Kapitalgutpreismodell

_LINK_POOL:

• Expected Return
• Risk-Free Rate
• Market Risk Premium
• Beta
• Diversification
• Modern Portfolio Theory
• Systematic Risk
• Asset Pricing
• Cost of Equity
• Capital Budgeting
• Security Market Line
• Portfolio Management
• Investment Decisions
• Market Efficiency
• Arbitrage Pricing Theory

What Is Kapitalgutpreismodell?

The Kapitalgutpreismodell, more commonly known as the Capital Asset Pricing Model (CAPM), is a financial model that calculates the expected rate of return for an asset or investment based on its systematic risk. It is a cornerstone of modern portfolio theory and falls under the broader category of asset pricing models. The CAPM establishes a linear relationship between the required return on an investment and its risk, helping investors determine if a security is fairly valued given its risk level.

History and Origin

The Capital Asset Pricing Model (CAPM) was developed independently by several economists in the early 1960s, notably William Sharpe (1964), John Lintner (1965), and Jan Mossin (1966), building upon the foundational work of Harry Markowitz on diversification and modern portfolio theory³², ³³, ³⁴, ³⁵, ³⁶. Sharpe's paper, "Capital Asset Prices—A Theory of Market Equilibrium Under Conditions of Risk," published in 1964, was a significant contribution for which he was later awarded the Nobel Memorial Prize in Economic Sciences in 1990. ²⁸, ²⁹, ³⁰, ³¹The development of the CAPM provided the first coherent framework for relating the required return on an investment to its risk, revolutionizing the field of finance by simplifying the portfolio selection problem.
²⁶, ²⁷

Key Takeaways

• The Kapitalgutpreismodell (CAPM) is a model used to determine the theoretically appropriate required rate of return of an asset.
• It quantifies the relationship between an asset's expected return and its systematic risk, also known as market risk.
• The model assumes that investors should only be compensated for systematic risk, as diversifiable risk can be eliminated through portfolio diversification.
• Despite its simplifying assumptions, the CAPM remains widely used in finance for applications such as estimating the cost of equity and evaluating portfolio performance.
• The CAPM is a single-factor model, meaning it explains asset returns based on their sensitivity to overall market movements.

Formula and Calculation

The formula for the Kapitalgutpreismodell (CAPM) 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 (typically the return on a long-term government bond)
• (\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 suggests that the expected return of an asset is equal to the risk-free rate plus a risk premium, which is calculated by multiplying the asset's beta by the market risk premium.

Interpreting the Kapitalgutpreismodell

Interpreting the Kapitalgutpreismodell involves understanding the interplay of its components to assess an asset's expected return relative to its risk. The model's output, (E(R_i)), represents the minimum expected return an investor should require for holding a particular asset, given its systematic risk. If an asset's projected return exceeds the return calculated by the CAPM, it may be considered undervalued, suggesting it could be a worthwhile investment decision. Conversely, if the projected return is lower than the CAPM result, the asset might be overvalued.

The beta coefficient is central to this interpretation, indicating how sensitive an asset's return is to changes in the overall market. A beta greater than 1 suggests the asset is more volatile than the market, while a beta less than 1 implies lower volatility. The Security Market Line (SML) graphically illustrates the CAPM, showing the relationship between systematic risk (beta) and expected return. Assets that plot above the SML are considered undervalued, and those below are overvalued.

Hypothetical Example

Consider an investor evaluating a stock, Company XYZ.

• Current risk-free rate (R_f) is 3%.
• The expected return of the market portfolio (E(R_m)) is 10%.
• Company XYZ has a beta ((\beta_i)) of 1.2.

Using the Kapitalgutpreismodell 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 investor should expect an 11.4% return from Company XYZ to compensate for its level of systematic risk. If the investor projects a higher return for Company XYZ, it might be considered an attractive investment. Conversely, if the projected return is lower, the stock might be overvalued given its risk.

Practical Applications

The Kapitalgutpreismodell is widely applied in various areas of finance despite its theoretical assumptions. One primary application is in estimating the cost of equity for firms. ²³, ²⁴, ²⁵Companies use this calculated cost of equity as a discount rate in capital budgeting decisions to evaluate potential projects and investments. If a project's expected return is greater than the cost of equity derived from the CAPM, it may be deemed acceptable.

Furthermore, the CAPM is used in portfolio management to assess the performance of managed funds. Fund managers' returns can be compared against the expected return predicted by the CAPM for a given level of systematic risk. If a fund consistently outperforms its CAPM-derived expected return, it suggests the manager is generating alpha, or excess returns not explained by market risk. Academic institutions and central banks, such as the Federal Reserve, also engage in research and modeling related to asset pricing, including robust versions of the CAPM, to understand market dynamics and financial stability.
²⁰, ²¹, ²²

Limitations and Criticisms

Despite its widespread use and theoretical elegance, the Kapitalgutpreismodell faces several limitations and criticisms. A significant point of contention revolves around its underlying assumptions, many of which are considered unrealistic in real-world financial markets. These assumptions include perfect market efficiency, no transaction costs or taxes, and investors having homogeneous expectations.
¹⁷, ¹⁸, ¹⁹
Empirical tests have often shown that the CAPM's predictions do not fully align with observed market behavior. ¹⁴, ¹⁵, ¹⁶For example, the model has been criticized for its inability to fully explain the cross-section of stock returns. ¹², ¹³Critics argue that factors beyond systematic market risk influence asset returns. This led to the development of multi-factor models, such as the Fama-French Three-Factor Model, which incorporate additional factors like company size and value (book-to-market ratio) to explain return variations. ⁸, ⁹, ¹⁰, ¹¹While these alternative models aim to address some of the CAPM's shortcomings, they also have their own limitations and are subject to ongoing debate in academic literature, with some arguing the Fama-French model might be prone to "data mining".
⁴, ⁵, ⁶, ⁷

Kapitalgutpreismodell vs. Fama-French Three-Factor Model

The Kapitalgutpreismodell (CAPM) and the Fama-French Three-Factor Model are both widely used asset pricing models, but they differ in their approach to explaining asset returns and identifying risk factors.

While the CAPM suggests that the expected return of a security is solely a function of its sensitivity to the overall market (beta), the Fama-French Three-Factor Model posits that smaller companies and value stocks (those with high book-to-market ratios) tend to outperform larger companies and growth stocks, even after accounting for market risk. This means that the Fama-French model attempts to provide a more comprehensive explanation of observed stock returns by including these additional factors.