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INVESTMENTS | BODIE, KANE, MARCUS Chapter Nine The Capital Asset Pricing Model INVESTMENTS | BODIE, KANE, MARCUS 9-* Capital Asset Pricing Model (CAPM) It is the equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development * INVESTMENTS | BODIE, KANE, MARCUS 9-* Assumptions Investors optimize portfolios a la Markowitz Investors use identical input list for efficient frontier Same risk-free rate, tangent CAL and risky portfolio Market portfolio is aggregation of all risky portfolios and has same weights INVESTMENTS | BODIE, KANE, MARCUS 9-* Resulting Equilibrium Conditions All investors will hold the same portfolio for risky assets – market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value INVESTMENTS | BODIE, KANE, MARCUS 9-* Figure 9.1 The Efficient Frontier and the Capital Market Line INVESTMENTS | BODIE, KANE, MARCUS 9-* Market Risk Premium The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor: E(RM) = Ᾱσ2M Where σ2M is the variance of the market portfolio and á¾¹ is the average degree of risk aversion across investors INVESTMENTS | BODIE, KANE, MARCUS 9-* Return and Risk For Individual Securities The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio.

An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio. INVESTMENTS | BODIE, KANE, MARCUS 9-* GE Example Covariance of GE return with the market portfolio: Therefore, the reward-to-risk ratio for investments in GE would be: INVESTMENTS | BODIE, KANE, MARCUS 9-* GE Example Reward-to-risk ratio for investment in market portfolio: Reward-to-risk ratios of GE and the market portfolio should be equal: INVESTMENTS | BODIE, KANE, MARCUS 9-* GE Example The risk premium for GE: Restating, we obtain: INVESTMENTS | BODIE, KANE, MARCUS 9-* Expected Return-Beta Relationship CAPM holds for the overall portfolio because: This also holds for the market portfolio: INVESTMENTS | BODIE, KANE, MARCUS 9-* Figure 9.2 The Security Market Line INVESTMENTS | BODIE, KANE, MARCUS 9-* Figure 9.3 The SML and a Positive-Alpha Stock INVESTMENTS | BODIE, KANE, MARCUS 9-* Single-Index Model and Realized Returns To move from expected to realized returns, use the index model in excess return form: The index model beta coefficient is the same as the beta of the CAPM expected return-beta relationship.

INVESTMENTS | BODIE, KANE, MARCUS 9-* Assumptions of the CAPM Individuals Mean-variance optimizers Homogeneous expectations All assets are publicly traded Markets All assets are publicly held All information is available No taxes No transaction costs INVESTMENTS | BODIE, KANE, MARCUS 9-* Extensions of the CAPM Zero-Beta Model Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks Consideration of labor income and non-traded assets INVESTMENTS | BODIE, KANE, MARCUS 9-* Extensions of the CAPM Merton’s Multiperiod Model and hedge portfolios Incorporation of the effects of changes in the real rate of interest and inflation Consumption-based CAPM Rubinstein, Lucas, and Breeden Investors allocate wealth between consumption today and investment for the future INVESTMENTS | BODIE, KANE, MARCUS 9-* Liquidity and the CAPM Liquidity: The ease and speed with which an asset can be sold at fair market value Illiquidity Premium: Discount from fair market value the seller must accept to obtain a quick sale.

