C. Capital Asset Pricing and Arbitrage Pricing Theory

1.  Capital Asset Pricing Model (CAPM)

a.  Assumptions

(1) Market structure

(a) No investor is wealthy enough to affect the market price

(b) All information is publicly available

(c) All securities are publicly owned and traded

(d) No taxes

(e) No transactions costs

(f)  Unlimited borrowing or lending at a common risk-free rate

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(2) Individual behavior

(a) Planning horizon is a single period

(b) Investors are rational, mean-variance optimizers

(c) Investors have homogeneous expectations - use same inputs and consider identical portfolio opportunity sets

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b.  Equilibrium

(1)  All investors will hold the market portfolio (M) - each security held in proportion to total market value

• Mean-variance criterion used on same universe of securities, with identical time horizon, using same security analysis, and with same returns

• If a security is missing, price drops until it is attractive enough to be in portfolio

• Passive strategy is efficient - mutual fund theorem

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(2)  Market portfolio will be on the efficient frontier

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• Capital allocation line becomes capital market line (CML)

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(3)  Risk premium of the market portfolio

• Proportional to variance of market portfolio and investors' typical degree of risk aversion

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(4) Expected returns on individual securities

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• Security market line

  • Deals with individual securities

  • Examine contribution of the asset to the risk of the portfolio

  • Use beta to measure risk

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• Security market line provides a benchmark for evaluation of investment performance

- Provides required rate of return necessary to compensate investors for risk and time value of money

- Fairly priced assets are on SML

- Underpriced stocks are above the SML

- Overpriced stocks are below the SML

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• Alpha - difference between the fair and actually expected rates of return on a stock

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c.  Applications of the CAPM

(1) Provides benchmark for fair return on a risky asset

(2) Can also provide the required rate of return a project must yield in capital budgeting decisions

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2.  Index models

a.  Problems with CAPM

(a) Relies on theoretical market portfolio

(b) Applies to expected returns, not actual returns

• Use index model and realized returns to implement CAPM

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b. Index model

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c.  Estimating the model

• Use regression

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3.  Arbitrage pricing theory