1 Finance School of Management Chapter 13: The Capital Asset Pricing Model Objective The Theory of the CAPM Use of CAPM in benchmarking Using CAPM to determine correct rate for discounting

2 Finance School of Management Chapter 13 Contents  The Capital Asset Pricing Model in Brief  Determining the Risk Premium on the Market Portfolio  Beta and Risk Premiums on Individual Securities  Using the CAPM in Portfolio Selection  Valuation & Regulating Rates of Return  Modifications and Alternatives to the CAPM

3 Finance School of Management 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, and –A way to estimate expected rates of return for use in evaluating stocks and projects.

4 Finance School of Management The Capital Asset Pricing Model in Brief  CAPM is an equilibrium theory based on the theory of portfolio selection.  The basic question: What would risk premiums on securities be in equilibrium if people had the same set of forecasts of expected returns and risks, and all chose their portfolios optimally according to the principles of efficient diversifications?

5 Finance School of Management Assumptions of CAPM  Assumption 1 (homogeneous in information processing) Investors agree in their forecasts of expected rates of return, standard deviation, and correlations of the risky securities.  Assumption 2 (homogeneous in behavior) Investors generally behave optimally according to the theory of portfolio selection.

6 Finance School of Management Intuitive of CAPM  All the investors will allocate their investments between the riskless asset and the same tangent portfolio.  In equilibrium, the aggregate demand for each security is equal to its supply.  The only way the asset market can clear is if the relative proportions of risky assets in tangent portfolio are the proportions in which they are valued in the market place, i.e. the market portfolio.

7 Finance School of Management Expected Return (%) rfrf The Capital Market Line (CML) Standard Deviation  Lending Borrowing MM CML Market Portfolio ● E(r M )- r f

8 Finance School of Management Efficient Risk-Reward  In equilibrium, any efficient portfolio should be a combination of the market portfolio and the riskless asset.  The best risk-reward depends on how much the market-related risk a portfolio bears.

9 Finance School of Management Determining the Risk Premium on the Market Portfolio  The equilibrium risk premium on the market portfolio is the product of –variance of the market, σ 2 M –weighted average of the degree of risk aversion of holders of risk, A

10 Finance School of Management Example: To Determine ‘A’

11 Finance School of Management Contribution of Security i to the Market Risk

12 Finance School of Management Team Work  To express the covariance between a risky security and the tangent portfolio, Cov(r i, r T ), in our example in Chapter 12, as the functions of r f, E[r i ], E[r T ], and σ T.

13 Finance School of Management Security Market Line (SML)

14 Finance School of Management Security Market Line (SML) Risk =  Expected Return SML rfrf Market Portfolio E(r M ) 1

15 Finance School of Management A Simple Derivation of CAPM  Utility maximization –risk tolerance, risk-adjusted expected return

16 Finance School of Management A Simple Derivation of CAPM

17 Finance School of Management A Simple Derivation of CAPM –For investor k –Aggregation

18 Finance School of Management A Simple Derivation of CAPM

19 Finance School of Management The Value Form of CAPM

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21 Finance School of Management Table of Prices

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23 Finance School of Management Model and Measured Values of Statistical Parameters

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25 Finance School of Management The Beta of a Portfolio  When determining the risk of a portfolio –using standard deviation results in a formula that’s quite complex –using beta, the formula is linear

26 Finance School of Management Return-Generating Process Where

27 Finance School of Management Mispriced · A Q · SML Return. rfrf Market Portfolio 1 Risk =  i

28 Finance School of Management Risk Decomposition  Total risk for a security = Market risk + Unique risk  Since the unique risk can be diversified out, the market compensates only for the market-related risk.

29 Finance School of Management Using the CAPM in Portfolio Selection  Passive portfolio management –Proxy for market portfolio –indexing  Active portfolio management –Positive ALPHA –Beat the market

30 Finance School of Management The Market Portfolio and Index Funds  The most important implication of CAPM, that the market portfolio is an efficient portfolio, forms the theoretical basis for constructing proxies of the market portfolio—the index portfolio and index funds.  However, structuring an index portfolio from the primitive securities and making adjustments are inefficient and costly.  The efficient and cheap instruments, index futures contracts were not available until  In the U.S. market, the market value of outstanding index funds was only 6 million dollars in  After ten years, the value increased to 10 billion dollars.  In 1992, the value increased to 270 billion dollars with about 1/3 pension funds being in the state of indexing.

31 Finance School of Management Valuation and Regulating Rates of Return  Discounted Cash Flow Valuation Models – Suppose you are considering investing in a new project in the same industry of Betaful Corp. – The market rate is 15%, and the risk-free rate is 5%. – The beta of Betaful’s stock is 1.3. – The capital structure of Betaful: 80% of equity, 20% of bond.

32 Finance School of Management  Compute the beta of Betaful’s operations Valuation and Regulating Rates of Return

33 Finance School of Management  Beta of Betaful’s operations is equal to the beta of the new project.  Applying the CAPM to find the required return on the new project. Valuation and Regulating Rates of Return Cost of capital

34 Finance School of Management  Assume that you start up a company which is just a vehicle for the new project, 60% capital is financed by issuing equity and 40% by issuing bond.  The beta of your unquoted equity is Valuation and Regulating Rates of Return

35 Finance School of Management  Your company is all-equity financed.  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 Valuation and Regulating Rates of Return

36 Finance School of Management Modifications and Alternatives to CAPM  Empirical testing of CAPM  Modifications –The proxy of market portfolio –Market imperfection –Multifactor Intertemporal CAPM (ICAPM): beta, sensitivity to changes in interest rates and in consumption good prices  Alternatives –Arbitrage Pricing Theory (APT)