1 Chapter 13: The Capital Asset Pricing Model Copyright © Prentice Hall Inc Author: Nick Bagley, bdellaSoft, Inc. Objective The Theory of the CAPM Use of CAPM in benchmarking Using CAPM to determine correct rate for discounting

2 Chapter 13 Contents 1 The Capital Asset Pricing Model in Brief 2 Determining the Risk Premium on the Market Portfolio 3 Beta and Risk Premiums on Individual Securities 4 Using the CAPM in Portfolio Selection 5 Valuation & Regulating Rates of Return

3 Introduction  CAPM is a theory about equilibrium prices in the markets for risky assets  It is important because it provides a justification for the widespread practice of passive investing called indexing a way to estimate expected rates of return for use in evaluating stocks and projects

4 CAPM Assumptions 1. Investors agree in their forecasts of expected rates of return, standard deviations, and correlations of the risky securities. 2. Investors generally behave optimally. In equilibrium, when investors hold their optimal portfolios, the aggregate demand for each security is equal to its supply.

5 Market Portfolio Investor’s relative holdings of risky assets is the same, thus the only way the asset market can clear is if those proportions are the proportions in which they are valued in the market place. A portfolio that holds all assets in proportion to their observed market values is called the market portfolio.

6 Market Portfolio Suppose that the market consists of n Assets with values, there are m investors with capitals participating in the markets, and they all invest in proportions in the existing assets. Then we have

7 Market Portfolio

8 The Capital Market Line

9 The Capital Market Line (CML)

10 Determining the Risk Premium on the Market Portfolio  CAPM states that the equilibrium risk premium on the market portfolio is the product of  variance of the market,  2 M  weighted average of the degree of risk aversion of holders of risk, A

11 Example: To Determine ‘A’

12 Beta The marginal contribution of the security’s return to the standard deviation of the market portfolio’s return

13 CAPM Risk Premium on any Asset  According the the CAPM, in equilibrium, the risk premium on any asset is equal to the product of  the risk premium on the market portfolio

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15 The Beta of a Portfolio  When determining the risk of a portfolio using standard deviation results in a formula that is quite complex using beta, the formula is linear

16 Using CAPM in Portfolio Selection  Diversify your holdings of risky assets in the proportions of the market portfolio, and  Mix this portfolio with the risk-free asset to achieve a desired risk- reward combination.

17 CAPM and Portfolio Selection  The portfolio used as a proxy for the market portfolio often has the same weights as well-known stock market indexes such as S&P’s 500  Thus the CAPM strategy in selecting portfolio has come to be known as indexing

18 Indexing Indexing is an attractive investment strategy because 1. As an empirical matter, it has historically performed better than most actively managed portfolios 2. It costs less to implement, no costs of research, less cost of transactions

19 CML, SML and alpha  CML provides a benchmark for measuring the performance of the investor’s entire portfolio  SML provides a benchmark for the performance of different parts of the whole portfolio  alpha: The difference between the risk premium of a portfolio and its risk premium according to SML

20 Positive alpha, Example

21 Alpha Fund and SML

22 Alpha Fund and CML

23 Valuation and Regulating Rates of Return  Assume the market rate is 15%, and the risk-free rate is 5%  A company’s capital structure consists of 80% equity with a beta of 1.3, and 20% dept. The price of one share of the company?

24  Compute the beta

25 Valuation and Regulating Rates of Return  To find the required return on the new project, apply the CAPM

26 Valuation and Regulating Rates of Return  Assume that your company has an expected dividend of $6 next year, and that it will grow annually at a rate of 4% for ever, the value of a share is

27 CAPM in Practice Empirically it is observed that CAPM does not explain fully the structure of expected returns on assets

28 Explanations 1. CAPM does hold, but the market portfolios used for testing it are incomplete representations of market portfolio 2. Market imperfections, Like borrowing costs are not contemplated in CAPM 3. Greater realism should be added to the modeling assumptions

29 Modifications ICAPM, Intertemporal CAPM In this dynamic model equilibrium risk premiums come from several dimensions of risks, not only from their beta

30 Alternatives APT, Arbitrage Pricing Theory APT gives a rationale for the expected return-beta relation that relies on the condition that there be no arbitrage profit opportunities. APT and CAPM complement each other