Factor Models

What are Factor Models?

Factor Models are financial modelsFinancial ModelsFinancial modeling refers to the use of excel-based models to reflect a company's projected financial performance. Such models represent the financial situation by taking into account risks and future assumptions, which are critical for making significant decisions in the future, such as raising capital or valuing a business, and interpreting their impact.read more that incorporate factors (macroeconomic, fundamental, and statistical) to determine the market equilibrium and calculate the required rate of return. Such models associate the return of a security to single or multiple risk factors in a linear model and can be used as alternatives to Modern Portfolio Theory.Modern Portfolio Theory.An investment model like modern portfolio theory or MPT allows investors to choose from a variety of investment options comprising of a single portfolio for earning maximum benefits and that too at a market risk which is way lower than the various underlying investments or assets.read more

Below are some of the functions related to factor models

  • Maximization of the excess return, i.e., Alpha (α) (to be dealt in the later part of this article) of the portfolio;
  • Minimization of the volatility of the portfolio, i.e., the Beta (β) of the portfolio;
  • Ensure sufficient diversification to cancel out the firm-specific risk.

Types of Factor Model

There are primarily two types  –

  1. Single Factor
  2. Multiple Factor
Factor Models

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For eg:
Source: Factor Models (wallstreetmojo.com)

#1 – Single Factor Model

The most common application of this model is the Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)The Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more.

The CAPM is a model that precisely communicates the relationship between the systematic riskSystematic RiskSystematic Risk is defined as the risk that is inherent to the entire market or the whole market segment as it affects the economy as a whole and cannot be diversified away and thus is also known as an “undiversifiable risk” or “market risk” or even “volatility risk”.read more and expected return of the stocks. It calculates the required return based on the risk measurement. To do this, it relies on a risk multiplier called the Beta coefficientBeta CoefficientThe beta coefficient reflects the change in the price of a security in relation to the movement in the market price. The Beta of the stock/security is also used for measuring the systematic risks associated with the specific investment.read more (β).

You can download this Factor Models Excel Template here – Factor Models Excel Template
E(R)i = Rf+ β(E(Rm)- Rf)

Where E(R)I is the Expected return of investment


Consider the following example:

The Beta of a particular stock is 2.The market return is 8%, a Risk-free rate 4%.

SingleFactor Example

The Expected return as per the above formula would be:

  • Expected return E(R)i= 4+2(8-4)
  • = 12%

The CAPM is a simple model and is most commonly used in the finance industry. It is used in the calculation of the Weighted Average Cost of Capital/ Cost of equityCost Of EquityCost of equity is the percentage of returns payable by the company to its equity shareholders on their holdings. It is a parameter for the investors to decide whether an investment is rewarding or not; else, they may shift to other opportunities with higher returns.read more.

But this model is based on a few slightly unreasonable assumptions such as ‘the riskier the investment, the higher the return’ which might not be necessarily true in all the scenarios, an assumption that historical data accurately predicts the future performance of the asset/stocks, etc.

And, what if there are many factors and not just one which determines the rate of return? Hence, we move on to the financial Models and discuss such models in depth.

#2 – Multiple Factor Model

Multiple factor models are adjunctions to single financial models. Arbitrage Pricing Theory is one of its predominant application.

Multiple Factor Model

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For eg:
Source: Factor Models (wallstreetmojo.com)

Rs,t   = Rf +α+ β1×F1,t + β2×F2,t + β3×F3,t+ …….βn×Fn,t+ Ě

Where Rs,t is the Return of security s at Time t


Consider the following example:

FactorFactor Sensitivity (β)Risk Premium (F1,t)
Factor 10.600.05
Factor 20.540.08

Assume the Risk-free Rate of Return to be 4%.

The Return as calculated for the above example is as follows:

Multiple factor models Example 1-1
  • R= Rf + β1×F1,t + β2×F2,t + Ě
  • = 4% + 0.6(5) + 0.54(8)
  • = 11.32%

The arbitrage pricing theory being one of the common types of Financial models, is based on the following assumptions:

  • Asset returns can be described by a linear factor model
  • Asset/Firm-specific risk shall possibly be eliminated by diversification.
  • No further arbitrage opportunity exists.


This model allows professionals to


  • It is hard to decide how many factors to include in a model.
  • Interpretation of the meaning of the factors is subjective.
  • Selecting a good set of questions is complicated, and different researchers will choose different sets of questions.
  • An improper inquiry might lead to complicated outcomes.

Recommended Articles

This article has been a guide to what are Factor Models & its definition. Here we discuss types of factor models in finance – single and multi-factor, along with examples. You can learn more about Finance from the following articles –

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