The CAPM (cont’d)

1. The CAPM (cont’d) Market portfolio Capital market line Security market line Fama and French model

2. CAPM: recap • Equilibrium relationship between the risk and expected return on risky assets • Builds on Markowitz portfolio theory • Each investor is assumed to diversify his or her portfolio • Only compensate investors for bearing non-diversifiable, or systematic risk

3. A. Market Portfolio • From the Markowitz Portfolio Selection model • Mutual Fund Separation Theorem (Separation Property) • All investors hold the same portfolio of risky assets • CAPM: extension of the Markowitz model • In equilibrium: this risky portfolio consists of all risky securities in the market • Hence, the name - market portfolio

4. Characteristics of the Market Portfolio • All risky assets must be in the market portfolio, so it is completely diversified • Contains only systematic risk • All securities included in proportion to their market value • Unobservable, need to find a proxy when applying the CAPM in practice • In theory, should contain all risky assets worldwide

5. B. Capital Market Line L • Line from RF to L is the capital market line (CML) • x = market risk premium = E(rM) - rF • y = risk = M • Slope x/y = [E(rM) - rF]/M M E(rM) x rF y M Risk

6. CML (cont’d) • Hence, the relationship between risk and expected return for portfolio P (equation for CML): • Slope of the CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market (market risk premium per unit of risk)

7. C. Security Market Line (SML) • The CML applies to markets in equilibrium and to the selection of efficient portfolios • The SML depicts the tradeoff between risk and expected return for individual securities in equilibrium • Under the CAPM, all investors hold the market portfolio • How does an individual security contribute to the risk of the market portfolio? Focus: covariance between security and market

8. SML (cont’d) • Equation for the expected return for an individual security, E(Ri), is similar to the CML equation: • Difference is the risk of security i is not its standard deviation, it’s beta • All securities lie on the SML in equilibrium

9. SML (cont’d) • Beta = 1.0 implies: as risky as market • Securities A and B are riskier than the market • Beta > 1.0 • Security C is less risky relative to the market • Beta < 1.0 SML E(r) A E(rM) B C rF 0 0.5 1.0 1.5 2.0 BetaM

10. SML: Applications • Evaluation of portfolio performance • Hurdle rate for capital budgeting, cost of equity, or the required rate of return (ki): ki = RF +i [ E(RM) - RF ] • The greater the systematic risk, the greater the required return

11. D. Fama and French Model • Newer model, gaining acceptance in industry • Takes into account additional factors: size, and book-to market factors • Previous research has shown that beta is not the only factor that explains stock or portfolio returns • No theory behind the model, entirely driven by data

12. Fama and French (cont’d) • Asset return as a function of three types of risk premia: • Market return minus risk-free rate • SMB (Small Minus Big): return on small-cap stocks minus return on large-cap stocks • HML (High Minus Low): return on high book-to-market stocks minus return on low book-to-market stocks

13. Fama and French (cont’d) • FF (1993) proposes this model: • FF provide free data (annual, monthly, daily) for the three factors (see Kenneth French’s website) • Ibbotson Associates (now part of Morningstar) sells two types of cost of equity data: one using the CAPM, and the other using the FF model