Capital assets pricing model: Meaning, Criticisms & Real-World Uses

What Is Capital Assets Pricing Model?

The Capital Asset Pricing Model (CAPM) is a fundamental model within portfolio theory and asset pricing that calculates the expected return for an asset or investment, given its risk. It posits that the expected return of an investment should be equal to the risk-free rate plus a risk premium that accounts for its systematic risk. The CAPM is widely used in finance to determine the appropriate discount rate for valuing assets and making investment decisions. It differentiates between systematic risk, which cannot be eliminated through diversification, and unsystematic risk, which can be diversified away.

History and Origin

The Capital Asset Pricing Model was developed in the early 1960s by several economists working independently: William Sharpe (1964), John Lintner (1965a, b), Jan Mossin (1966), and Jack Treynor (1962).¹⁷, ¹⁸ Their work built upon Harry Markowitz's groundbreaking "Portfolio Selection" paper from 1952, which laid the foundation for modern portfolio theory by demonstrating how investors could construct efficient portfolios.¹⁶

Before the CAPM, the relationship between risk and return was not clearly defined. The model provided a coherent framework for understanding which types of risk should affect asset prices, specifically identifying that only systematic risk, or market risk, should be compensated with higher expected returns.¹⁵ William Sharpe, in particular, was recognized for his contributions with the Nobel Memorial Prize in Economic Sciences in 1990, shared with Harry Markowitz and Merton Miller.¹³, ¹⁴

Key Takeaways

The Capital Asset Pricing Model (CAPM) calculates the expected return of an investment based on its systematic risk.
It posits that investors are compensated only for systematic risk, which cannot be diversified away.
The model incorporates the risk-free rate, the asset's beta coefficient, and the equity risk premium.
CAPM is a foundational concept in finance used for asset valuation and capital budgeting.
Despite its theoretical importance, the CAPM faces criticisms regarding its simplifying assumptions and empirical limitations.

Formula and Calculation

The Capital Asset Pricing Model (CAPM) formula is expressed as:

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

Where:

(E(R_i)) = Expected return of the investment
(R_f) = Risk-free rate (typically the yield on a long-term government bond)
(\beta_i) = Beta coefficient of the investment (a measure of its systematic risk relative to the market)
(E(R_m)) = Expected return of the market (the overall market portfolio)
((E(R_m) - R_f)) = Equity risk premium (the additional return investors expect for investing in the market rather than a risk-free asset)

Interpreting the Capital Assets Pricing Model

The Capital Asset Pricing Model helps investors and analysts understand the fair expected return for an asset given its exposure to market risk. The core of its interpretation lies in the Security Market Line (SML), a graphical representation of the CAPM formula.¹¹, ¹² The SML plots beta on the x-axis and expected return on the y-axis.

Assets on the SML: An asset whose expected return plots directly on the SML is considered fairly valued, meaning it offers an appropriate return for its level of systematic risk.
Assets above the SML: An asset whose expected return plots above the SML is considered undervalued. It offers a higher expected return for its level of systematic risk than the market currently demands, making it a potentially attractive investment.
Assets below the SML: An asset whose expected return plots below the SML is considered overvalued. It offers a lower expected return for its level of systematic risk, suggesting it is a less attractive investment compared to other options in the market.

This interpretation allows for quick visual assessment in asset valuation and helps in making buy or sell decisions.

Hypothetical Example

Consider an investor evaluating whether to purchase shares of "Tech Innovations Inc." To estimate its expected return using the Capital Asset Pricing Model, the following values are gathered:

Current risk-free rate ((R_f)): 3% (e.g., yield on a 10-year U.S. Treasury bond)
Beta coefficient of Tech Innovations Inc. ((\beta_i)): 1.2 (indicating it's 20% more volatile than the market)
Expected return of the overall market ((E(R_m))): 8%

Using the CAPM formula:

$E(R_i) = R_f + \beta_i (E(R_m) - R_f)$
$E(R_i) = 0.03 + 1.2 (0.08 - 0.03)$
$E(R_i) = 0.03 + 1.2 (0.05)$
$E(R_i) = 0.03 + 0.06$
$E(R_i) = 0.09 \text{ or } 9\%$

Based on the CAPM, the expected return for Tech Innovations Inc. should be 9% to compensate investors for its systematic risk. If the actual expected return (e.g., from analysts' forecasts) is higher than 9%, the stock might be undervalued. If it's lower, it might be overvalued.

