Ch. 11: Risk and Return

1. Ch. 11: Risk and Return • Expected Returns & Variances • Relevant Risk & Portfolio Diversification • Beta • Security Market Line, CAPM

2. Expected Returns & Variances • Expected return: historic versus projected • Expected risk premium = • Expected return - Risk-free rate • Expected return of a portfolio • Portfolio variance and standard deviation

3. Example Returns for Stock W, Stock X, & Portfolio (25%X + 75%W) Year W X PortfolioExcel Formula 1991 40% 33% 38% 1992 -10% 2% -7% 1993 35% -20% 21% 1994 -5% 10% -1% 1995 15% 15% 15% =0.75*B29+0.25*C29 mean 15.0% 8.0% 13.2% =SUM(D25:D29)/5 stdev 22.6% 19.4% 18.1% =STDEV(D25:D29) correlation W&X = 0.10 =CORREL(B25:B29,C25:C29)

4. Surprise & Risk Return = Expected return + Unexpected return R = E(R) + U Announcement = Expected part + Surprise Systematic (market) risk Unsystematic (unique, diversifiable) risk R = E(R) + Systematic portion + Unsystematic portion

5. Portfolio Diversification & Beta • See Fig. 11.1, p. 319 • Some individual asset risk can be eliminated by portfolio diversification and some cannot • Unsystematic risk can be • Systematic risk cannot be • The reward for bearing risk depends on the systematic risk of the investment • Beta () measures the systematic risk of an asset relative to the average asset’s systematic risk. Beta for the average asset = 1 • Portfolio beta is weighted average of asset betas

6. Beta  measures a stock’s contribution to the riskiness of a well-diversified portfolio  = slope coefficient from regressing stock’s returns on market portfolio’s returns. The regression equation is y = a + x + e, where y is the dependent variable (stock return), a is the intercept, x is the market return, and e is the error

7. Example (A) (B) (C) (D) Year Stock X Stock Y Market 1994 14 13 12 1995 19 7 10 1996 -16 -5 -12 1997 3 1 1 1998 20 11 15 a. Find betas: Use Function Wizard's LINEST function to regress stock returns on market returns: beta for X = 1.347 =LINEST(B70:B74,D70:D74) beta for Y = 0.651 =LINEST(C70:C74,D70:D74)

8. Security Market Line (SML) • Beta of a risk-free asset = 0 Why? • Beta of market portfolio = 1 Why? • Derive SML graphically (p. 330) • SML: E(Ri) = Rf + (E(RM) - Rf) * i • Slope = E(RM) - Rf = “market risk premium,” measures risk aversion, how much return over the risk-free rate is required to get investors to bear the market portfolio’s risk • Intercept: Rf • Reward-to-risk ratio is same for all assets in market

9. Example continued Part b): Assume risk-free rate = 6%, market risk premium = 5% Find required rates of return, using Security Market Line: SML: E(Ri) = Rf + (E(RM) - Rf) * i We know E(RM) - Rf is the market risk premium, 5% Therefore, according to the SML, for X, kX = 6 + 5*1.347 = 12.736 for Y, kY = 6 + 5*.651 = 9.254 The betas were calculated earlier

10. CAPM • Capital Asset Pricing Model (CAPM): definition • E(Ri) = Rf + (E(RM) - Rf) * i • Expected return depends on pure time value of money, reward for bearing systematic risk, and amount of systematic risk • Out-of-equilibrium: • An undervalued stock will graph above the SML • How does it reach equilibrium? • An overvalued stock will graph below the SML • How does it reach equilibrium? • Why do stocks (assets) get out-of-equilibrium?

11. Example finished Portfolio’s beta = weighted average of individual betas Part c): Find the required rate of return for the portfolio of 80% X and 20% Y Beta for Portfolio = .8*1.347 + .2*.651 = 1.208 Using the SML, the expected return on the portfolio is E(RP) = 6 + 5*1.208 = 12.039 Also E(RP) is the weighted average of E(Rx) & E(Ry) from above: E(RP) = .8(12.736) + .2(9.254)

12. Recommended Practice • Self-Test Problems 11.3 & 11.4, pp. 333-4 • Questions 2, 6, 7, p. 335 • Problems on pp. 336-41: 3, 11, 13, 15, 19, 37, 39 (answers are on p. 549)