide to Multi-Factor Model & its definition. We explain its examples, comparison with CAPM & single factor model, advantages & disadvantages. You can learn more about it from the following articles -

• Factor Models
• Cost of Equity Formula
• Factor Investing