Practical Applications

The Capital Asset Pricing Model is a cornerstone of modern financial analysis, with several practical applications across various financial disciplines:

Cost of Equity Calculation: One of the primary uses of the CAPM is to determine a company's cost of equity, which represents the return required by investors for holding the company's stock. This is a crucial input for calculating the Weighted Average Cost of Capital (WACC), a key metric in corporate finance for evaluating investment projects and valuing businesses.⁹, ¹⁰
Investment Performance Evaluation: Fund managers and analysts use the CAPM to evaluate the performance of their portfolios or individual securities. By comparing an asset's actual return to its CAPM-derived expected return, they can assess if it has generated excess returns (alpha) relative to its risk.
Capital Budgeting: Companies utilize the CAPM-derived cost of equity as a discount rate for evaluating potential investment projects. This helps in deciding which projects to undertake by comparing the project's expected return to the required rate of return, ensuring that the project generates sufficient returns to compensate shareholders for the risk taken.⁸
Portfolio Management: Investors use the CAPM to decide whether a stock should be included in a diversified portfolio. It provides a framework for understanding how an asset's risk contributes to the overall portfolio risk and how it should be compensated with expected returns.⁷

Limitations and Criticisms

Despite its widespread use and theoretical elegance, the Capital Asset Pricing Model has faced significant criticisms and has known limitations:

Unrealistic Assumptions: The CAPM is built upon several simplifying assumptions that do not fully hold in the real world. These include assumptions that all investors have homogeneous expectations, that they can borrow and lend at the risk-free rate, that there are no taxes or transaction costs, and that markets are perfectly efficient.⁵, ⁶ The assumption of market efficiency, for instance, implies that all information is immediately and fully reflected in asset prices.
Beta Instability and Measurement Issues: The model's reliance on beta as the sole measure of systematic risk is a major point of contention. Beta is not always stable over time and its estimation can be sensitive to the chosen market index and data frequency.⁴ This makes it challenging to accurately predict future returns using the CAPM.³
Single-Factor Model: Critics argue that the CAPM, as a single-factor model, does not adequately explain the variations in asset returns. Empirical studies have shown that other factors, such as company size and value (book-to-market ratio), can also influence asset returns, which the CAPM does not account for.² This led to the development of multi-factor models.
Market Portfolio Problem (Roll's Critique): Perhaps the most significant critique, Roll's Critique, argues that the true market portfolio, which includes all assets (stocks, bonds, real estate, human capital, etc.), is unobservable. If the proxy for the market portfolio used in the CAPM is not the true market portfolio, then the CAPM cannot be empirically tested or validated.¹

These limitations highlight that while the Capital Asset Pricing Model provides a valuable theoretical framework, its direct applicability in real-world scenarios is often constrained by its inherent simplifications.

Capital Assets Pricing Model vs. Fama-French Three-Factor Model

The Capital Asset Pricing Model (CAPM) is a single-factor model, meaning it asserts that the only factor influencing an asset's expected return, beyond the risk-free rate, is its exposure to market risk, as measured by beta coefficient. It implies that investors are compensated solely for taking on systematic risk.

In contrast, the Fama-French Three-Factor Model, introduced by Eugene Fama and Kenneth French in 1992, expands upon the CAPM by adding two additional factors beyond the market risk premium. These factors are:

Size (SMB - Small Minus Big): This factor accounts for the historical tendency of small-cap stocks to outperform large-cap stocks.
Value (HML - High Minus Low): This factor captures the observed tendency of value stocks (high book-to-market ratio) to outperform growth stocks (low book-to-market ratio).

The Fama-French model was developed in response to empirical evidence suggesting that the CAPM could not fully explain variations in stock returns. It provides a more nuanced view of asset pricing by incorporating additional risk factors that have been historically linked to excess returns. While the CAPM remains foundational, the Fama-French model offers a more robust explanatory power for historical stock returns by acknowledging these additional dimensions of risk and return.

FAQs

What is systematic risk in the context of CAPM?

Systematic risk, also known as market risk or non-diversifiable risk, refers to the inherent risks that affect the entire market or a large segment of it, rather than just a specific company or industry. Examples include economic recessions, interest rate changes, or political events. The Capital Asset Pricing Model posits that investors are compensated only for bearing this type of risk, as it cannot be eliminated through diversification of a portfolio.

How is the risk-free rate typically determined for the CAPM?

The risk-free rate is usually approximated by the yield on a highly liquid government bond of a stable economy, such as the yield on a U.S. Treasury bond. The maturity of the bond chosen often corresponds to the investment horizon, though a 10-year Treasury yield is a common convention due to its liquidity and frequent quotation.

What does a beta of 1 mean in CAPM?

A beta coefficient of 1 indicates that an asset's price tends to move in line with the overall market. If the market goes up by 10%, an asset with a beta of 1 is expected to go up by 10%. A beta greater than 1 suggests higher volatility than the market, while a beta less than 1 suggests lower volatility.

Can CAPM predict future stock prices?

The Capital Asset Pricing Model is a tool to determine the theoretical expected return of an asset given its risk, not to predict its future price. It helps in assessing whether an asset is overvalued or undervalued based on its risk-return characteristics, guiding investment decisions rather than offering precise price forecasts.