Comparisons

What Is Capital Asset Pricing Model?

The Capital Asset Pricing Model (CAPM) is a foundational model in asset pricing that calculates the expected return of an investment, given its systematic risk. Within the broader field of portfolio theory, the CAPM helps investors determine if an asset is fairly valued by comparing its expected return to the return required for its level of risk. The model posits that the expected return on an asset is equal to the risk-free rate plus a risk premium, which is based on the asset's beta and the expected market return.

History and Origin

The Capital Asset Pricing Model emerged in the early 1960s, building upon the groundbreaking work of Harry Markowitz's Modern Portfolio Theory. Independently developed by economists William F. Sharpe (1964), John Lintner (1965), and Jan Mossin (1966), the CAPM provided a more practical framework for understanding the relationship between risk and return in financial markets. William Sharpe, then an assistant professor at the University of Washington, published his seminal paper "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk" in 1964, which laid out the core principles of the model.⁴ This work, which simplified Markowitz's complex covariance calculations by linking asset returns to a single market factor, revolutionized modern finance and earned Sharpe, Markowitz, and Merton Miller the Nobel Memorial Prize in Economic Sciences in 1990.³ The CAPM quickly became a cornerstone for investment decisions and remains highly influential.²

Key Takeaways

• The Capital Asset Pricing Model (CAPM) is used to calculate the theoretically appropriate required rate of return of an asset.
• It quantifies the relationship between an asset's expected return and its systematic risk, often represented by beta.
• The CAPM assumes that investors are rational, seek to maximize utility, and can borrow and lend at the risk-free rate.
• It implies that the expected return of a security is determined only by its systematic risk, as unsystematic risk can be eliminated through diversification.
• Despite empirical challenges, the CAPM remains widely taught and applied in various financial contexts due to its simplicity and intuitive appeal.

Formula and Calculation

The formula for the Capital Asset Pricing Model is:

$E(R_i) = R_f + \beta_i (E(R_m) - R_f)$

Where:

• ( E(R_i) ) = Expected return of the investment
• ( R_f ) = Risk-free rate
• ( \beta_i ) = Beta of the investment (a measure of its systematic risk)
• ( E(R_m) ) = Expected return of the market portfolio
• ( (E(R_m) - R_f) ) = Market risk premium

This formula calculates the return an investor should expect for taking on the additional risk associated with a particular asset, beyond the risk-free rate.

Interpreting the Capital Asset Pricing Model

The Capital Asset Pricing Model provides a framework for evaluating whether an investment offers an adequate expected return for its associated systematic risk. If an asset's expected return, calculated using the CAPM, is higher than its actual or projected return, it might be considered overvalued. Conversely, if the CAPM-derived expected return is lower than the asset's actual or projected return, it could be undervalued.

The model essentially describes a theoretical line, known as the Security Market Line (SML), which graphs the relationship between systematic risk (beta) and expected return. Assets plotting above the SML are considered undervalued, as they offer a higher expected return for their given risk. Assets plotting below the SML are considered overvalued, offering less return for their risk. This interpretation is crucial for portfolio management and helps investors align their holdings with their risk tolerance.

Hypothetical Example

Consider an investor evaluating a stock, Company XYZ.

Assume the following:

• Risk-free rate (( R_f )) = 3%
• Expected return of the market portfolio (( E(R_m) )) = 10%
• Beta of Company XYZ (( \beta_{XYZ} )) = 1.2

Using the CAPM formula:

$E(R_{XYZ}) = R_f + \beta_{XYZ} (E(R_m) - R_f)$
$E(R_{XYZ}) = 0.03 + 1.2 (0.10 - 0.03)$
$E(R_{XYZ}) = 0.03 + 1.2 (0.07)$
$E(R_{XYZ}) = 0.03 + 0.084$
$E(R_{XYZ}) = 0.114 \text{ or } 11.4\%$

Based on the CAPM, the expected return for Company XYZ, given its systematic risk, should be 11.4%. If the investor projects Company XYZ to actually return 13%, the stock might be considered undervalued and a potentially good buy, as it offers a higher return than what is theoretically required for its risk. If the projected return is only 9%, it might be overvalued. This analysis helps in making informed asset allocation decisions.

