Capital Asset Pricing Model (CAPM)

Definition

The Capital Asset Pricing Model (CAPM) is a financial theory that establishes a linear relationship between the expected return on an asset and its systematic risk, as measured by beta. The formula for CAPM is:

\[ \text{E}(R_i) = R_f + \beta_i [\text{E}(R_m) - R_f] \]

where:

\( \text{E}(R_i) \) = Expected return on asset \( i \)
\( R_f \) = Risk-free rate
\( \beta_i \) = Beta of the asset \( i \)
\( \text{E}(R_m) \) = Expected return of the market

Examples

Stock Investment: If the risk-free rate \(R_f\) is 3%, the expected market return \(E(R_m)\) is 8%, and the beta (\(\beta\)) of the stock is 1.5, then the expected return on the stock using CAPM would be calculated as follows: \[ E(R_i) = 0.03 + 1.5 \times (0.08 - 0.03) = 0.105 \text{ or } 10.5% \]
Bond Valuation: Suppose a corporate bond has a beta of 0.7, with the risk-free rate at 2% and expected market return at 7%. Then the expected return on the bond is: \[ E(R_i) = 0.02 + 0.7 \times (0.07 - 0.02) = 0.055 \text{ or } 5.5% \]

Frequently Asked Questions

What is Beta in CAPM?

Beta measures the volatility, or systematic risk, of a security or a portfolio compared to the market as a whole. A beta of 1 indicates that the security’s price will move with the market. A beta greater than 1 indicates greater volatility than the market, while a beta less than 1 indicates less volatility.

What Does the Risk-Free Rate Represent?

Risk-Free Rate (R_f) represents the return of an investment with zero risk, typically associated with government bonds like U.S. Treasury bills.

How Does CAPM Help Investors?

CAPM helps investors assess whether a security is fairly valued, by comparing the expected return calculated by CAPM with the actual return. If the actual return is higher than the CAPM expected return, the security may be undervalued.

What Are the Limitations of CAPM?

It assumes investors can borrow and lend at the risk-free rate.
The model relies on historical data for Beta, which may not accurately predict future risk.
It assumes markets are perfectly competitive and all investors have the same expectations.

Systematic Risk: The risk inherent to the entire market or market segment.
Unsystematic Risk: The risk unique to a specific company or industry.
Alpha: A measure of performance on a risk-adjusted basis.
Sharpe Ratio: A measure for calculating risk-adjusted return, comparing the return of an investment to its risk.

Online References

Suggested Books for Further Studies

“Investments” by Zvi Bodie, Alex Kane, and Alan J. Marcus: Offers a comprehensive introduction to the principles of finance, including CAPM.
“Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen: Provides detailed insights into corporate finance concepts including risk management and asset pricing.
“Modern Portfolio Theory and Investment Analysis” by Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, and William N. Goetzmann: Covers modern financial theory and empirical evidence, including CAPM.

Accounting Basics: “Capital Asset Pricing Model (CAPM)” Fundamentals Quiz

### What does CAPM primarily help to determine? - [ ] The past profitability of an asset. - [x] The expected return on an asset given its risk. - [ ] The future price of a commodity. - [ ] The expense ratio of mutual funds. > **Explanation:** The CAPM is used to determine the expected return on an asset for a given level of risk, based on the risk-free rate, the asset's beta, and the expected market return. ### What is the formula to calculate CAPM? - [ ] \\( E(R_i) = R_f + \alpha_i [E(R_m) - R_f] \\) - [x] \\( E(R_i) = R_f + \beta_i [E(R_m) - R_f] \\) - [ ] \\( E(R_i) = R_f - \beta_i [E(R_m) - R_f] \\) - [ ] \\( E(R_i) = R_f \times [E(R_m) - R_f] \\) > **Explanation:** The correct formula for CAPM is \\( E(R_i) = R_f + \beta_i [E(R_m) - R_f] \\), where \\(R_f\\) is the risk-free rate, \\(\beta_i\\) is the beta of the asset, and \\(E(R_m)\\) is the expected market return. ### What does Beta (β) represent in the CAPM formula? - [ ] The expected return of an asset. - [ ] The risk-free rate. - [x] The measure of an asset's volatility in relation to the market. - [ ] The average market return. > **Explanation:** Beta (β) measures the volatility of an asset in relation to the overall market. A higher beta indicates higher volatility compared to the market. ### Which rate is generally considered as the risk-free rate? - [ ] Corporate bond yields - [x] Government T-bill yields - [ ] Stock market index returns - [ ] Corporate equity returns > **Explanation:** Government T-bill yields are generally considered the risk-free rate because they have virtually no risk of default. ### If the risk-free rate is 3%, the expected market return is 8%, and the beta (β) of the stock is 1.5, what is the expected return of the stock according to CAPM? - [ ] 7.5% - [ ] 9.0% - [x] 10.5% - [ ] 12.0% > **Explanation:** Using the CAPM formula, \\(E(R_i) = 0.03 + 1.5 \times (0.08 - 0.03) = 0.105\\) or 10.5%. ### What assumption does the CAPM make about investors? - [ ] Investors have different expectations. - [ ] Investors can't lend or borrow money. - [x] Investors can borrow and lend at the risk-free rate. - [ ] Investors do not diversify their investments. > **Explanation:** The CAPM assumes that investors can borrow and lend at the risk-free rate, which simplifies the model but may not reflect reality. ### Why might the CAPM be criticized? - [ ] It relies on beta which is difficult to calculate. - [ ] It only works for bonds. - [x] It assumes markets are perfectly competitive and beta accurately predicts future risk. - [ ] It provides a guaranteed return. > **Explanation:** The CAPM is criticized because it assumes that markets are perfectly competitive and that beta, derived from historical data, can accurately predict future risk. ### How is the expected market return \\(E(R_m)\\) typically estimated? - [ ] From historical bond rates - [ ] Using only short-term data - [ ] From expert opinions - [x] From historical market performance > **Explanation:** The expected market return \\(E(R_m)\\) is usually estimated from the historical performance of the market. ### Why is CAPM useful in portfolio management? - [ ] It guarantees the highest return. - [ ] It avoids any financial risks. - [x] It helps in determining the trade-off between risk and return. - [ ] It is useful for predicting market crashes. > **Explanation:** CAPM helps investors understand the trade-off between risk and expected return, aiding in more informed portfolio management decisions. ### In CAPM, which type of risk is considered relevant for pricing? - [ ] Unsystematic risk - [x] Systematic risk - [ ] Credit risk - [ ] Operational risk > **Explanation:** In CAPM, only systematic risk is considered relevant for pricing because it affects the entire market and cannot be diversified away.

Thank you for exploring the Capital Asset Pricing Model with us and taking our sample quiz. Keep refining your financial acumen!

$$$$