Capital Asset Pricing Model (CAPM): Formula, Beta, Example & Cost of Equity

Introduction

The Capital Asset Pricing Model (CAPM) is a significant and popular financial model in modern finance. It helps to identify the expected return on investment based on its risk in comparison to the overall market. CAPM was developed in the 1960s, and it completely changed the manner in which investors, analysts, and financial managers of corporations assess investment opportunities and make capital budgeting decisions.

The basis of CAPM is Modern Portfolio Theory (MPT), which was developed by Harry Markowitz. Later, economists William F. Sharpe, John Lintner, and Jan Mossin further developed the theory and formulated the Capital Asset Pricing Model. William Sharpe was awarded the Nobel Prize in Economics in 1990 for his work on CAPM.

The CAPM model defines a positive link between systematic risk (market risk) and expected return. The CAPM model assumes that investors demand higher returns for higher risk, but only for the risk that cannot be diversified away. The model clearly states that unsystematic risk (firm-specific risk) can be diversified away, but systematic risk cannot.

The key purpose of CAPM is to calculate the cost of equity, which is essential for:

• Investment appraisal
• Valuation of shares
• Corporate finance decisions
• Portfolio management
• Risk assessment

In today’s financial world, CAPM remains a foundational tool in equity valuation, project analysis, and capital budgeting decisions.

Objectives

• To Determine Expected Return
CAPM assists in determining the expected return on an investment based on its risk.
It illustrates the amount of return an investor can expect in exchange for market risk.

• To Measure Risk (Beta)
It measures market or systematic risk through Beta (β).
Beta measures the relative sensitivity of a stock to the overall market.

• To Establish Risk-Return Relationship
CAPM illustrates that risk and return are directly proportional to each other.
It demonstrates that investors receive a return only on market risk.

• To Calculate Cost of Equity
CAPM assists firms in calculating the cost of equity capital.
It aids in capital budgeting and investment decisions.

• To Help in Investment Decisions
Investors compare the return on investment with CAPM return.
If the return is greater, then the investment is worthwhile.

• To Provide Performance Benchmark
CAPM assists in determining whether a portfolio is overperforming or underperforming.

Concept of Risk and Return

Risk

Risk is the uncertainty of return on an investment. There are two types of risk in finance:

• Systematic Risk (Market Risk)
It affects the whole market.
It cannot be removed by diversification.
It is caused by factors like inflation, interest rates, recession, and political instability.

• Unsystematic Risk (Specific Risk)
It is related to a particular company or industry.
It can be removed by diversification.
It includes management problems, product failure, and strikes.

CAPM ignores unsystematic risk because it can be removed by diversification.

Return

Return is the gain or loss of investment over a period of time. Investors demand higher returns for higher risk investments.

CAPM gives a formula to calculate the return based on the risk level.

CAPM Formula

The basic formula of CAPM

E(Ri) = Rf + βi (Rm–Rf)

E(Ri) = Expected return on security
Rf = Risk-free rate
βi (Beta) = Measure of systematic risk
Rm = Expected market return
(Rm – Rf) = Market risk premium

Components of CAPM

Risk-Free Rate (Rf)

Risk-free rate is the return on an investment with no risk. In reality, government treasury bonds are taken as risk-free investments.

• In India – Government of India Treasury Bills
• In the US – US Treasury Bonds

Risk-free rate is the compensation for the time value of money.

Market Return (Rm)

Market return is the average return on the whole stock market. It is calculated using a market index.

• NIFTY 50
• S&P 500

Market return includes both growth and dividend components.

Market Risk Premium (Rm – Rf)

This is the extra return that investors demand for bearing market risk.

Market Risk Premium = Market Return – Risk-Free Rate

The higher market risk premium indicates that investors demand higher compensation for risk.

Beta (β)

Beta is the measure of the sensitivity of the stock return to the market return.

• β = 1 → Stock moves with the market
• β > 1 → More volatile than the market
• β < 1 → Less volatile than the market
• β = 0 → No relation with the market

Example:

• High-growth stocks like Tesla, Inc. have high beta values.
• Stable stocks like Hindustan Unilever have lower beta values.

Assumptions of CAPM

• Investors Are Rational and Risk-Averse
Investors prefer lower risk for the same return and demand higher return for higher risk.

• Investors Have Homogeneous Expectations
All investors have the same expectations regarding future returns, risk levels, and market conditions.

• No Taxes or Transaction Costs
Investors can buy and sell securities freely without extra costs.

• Perfectly Competitive Markets
No investor can influence market prices and information is freely available.

• Investors Can Borrow and Lend at Risk-Free Rate
Borrowing and lending is assumed at the same rate.

• All Assets Are Divisible and Liquid
Securities can be traded easily in any quantity.

• Single Investment Period
Investment decisions are made for one time period.

• Investors Hold Diversified Portfolios
Unsystematic risk is eliminated through diversification.

Importance of CAPM

• Helps in Calculating Cost of Equity
• Supports Capital Budgeting Decisions
• Assists in Investment Decision-Making
• Measures Systematic Risk
• Provides Performance Benchmark
• Foundation of Modern Financial Theory

Applications of CAPM

• Corporate Finance
Used to calculate cost of equity in WACC.

• Investment Decision
Compare expected return with CAPM return.

• Valuation of Shares
Used in DCF valuation.

• Portfolio Management
Helps build diversified portfolios.

Advantages of CAPM

• Simple and Easy to Use
• Focuses on Systematic Risk
• Helps Calculate Cost of Equity
• Provides Investment Benchmark
• Theoretical Foundation

Limitations of CAPM

• Unrealistic Assumptions
• Beta Is Unstable
• Ignores Other Risk Factors
• Difficult to Estimate Market Return
• Assumes Borrowing at Risk-Free Rate

Comparison with Other Models

• Arbitrage Pricing Theory (APT)
Uses multiple factors.

• Fama-French Three Factor Model
Adds size and value factors.

Conclusion of CAPM

The Capital Asset Pricing Model (CAPM) is one of the most important theories in modern financial management. Developed by William F. Sharpe and based on the portfolio theory of Harry Markowitz, CAPM provides a clear framework to understand the relationship between risk and return.

CAPM helps calculate the expected return of a security using three key components: risk-free rate, beta, and market risk premium. This makes it highly useful for determining the cost of equity, evaluating investment opportunities, and making capital budgeting decisions.

Although CAPM has certain limitations, it still remains widely accepted in both academic and practical finance. Many advanced models are developed as extensions of CAPM, showing its strong foundation.

In conclusion, CAPM is a powerful and foundational financial model that simplifies complex risk-return relationships into a practical formula.