Practical Applications

The Capital Asset Pricing Model is widely used across various facets of finance:

• Cost of Capital Estimation: Firms use the CAPM to estimate their cost of capital, specifically the cost of equity. This figure is vital for capital budgeting decisions, helping companies evaluate potential projects by discounting future cash flows at an appropriate rate.
• Performance Evaluation: The CAPM provides a benchmark for evaluating the performance of managed portfolios, mutual funds, or individual stocks. Portfolio managers' actual returns can be compared against the returns predicted by the CAPM for a given level of risk to determine if they've generated alpha (excess return).
• Security Valuation: Investors and analysts use the CAPM to determine the appropriate discount rate for valuing individual securities or entire companies. By deriving a required rate of return, they can ascertain whether a stock is overvalued, undervalued, or fairly priced.
• Regulatory Settings: In some regulatory contexts, such as utility rate setting, the CAPM may be used to determine a fair rate of return for regulated companies.
• Capital Budgeting: Companies use the CAPM-derived cost of equity as the discount rate for evaluating investment projects, ensuring that only projects expected to yield returns above the cost of capital are undertaken. Investment advisors and financial professionals must adhere to strict guidelines when presenting performance results or making claims, as outlined by bodies like the Securities and Exchange Commission (SEC) to ensure transparency and prevent misleading statements. SEC Investment Adviser Marketing Rule

Limitations and Criticisms

Despite its widespread use, the Capital Asset Pricing Model faces several significant limitations and criticisms:

• Assumptions: The CAPM relies on highly restrictive and often unrealistic assumptions, such as investors having homogenous expectations, no transaction costs, no taxes, investors being able to borrow and lend at the risk-free rate, and assets being infinitely divisible. The real world rarely aligns perfectly with these ideal conditions.
• Single-Factor Model: A primary criticism is that the CAPM is a single-factor model, meaning it only considers systematic risk (beta) as the sole determinant of expected returns. Empirical studies have shown that other factors, such as company size and value, may also influence asset returns.¹ This has led to the development of multi-factor models.
• Market Portfolio Definition: The model requires the "market portfolio" to include all risky assets, both financial and non-financial (like real estate and human capital), which is practically impossible to observe or construct. Proxies, such as broad stock market indices, are often used, but these may not accurately represent the true market portfolio.
• Beta Stability: Beta, a key input, is not always stable over time and can vary depending on the data frequency and estimation period used. This instability can lead to inaccurate CAPM results.
• Empirical Performance: Numerous empirical tests have struggled to consistently validate the CAPM's predictions, particularly the linear relationship between beta and return. Some studies suggest that low-beta stocks have historically outperformed high-beta stocks, contradicting the model's core premise.

Capital Asset Pricing Model vs. Arbitrage Pricing Theory

The Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) are both models used to explain the relationship between risk and expected return for assets. However, they differ fundamentally in their approach and assumptions.

The main point of confusion often arises because both models attempt to price assets based on risk. However, the CAPM simplifies risk down to one market-wide factor, whereas APT acknowledges that multiple, distinct economic factors might influence asset returns, without explicitly identifying what those factors are. This makes APT more flexible in theory but potentially more complex to implement as the relevant factors must be identified empirically.

FAQs

What is systematic risk in the context of CAPM?

Systematic risk, also known as market risk or non-diversifiable risk, refers to the risk inherent to the entire market or market segment. It cannot be eliminated through diversification and includes factors like interest rate changes, inflation, wars, and recessions. The CAPM suggests that investors are compensated only for taking on systematic risk.

Why is the risk-free rate important in CAPM?

The risk-free rate is crucial because it represents the minimum return an investor expects for any investment, as it's the return from an investment with zero risk. It serves as the baseline from which all additional risk premiums are calculated in the CAPM formula. Typically, the yield on short-term government bonds, such as U.S. Treasury bills, is used as a proxy for the risk-free rate.

Can CAPM predict future stock prices?

No, the Capital Asset Pricing Model is not designed to predict future stock prices. Instead, it calculates the expected return an investor should demand for holding an asset given its systematic risk. It helps in valuation by providing a discount rate or a benchmark return, but it does not forecast specific price movements.

What is the relationship between beta and expected return according to CAPM?

According to the CAPM, there is a linear relationship between an asset's beta and its expected return. A higher beta indicates higher systematic risk, and thus, the CAPM predicts a higher expected return to compensate investors for that increased risk. Conversely, a lower beta implies lower systematic risk and a lower expected return. This relationship is graphically represented by the Security Market Line.