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. 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.
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 –
- Single Factor
- Multiple Factor
#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..
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”. 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. (β).
Where E(R)I is the Expected return of investment
- Rf is the Risk-Free Rate of ReturnRisk-Free Rate Of ReturnA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk. defined is a theoretical rate of return with zero risks.
- β is the BetaBetaBeta is a financial metric that determines how sensitive a stock's price is to changes in the market price (index). It's used to analyze the systematic risks associated with a specific investment. In statistics, beta is the slope of a line that can be calculated by regressing stock returns against market returns. of the Investment that represents the volatility of the investment as compared to the overall market
- E(Rm) is the Expected returnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. of the market.
- E(Rm)- Rf is the Market Risk PremiumMarket Risk PremiumThe market risk premium is the supplementary return on the portfolio because of the additional risk involved in the portfolio; essentially, the market risk premium is the premium return investors should have to make sure to invest in stock instead of risk-free securities..
Consider the following example:
The Beta of a particular stock is 2.The market return is 8%, a Risk-free rate 4%.
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..
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.
Where Rs,t is the Return of security s at Time t
- Rf is the Risk-Free Rate of Return
- α is the Alpha of the security -Alpha is the constant term of the factor model. It represents the excess return of the investment relative to the return of the benchmark index. It is the value by which the investment outperforms the index. Higher the alpha, the better it is for investors
- F1,t, F2,t, F3,t are the factors – Macroeconomic factors like exchange rate, Inflation rate, Foreign Institutional InvestorsInstitutional InvestorsInstitutional investors are entities that pool money from a variety of investors and individuals to create a large sum that is then handed to investment managers who invest it in a variety of assets, shares, and securities. Banks, NBFCs, mutual funds, pension funds, and hedge funds are all examples., GDP, etc. Fundamental factors P/E ratio, Market capitalization, etc.
- β1, β2, β3 are the factor loadings. – The factor loadings, also known as component loadings, are coefficients of the factors, as mentioned above. For example, Beta calculation assists the investors to analyze the magnitude by which a stock moves in relation to change in the market.
- Ě represents the error term – The equation contains an error term which is used to give further precision to the calculation. It can sometimes be used to define the security specific news that becomes available to the investors.
Consider the following example:
|Factor||Factor Sensitivity (β)||Risk Premium (F1,t)|
Assume the Risk-free Rate of Return to be 4%.
The Return as calculated for the above example is as follows:
- 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
- Understand risk exposuresUnderstand Risk ExposuresRisk Exposure refers to predicting possible future loss incurred due to a particular business activity or event. You can calculate it by, Risk Exposure = Event Occurrence Probability x Potential Loss of equity, fixed income, and other asset class returns.
- Ensure that an investor’s aggregate portfolio meets his risk appetiteRisk AppetiteRisk appetite refers to the amount, rate, or percentage of risk that an individual or organization (as determined by the Board of Directors or management) is willing to accept in exchange for its plan, objectives, and innovation. and return expectations.
- Build Portfolios that obtain a consistent result or remodel according to the characteristics of a particular index.
- Estimate cost of equity capital for valuation
- Manage Risk and hedge.
- 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.
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 –