Kapitalkostenmodell capm

The Capital Asset Pricing Model (CAPM) is a foundational model in portfolio theory used to determine the theoretically appropriate required rate of return of an asset, typically a stock. It posits that an asset's expected return is equal to the risk-free rate plus a risk premium that is proportional to the asset's beta, a measure of its systematic risk. The CAPM helps investors understand the relationship between risk and expected return, providing a framework for pricing risky securities and generating expected returns on assets, given their risk.

History and Origin

The Capital Asset Pricing Model was independently developed in the early 1960s by economists William F. Sharpe, John Lintner, and Jan Mossin, building on the groundwork laid by Harry Markowitz's Modern Portfolio Theory (MPT). Sharpe's seminal paper, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," published in 1964, formalized the relationship between an asset's risk and its expected return within a diversified portfolio.¹⁴, ¹⁵ This breakthrough earned William F. Sharpe a share of the Nobel Memorial Prize in Economic Sciences in 1990.¹³ The CAPM provided a coherent framework that connected the required return on an investment to the inherent risk of that investment, revolutionizing financial analysis.¹²

Key Takeaways

• The Capital Asset Pricing Model (CAPM) calculates the required rate of return for an asset, linking its risk to its expected return.
• It differentiates between systematic risk (market risk) and unsystematic risk, positing that only systematic risk is rewarded with higher returns in a diversified portfolio.
• The model relies on several assumptions, including efficient markets and rational investors, which have been subject to academic scrutiny.
• CAPM is widely applied in corporate finance for calculating the cost of equity and in portfolio management for evaluating investment performance.

Formula and Calculation

The formula for the Capital Asset Pricing Model is expressed as:

Where:

• (E(R_i)) = Expected return on investment (i)
• (R_f) = Risk-free rate (e.g., the yield on a U.S. Treasury bond)
• (\beta_i) = Beta of investment (i) (a measure of its sensitivity to market movements)
• (E(R_m)) = Expected return of the market portfolio
• ((E(R_m) - R_f)) = Market risk premium (the excess return expected from the market portfolio over the risk-free rate)

To illustrate, the risk-free rate is typically derived from the yield of government bonds, such as the 10-year U.S. Treasury Note.⁹, ¹⁰, ¹¹

Interpreting the CAPM

The Capital Asset Pricing Model provides a theoretical minimum expected return for an investment, given its systematic risk. If an asset's expected return, as projected by the CAPM, is lower than an investor's required return, the asset might be considered overvalued or not worth the risk. Conversely, if the asset's expected return is higher than the required return, it may be undervalued.

Beta is central to this interpretation. A beta of 1 implies the asset's price will move with the market. A beta greater than 1 suggests the asset is more volatile than the market, implying a higher expected return (and higher risk). A beta less than 1 indicates lower volatility, implying a lower expected return (and lower risk). The relationship is often visualized on the Security Market Line (SML), which plots expected return against beta. Assets plotting above the SML are considered undervalued, while those below are overvalued.

Hypothetical Example

Consider an investor evaluating the purchase of shares in "Tech Growth Co." They gather the following data:

• Current Risk-free rate ((R_f)): 3%
• Expected market return ((E(R_m))): 10%
• Beta ((\beta)) of Tech Growth Co.: 1.5

Using the CAPM formula:

(E(R_{Tech Growth}) = 0.03 + 1.5 * (0.10 - 0.03))
(E(R_{Tech Growth}) = 0.03 + 1.5 * (0.07))
(E(R_{Tech Growth}) = 0.03 + 0.105)
(E(R_{Tech Growth}) = 0.135) or 13.5%

Based on the CAPM, the expected return for Tech Growth Co. is 13.5%. If the investor's analysis suggests the stock is likely to return less than 13.5%, it may not be an attractive investment decision given its systematic risk.