Measured partly by bid-asked spread As trading costs are higher, the illiquidity discount will be greater. INVESTMENTS | BODIE, KANE, MARCUS 9-* Figure 9.5 The Relationship Between Illiquidity and Average Returns INVESTMENTS | BODIE, KANE, MARCUS 9-* Liquidity Risk In a financial crisis, liquidity can unexpectedly dry up. When liquidity in one stock decreases, it tends to decrease in other stocks at the same time. Investors demand compensation for liquidity risk Liquidity betas INVESTMENTS | BODIE, KANE, MARCUS 9-* CAPM and World Academic world Cannot observe all tradable assets Impossible to pin down market portfolio Attempts to validate using regression analysis Investment Industry Relies on the single-index CAPM model Most investors don’t beat the index portfolio ðºð¸â€²ð‘ ð‘ð‘œð‘›ð‘¡ð‘Ÿð‘–ð‘ð‘¢ð‘¡ð‘–ð‘œð‘› ð‘¡ð‘œ ð‘Ÿð‘–ð‘ 𑘠ð‘ð‘Ÿð‘’ð‘šð‘–ð‘¢ð‘š ðºð¸ ′ ð‘ ð‘ð‘œð‘›ð‘¡ð‘Ÿð‘–ð‘ð‘¢ð‘¡ð‘–ð‘œð‘› ð‘¡ð‘œ ð‘£ð‘Žð‘Ÿð‘–ð‘Žð‘›ð‘ð‘’ = 𑤠ðºð¸ ð¸(ð‘… ðºð¸ ) 𑤠ðºð¸ ð¶ð‘œð‘£(ð‘… ðºð¸ ,ð‘… ð‘€ ) = ð¸(ð‘… ðºð¸ ) ð¶ð‘œð‘£(ð‘… ðºð¸ ,ð‘… ð‘€ ) à·ð‘¤ ð‘– ð¶ð‘œð‘£ (ð‘… ð‘– ð‘› ð‘–=1 ,ð‘… ðºð¸ )=à·ð¶ð‘œð‘£ (𑤠𑖠𑅠𑖠𑛠ð‘–=1 ,ð‘… ðºð¸ )=ð¶ð‘œð‘£àµà· 𑤠𑖠𑅠𑖠𑛠ð‘–=1 ,ð‘… ðºð¸ ൱ ð‘€ð‘Žð‘Ÿð‘˜ð‘’ð‘¡ ð‘Ÿð‘–ð‘ 𑘠ð‘ð‘Ÿð‘’ð‘šð‘–ð‘¢ð‘š ð‘€ð‘Žð‘Ÿð‘˜ð‘’ð‘¡ ð‘£ð‘Žð‘Ÿð‘–ð‘Žð‘›ð‘ð‘’ = ð¸(ð‘… ð‘€ ) 𜎠𑀠2 ð¸(ð‘… ðºð¸ ) ð¶ð‘œð‘£(ð‘… ðºð¸ ,ð‘… ð‘€ ) = ð¸(ð‘… ð‘€ ) 𜎠𑀠2 ( ) ( ) [ ] f M GE f GE r r E r r E - + = b ð¸ ሺ ð‘… ðºð¸ ሻ = ð¶ð‘œð‘£(ð‘… ðºð¸ ,ð‘… ð‘€ ) 𜎠𑀠2 ð¸(ð‘… ð‘€ ) P()() andPkkkkkkErwErwï¢ï¢ï€½ï€½ïƒ¥ïƒ¥ ()()MfMMfErrErrï¢ïƒ©ïƒ¹ï€½ï€«ï€ïƒ«ïƒ» iiiMiRReï¡ï¢ï€½ï€«ï€« Chapter 09 - The Capital Asset Pricing Model Chapter Nine The capital asset pricing Model CHAPTER OVERVIEW This chapter presents the capital asset pricing model (CAPM), which is an equilibrium model for the pricing of assets based upon risk.

This model rules out the possibility of arbitrage profits, that is, the exploitation of mispriced securities. The chapter begins with a simplified two-security example that develops the concept of demand for shares and how prices of securities would change with changes in demand. The presentation includes the assumptions that underlie the CAPM, major implications of model, and development of the Security Market Line. Extensions covered in the chapter include the zero beta model and incorporation of liquidity costs. LEARNING OBJECTIVES After studying this chapter, the student should be able to explain the theory of the capital asset pricing model (CAPM), and be able to construct and use the security market line.

