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

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

Example Returns for Stock W, Stock X, & Portfolio (25%X + 75%W) Year W X Portfolio Excel 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)

Surprise & Risk R = E(R) + U 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

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

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

Example (A) (B) (C) (D) Year Stock X Stock Y Market 1994 14 13 12 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)

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

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

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 Why do stocks (assets) get out-of-equilibrium?

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)

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)