Practical Applications

The Capital Asset Pricing Model is a widely used tool in various financial contexts:

• Capital Budgeting: Companies use the CAPM to estimate the cost of equity when evaluating potential projects. The expected return derived from CAPM serves as the discount rate for future cash flows, influencing capital allocation decisions.
• Portfolio Management: Fund managers utilize CAPM to assess whether a portfolio's expected returns adequately compensate for its systematic risk. It helps in constructing portfolios along the Capital Market Line and evaluating performance against benchmarks.
• Asset Valuation: Analysts use the model to determine the fair value of an asset. If an asset's actual expected return is higher than the CAPM-calculated return, it might be considered undervalued and a potential buying opportunity. Conversely, if lower, it may be overvalued.
• Regulatory Settings: In some regulated industries, authorities may use CAPM or similar models to determine the allowed rate of return for utilities or infrastructure projects, impacting pricing and investment.
• Financial Planning: Individual investors can apply the principles of CAPM to understand the risk-return characteristics of different asset classes and make informed decisions about their overall diversification strategy. Despite its theoretical drawbacks, the CAPM formula remains relevant for comparing investment alternatives due to its simplicity.⁸ Acknowledging its enduring utility, even prominent financial news outlets continue to discuss its application.⁷

Limitations and Criticisms

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

• Unrealistic Assumptions: The CAPM is built on strong, often unrealistic, assumptions, such as rational investors, zero transaction costs, no taxes, identical investor expectations, and the ability to borrow and lend at the risk-free rate. These idealized conditions rarely hold true in real-world markets.
• Market Portfolio Definition: The model assumes the existence of a true "market portfolio" that includes all risky assets globally. In practice, a proxy like a broad stock market index (e.g., S&P 500) is used, but this proxy may not accurately represent the theoretical market portfolio. This "market proxy problem" can significantly affect the model's empirical validity.⁶
• Beta Instability: Beta values can fluctuate over time and depend on the look-back period used for calculation. The historical beta may not accurately predict future risk sensitivity.
• Empirical Failures: Academic research, notably by Eugene Fama and Kenneth French, has shown that factors beyond beta, such as company size and book-to-market ratio, can explain variations in stock returns, suggesting that beta alone may not fully capture all relevant risks.², ³, ⁴, ⁵ These findings challenge the CAPM's core premise that systematic risk, as measured by beta, is the sole determinant of expected returns. Critics have pointed out these shortcomings, noting that the model's empirical record is "poor enough to invalidate the way it is used in applications."¹

The Federal Reserve Bank of San Francisco has also published on the assumptions and limitations of the Capital Asset Pricing Model, highlighting the debate around its applicability.

CAPM vs. Weighted Average Cost of Capital (WACC)

The Capital Asset Pricing Model (CAPM) and Weighted Average Cost of Capital (WACC) are both crucial concepts for determining the cost of capital, but they serve different purposes and represent different components of a company's financing costs.

While CAPM provides a specific measure for the cost of equity, WACC offers a holistic view of a company's financing costs by averaging the costs of all capital sources, weighted by their proportion in the company's capital structure. Therefore, the CAPM result for the cost of equity is often a direct input into the WACC calculation.

FAQs

What is the primary purpose of the Capital Asset Pricing Model?

The primary purpose of the Capital Asset Pricing Model is to estimate the expected return an investor should receive for taking on a certain level of systematic risk (market risk) in a diversified portfolio. It helps in evaluating whether an asset is fairly priced given its risk profile.

How does beta relate to CAPM?

Beta is a critical component of the CAPM. It measures the sensitivity of an asset's returns to changes in the overall market returns. A higher beta indicates higher volatility relative to the market, and according to CAPM, demands a higher expected return to compensate for that increased systematic risk.

Can CAPM predict future stock prices?

No, the Capital Asset Pricing Model does not predict future stock prices. Instead, it calculates a theoretical expected return for an asset based on its risk. Investors can then compare this expected return to their own forecasts or actual market returns to make informed decisions about whether an asset is overvalued or undervalued.

What is the difference between systematic and unsystematic risk in the context of CAPM?

Systematic risk, also known as market risk, is the risk inherent to the entire market or market segment. It cannot be eliminated through diversification. CAPM only compensates investors for bearing this type of risk. Unsystematic risk (or specific risk) is the risk unique to a specific company or industry, which can be mitigated or eliminated through proper diversification. The CAPM assumes investors are fully diversified and thus are not compensated for unsystematic risk.

Is CAPM still used by financial professionals today?

Despite its limitations and the development of more complex models, the Capital Asset Pricing Model remains widely taught and used by financial professionals. Its simplicity and intuitive framework for understanding the relationship between risk and return make it a valuable tool for initial analysis, especially in calculating the cost of equity for companies and for educational purposes in Modern Portfolio Theory.