# The Capital Asset Pricing Model

## Definition

**:**

## 1. Introduction

## 2. Deriving and Defining the Capital Asset Pricing Model

#### 2.1. Mean-Variance Optimization and the Tangency Portfolio

#### 2.2. Defining the Risk Premium and the Risk-Free Rate through the Securty Market Line

_{a}, r

_{m}, and r

_{f}represent returns on the asset, the broader market, and the risk-free baseline (respectively), and where σ

_{a}represents the individual asset’s volatility relative to the whole market. This formula takes the form of a linear function that defines return on an asset (r

_{a}) in terms of its volatility (σ

_{a}).

_{a}) against beta (β

_{a}) reveals the security market line [17]. Figure 2 depicts the security market line. Its slope indicates the risk premium (r

_{m}− r

_{f}), and its intercept is the risk-free return (r

_{f}). Permitting “riskless lending opportunities changes the nature of the market equilibrium in just one way …. The expected return on a security continues to be a linear function of its β” [15] (p. 454).

#### 2.3. The Treynor and Sharpe Ratios

## 3. Beta

#### 3.1. Correlated Relative Volatility

#### 3.2. Interpreting Beta: Systematic Versus Idiosyncratic Risk

## 4. Information Uncertainty and Higher-Moment CAPM

#### 4.1. Risk Versus Uncertainty

#### 4.2. Information Uncertainty

#### 4.3. Generalizing the CAPM to Accommodate Both Risk and Uncertainty

_{e}indicates excess return over the risk-free baseline. V indicates market-wide conditional volatility, and M measures uncertainty throughout the economy. The temporal indexing variable t governs all of these variables as well as the expectation operator.

#### 4.4. Higher-Moment CAPM

## 5. Applications of the CAPM

#### 5.1. The Regulatory CAPM

_{u}), but also measures risk borne by comparable firms engaged in the transport of water and wastewater (β

_{u}) [50] (pp. 692–693). As is evident from its formulation and the law’s simultaneous solicitude for firm revenue and investor reward, the regulatory CAPM reflects the model’s dual functionality as a gauge of firm-specific and market-wide risk and return.

#### 5.2. Measuring Portfolio and Managerial Performance

#### 5.2.1. The Sharpe Ratio

#### 5.2.2. Jensen’s Alpha

#### 5.3. Asset Allocation and Financial Planning

#### 5.3.1. Bond Allocations

#### 5.3.2. Defined Benefit and Defined Contribution Pension Plans

## 6. Criticisms of the CAPM

#### 6.1. Value, Size, and Momentum: The “Factor Zoo”

#### 6.2. Relaxing Temporal and Spatial Constraints

#### 6.2.1. The Intertemporal CAPM

#### 6.2.2. Roll’s Second Critique

#### 6.3. Consumption-Based CAPM

#### 6.4. Modeling Heterogeneous Agents

#### 6.4.1. From Heterogeneity to Heterodoxy

#### 6.4.2. Behavioral Capital Asset Pricing

## 7. Multifractality and the Fractal Market Hypothesis

#### 7.1. Beyond Homogeneous Agents and Efficient Markets

#### 7.2. Volatility, Fractality, and the Generalized Hurst Exponent

#### 7.3. Applications and Implications of Multifractal Analysis

## 8. Conclusions: The CAPM, Dead or Alive

- The evidence against the CAPM remains at best economically ambiguous.
- Alternative models enjoy no greater empirical support.
- Simplicity and interpretive clarity preserve the CAPM’s seductive appeal.

## Funding

## Acknowledgments

## Conflicts of Interest

## Entry Link on the Encyclopedia Platform

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Chen, J.M.
The Capital Asset Pricing Model. *Encyclopedia* **2021**, *1*, 915-933.
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**AMA Style**

Chen JM.
The Capital Asset Pricing Model. *Encyclopedia*. 2021; 1(3):915-933.
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2021. "The Capital Asset Pricing Model" *Encyclopedia* 1, no. 3: 915-933.
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