The student should also have a thorough understanding of the zero beta formulization and the impact that differential liquidity costs may have on expected return. Presentation of Material 9.1 The Capital Asset Pricing Model The introduction of the CAPM starts with an overview of the importance of the model and the assumptions that underlie it. The implications or conditions that result from the CAPM are described. Discussion of the equilibrium conditions that result from the model is very important before the analytical development of the CAPM. Once the major implications and conditions have been discussed, the Capital Market Line can be derived.

The market risk premium is displayed and The Capital Market Line (CML) is shown in Figure 9.1. In discussing the CML, it is helpful to tie in the concept of dominance covered in previous chapters. The conclusion that investors, regardless of their risk preferences, will combine the market portfolio with the risk free rate is an important topic to discuss. Since the equilibrium conditions result in all investors holding the same portfolio of risky investments, pricing on individual securities is related to the risk that individual securities have when they are included in the market portfolio. The relevant measure of risk is the covariance of returns on the individual securities with the market portfolio.

Given that the relevant measure of risk is the risk that is related to the market portfolio, the Security Market Line (SML) describes that relationship. The slope of the SML is the market risk premium. The beta for the individual security is . When first examining these concepts, students often confuse the slope of the SML with the slope of the Security Characteristic Line. It is useful to spend class discussion time clarifying the differences in these relationships.

The text considers GE as an example to help illustration these concepts. 9.2 Assumptions and Extensions of the CAPM The assumptions used in the equilibrium model are explained using investor expectations. Notably, the CAPM would predict alpha values of zero for all securities. We find that alphas are not exactly zero as suggested by the model but the distribution of alpha’s show that they are distributed around a mean of zero. While the model fails empirical tests, CAPM has been widely accepted and fairly robust.

Liquidity is an important factor in determining prices and expected returns. Data show that variations in liquidity are systematic, affecting all stocks. Later studies demonstrate the relationship between greater liquidity levels and higher average returns. A few other important extensions of the CAPM are presented in this section- Black’s Zero Beta Model, the incorporation of labor income and non-traded assets, and Merton’s Multi-period Model. 9.3The CAPM and the Academic World Testing of the unobservable CAPM market portfolio is targeted at the mean-beta relationship with respect to a stock index portfolio.

When assessing the empirical success of the CAPM, it is important to consider the econometric technique as demonstrated in a paper by Miller and Scholes. They considered a checklist of difficulties encountered in testing the model and showed how these problems potentially could bias conclusions. 9.4 The CAPM and the Investment Industry Despite failing empirical tests, the industry continues to use the single-index CAPM model. Tests over time prove it extremely difficult to outperform the broad market portfolio, as is evidenced by the alpha distributions of mutual funds in figure 9.5. These observations validate the passive strategy the CAPM deems optimal.

9-1 (,) () im m Covrr Varr Week 5 - Assignment: Compare and Contrast Pricing Models Instructions Evaluate the development of the Capital Asset pricing Model (CAPM) in a paper. Identify and analyze the different applications to the CAPM, looking at consumption-based CAPM and the zero-beta model. Be clear in illustrating how the model can be used to form important expected return measures and in turn valuation measure. Some of the illustrations should be from stock options and restricted stock. Conduct a comparative analysis of the potential outcomes associated and comparative benefits and risks for using the capital asset pricing model (CAPM) verse the arbitrage pricing theory (APT).

Support your paper with minimum of five (5) resources. In addition to these specified resources, other appropriate scholarly resources, including older articles, may be included. Length: 5-7 pages not including title and reference pages Your paper should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Capital Asset Pricing Model (CAPM) Bodie, Kane, and Marcus (2014) state that the CAPM assumes that investors are single-period planners who agree on a common input list from security analysis and seek mean-variance optimal portfolios.

The CAPM assumes that security markets are ideal in the sense that: a. They are large, and investors are price-takers. b. There are no taxes or transaction costs. c. All risky assets are publicly traded. d. Investors can borrow and lend any amount at a fixed risk-free rate.

With these assumptions, all investors hold identical risky portfolios. The CAPM holds that in equilibrium the market portfolio is the unique mean-variance efficient tangency portfolio. Thus a passive strategy is efficient. The CAPM market portfolio is a value-weighted portfolio. Each security is held in a proportion equal to its market value divided by the total market value of all securities.

If the market portfolio is efficient and the average investor neither borrows nor lends, then the risk premium on the market portfolio is proportional to its variance, σ2 M , and to the average coefficient of risk aversion across investors, A: The CAPM implies that the risk premium on any individual asset or portfolio is the product of the risk premium on the market portfolio and the beta coefficient: where the beta coefficient is the covariance of the asset with the market portfolio as a fraction of the variance of the market portfolio: Review the resources listed in the Books and Resources area below to prepare for this week's assignment. Bodie, Z., Kane, A., & Marcus, A. J. (2013). Investments New York, NY McGraw-Hill-Irwin.

Read Chapter 9 Carere, J. (2010, July 21). Capital Asset Pricing Model (CAPM) [Video file]. Graulich, V. (2013, March 3). CAPM: Capital Asset Pricing Model (a simple model of the Security Market Line) [Video file].

Paper for above instructions

The Capital Asset Pricing Model (CAPM) is a critical tool in modern finance as it establishes a linear relationship between the expected return of an asset and its risk. Rooted in the work of Markowitz, Sharpe, Lintner, and Mossin, CAPM simplifies numerous assumptions about investor behavior, portfolio management, and market equilibrium (Bodie, Kane, & Marcus, 2014). This paper will evaluate the development of CAPM, its applications including the Consumption-based CAPM and Black’s Zero-Beta model, and conduct a comparative analysis with Arbitrage Pricing Theory (APT).

Development of CAPM

At the core of CAPM is the assumption that investors are rational and aim for mean-variance efficiency—balancing return with risk. Investors are also presumed to make decisions based on the expected return and the volatility of their portfolios, with the market portfolio representing the optimal blend of risky assets (Bodie et al., 2014). The key formula for CAPM is:
\[
E(R_i) = R_f + \beta_i(E(R_m) - R_f)
\]
Where:
- \(E(R_i)\) is the expected return of the investment.
- \(R_f\) is the risk-free rate.
- \(E(R_m)\) is the expected return of the market portfolio.
- \(\beta_i\) measures the sensitivity of the asset’s returns relative to the market returns.

The Efficiency Frontier and Market Portfolio

The concept of efficient fronts developed by Markowitz plays a significant role in CAPM. Investors choose portfolios along this frontier to maximize returns for a given level of risk. When considering CAPM, all investors jointly hold the market portfolio, which encompasses all available risky assets proportionate to their market capitalization. This leads to the conclusion that if all investors adhere to the same risk-return relationship, the market must be in equilibrium as asserted by CAPM (Carere, 2010).

Applications of CAPM

Consumption-Based CAPM

Consumption-based CAPM (CCAPM) extends the insights from the traditional CAPM by incorporating consumer behavior into asset pricing. It acknowledges that the utility function of individuals is not solely based on wealth but also on consumption patterns across different time periods (Rubinstein, Lucas, & Breeden, 2008). Thus, the expected returns on assets must reflect their covariance with the consumption growth instead of just market returns. CCAPM can better capture real-world factors impacting investment decisions, acting more accurately in multi-period models (Merton, 1973).

Zero-Beta Model

Black’s Zero-Beta Model is another extension that addresses certain anomalies observed with traditional CAPM. This model posits the existence of a zero-beta asset—a theoretical asset that has no covariance with the market portfolio during equilibrium (Black, 1972). It suggests that the expected return can still be determined even if a portfolio does not have the same risk characteristics as the traditional market portfolio. This addresses the cases of negative beta assets, typically considered undesirable in standard CAPM.

Valuation of Stocks and Options Using CAPM

CAPM serves as a foundational tool for pricing various financial instruments, including stocks and options. By employing the CAPM framework, investors can estimate the cost of equity for firms, which is integral for valuation methods, such as the Discounted Cash Flow (DCF) approach. For example, if a company is evaluated using the CAPM, the expected return derived can influence decisions regarding stock purchases, ensuring that investors demand a higher return for higher risk (Huang & Litzenberger, 1988).
Similarly, in the context of options, CAPM provides a basis for evaluating the expected returns on investments in derivatives relative to their risk levels (Merton, 1973). Options pricing models may draw upon the expected return estimates grounded in CAPM to assess the inherent risk associated with various options strategies.

Comparative Analysis with Arbitrage Pricing Theory (APT)

While CAPM offers a consolidated view of expected returns based on systematic risk, Arbitrage Pricing Theory (APT) presents a more flexible approach by allowing multiple factors to influence asset returns. APT assumes that returns can be modeled as a linear function of various macroeconomic factors—or underlying risk factors—rather than exclusively relying on market risk (Ross, 1976).

Benefits of CAPM

1. Simplicity: CAPM’s straightforward linear relationship between risk and return provides a practical tool for portfolio management (Bodie et al., 2014).
2. Ease of Use: It readily allows investors to gauge expected returns based on historical data, making it accessible for both institutional and retail investors.

Drawbacks of CAPM

1. Assumptions: CAPM's reliance on assumptions of frictionless markets and rational investors may not always hold true in the real world (Fama & French, 2004).
2. Empirical Validity: Several empirical studies have shown that the relationship between expected returns and beta is weak, suggesting that CAPM may overlook certain risk factors (Fama, 1996).

Benefits of APT

1. Multi-Factor Framework: APT provides a more comprehensive model by acknowledging that multiple systematic risks can affect asset prices, thus capturing the complexities of market behavior (Ross, 1976).
2. Flexibility: It allows for greater customization by enabling analysts to include relevant factors impacting specific sectors or assets.

Drawbacks of APT

1. Complexity: APT can be considerably more complicated than CAPM and requires more sophisticated statistical and econometric analyses.
2. No Risk-Free Asset: Unlike CAPM, APT does not necessitate a risk-free asset, which complicates its practical application.

Conclusion

In summary, the Capital Asset Pricing Model serves as a cornerstone of modern asset pricing theory, offering valuable insights into the risk-return relationship. Through its extensions—Consumption-based CAPM and Black’s Zero-Beta model—CAPM adapts to real-world complexities and investor behavior. However, while CAPM remains a robust starting point for valuing assets, the Arbitrage Pricing Theory provides a nuanced alternative that accounts for multiple risk factors, potentially offering a more realistic depiction of market dynamics. Investors would benefit from understanding both models, considering the context of their portfolio strategies and market scenarios.

References

1. Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments. New York, NY: McGraw-Hill.
2. Black, F. (1972). Capital Market Equilibrium with Restricted Borrowing. Journal of Business, 45(3), 444-455.
3. Carere, J. (2010). Capital Asset Pricing Model (CAPM). Retrieved from [Video file].
4. Fama, E. F. (1996). The Behavior of Stock Market Prices. Journal of Business, 38(1), 34-105.
5. Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
6. Huang, C. F., & Litzenberger, R. H. (1988). Foundations for the Theory of Dynamic Asset Pricing. Journal of Finance, 43(5), 197-204.
7. Merton, R. C. (1973). An Intertemporal Capital Asset Pricing Model. Econometrica, 41(5), 867-887.
8. Rubinstein, M., Lucas, R. E., & Breeden, D. T. (2008). Consumption-Based Asset Pricing. Journal of Financial Economics, 93(1), 13-30.
9. Ross, S. A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, 13(3), 341-360.
10. Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. Journal of Finance, 19(3), 425-442.