1 Chapter 13 Return, Risk, and Security Market Line Konan Chan Financial Management, Spring 2018 Topics Covered Expected Return and Variance Portfolio Risk and Return Risk & Diversification Systematic Risk & Beta Security Market Line Financial Management Konan Chan 2 Expected Return & Risk Expected return: Returns expected to earn on a risky asset Risk Chance of an adverse outcome; uncertainty Riskiness of cash flows of assets If future outcome is anticipated, then it s risk-free Expected Return & Risk If we know the probability distribution Expected Return (Mean) Risk (Variance or Standard deviation) Variance Standard deviation is the square root of variance Financial Management Konan Chan 3 Financial Management Konan Chan 4 Return and Risk - Example State of Probability Stock Bond economy Boom 25% 80% 5% Return and Risk - Example r S = 0.25*0.8+0.6*0.3+0.15*(-0.3) = 0.335 r B = 0.25*0.05+0.6*0.1+0.15*0.15 = 0.095 Standard deviation Normal 60% 30% 10% Recession 15% -30% 15% Financial Management Konan Chan 5 Financial Management Konan Chan 6
Portfolio Risk and Return In previous example, r S =33.5% and r B =9.5% What is the expected return of a portfolio consisting of 60% stock and 40% bond? r P = 0.6*33.5%+0.4*9.5%=23.9% Portfolio Risk - Example State of Prob. Portfolio (60% S+40% B) economy Boom 25% 50% Normal 60% 22% Recession 15% -12% How about portfolio risk? It s not a weighted average of standard deviations Expected return=23.9% Standard deviation=19.1% Financial Management Konan Chan 7 Financial Management Konan Chan 8 Portfolio Risk The portfolio risk is affected by the relationship between returns of different assets In general, lower relationship among assets reduce the portfolio risk When the portfolio includes more assets, it s more likely that these assets are with lower relationship Financial Management Konan Chan 9 Financial Management Konan Chan 10 Risk and Diversification (Unique risk) (Market risk) Diversification Strategy designed to reduce risk by spreading the portfolio across many investments Unique Risk (diversifiable risk) Risk factors affecting only that firm or asset Market Risk (systematic risk) Economy-wide sources of risk that affect the overall stock market, cannot be diversified away Financial Management Konan Chan 11 Financial Management Konan Chan 12
Systematic Risk Principle There is a reward for bearing risk There is not a reward for bearing risk which is not necessary (e.g. unique risk) The expected return on a risky asset depends only on that asset s systematic risk since unsystematic risk can be diversified away Financial Management Konan Chan 13 Measuring Market Risk Market Portfolio Portfolio of all assets in the economy. A broad index, such as S&P 500, is used Beta Sensitivity of stock s return to the market portfolio return How stock s return changes with market return changes Proxy for market risk Financial Management Konan Chan 14 Computing Beta Beta is the slope of the regression line y = a +βx between a stock s return (y) and the market return (x) over time The Concept of Beta Beta (β) measures how the return of an individual asset (or even a portfolio) varies with the market portfolio (such as S&P 500). β = 1.0: same risk as the market (average stock) β < 1.0: less risky than market (defensive stock) β > 1.0: more risky than market (aggressive stock) Financial Management Konan Chan 15 Financial Management Konan Chan 16 Stock Betas Portfolio Betas The beta of a portfolio is the weighted average of betas of the securities in the portfolio If you owned all stocks of S&P 500 Index, you would have an average beta of 1.0 Financial Management Konan Chan 17 Financial Management Konan Chan 18
CAPM Capital Asset Pricing Model (CAPM) Theory of relationship between risk and return Expected (required) return = risk-free rate + beta * market risk premium Market risk premium = r m r f Expected (required) return E(r i ) = r f + [ E(r m ) r f ] Financial Management Konan Chan 19 CAPM - Example What is Yahoo s expected return if its =1.8, the current 3-month T-bill rate is 4%, and the historical market risk premium of 7% is demanded? r Yahoo = r f +β(r m r f ) = 4% + 1.8*7% = 16.6% Financial Management Konan Chan 20 CAPM and Valuation We can use CAPM to calculate a stock s expected return for valuation purposes. Also, in equilibrium, our previous expected return formulas should equal CAPM return. Expected return = expected dividend yield + capital gain yield = CAPM expected return CAPM and Valuation - example Your stockbroker calls you to buy Goody Inc. The stock is currently selling for $15 a share The risk free rate is 5%, and you demand a 17% return on the market. Goody's current dividend is $4 a share Some analyst has estimated that Goody's beta is 2.0 and that the stock's dividend will grow at a constant 8% Is recommendation to buy Goody a good one? What do you think the stock is worth? Financial Management Konan Chan 21 Financial Management Konan Chan 22 CAPM and Valuation - example D 0 = 4, g = 8%, r m = 17%, r f = 5%,β= 2 Based on CAPM, r = 5%+2*(17%-5%) = 29% P 0 = $4*(1 + 8%) / (29% - 8%)= $20.57 Intrinsic value $20.57 > market value $15 Good recommendation?? Market Equilibrium In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market Financial Management Konan Chan 23 Financial Management Konan Chan 24
The Security Market Line (SML) SML - Example 1.0 A graphical representation of the CAPM equation Y axis = expected return, X axis = beta Intercept = risk-free rate (β = 0) Slope of SML = market risk premium The change of the risk free rate will shift the SML The change of the market risk premium will change the slope of the SML Marge s stock currently sells for its equilibrium price of $30 a share Marge s current dividend is $1.91 and is expected to grow at a 10% constant annual rate forever The current risk-free rate is 3%, and the required return on the market is 11% What is the beta for Marge? What would be the new equilibrium stock price of Marge if the risk-free rate increases to 4% and the required market return increases to 13%? Financial Management Konan Chan 25 Financial Management Konan Chan 26 Marge s Beta Use the DDM model to calculate the required rate of return (r) D 0 = $1.91, P 0 = 30, g = 10% r =D 0 (1+g)/P 0 + g = 1.91*1.1/30+10% = 17% Based on CAPM, r =17%= 3%+ *(11%-3%) So, =1.75 Marge s New Price =1.75, D 0 = $1.91, P 0 = 30, g = 10% New r f = 4%, r m =13% Based on CAPM, r = 4% + 1.75*(13% - 4%) = 19.75% New price is $1.91*(1+10%)/(19.75%-10%) = $21.55 Financial Management Konan Chan 27 Financial Management Konan Chan 28 Expected vs. Unexpected Returns Realized returns are generally not equal to expected returns Return = expected return + unexpected return At any point in time, the unexpected return can be either positive or negative Over time, the average of the unexpected component is zero Announcements and News Announcements and news contain both an expected component and a surprise component It is the surprise component that affects a stock s price and therefore its return Stock prices move when an unexpected announcement is made or earnings are different than anticipated Financial Management Konan Chan 29 13-30
Efficient Markets Quick Quiz Efficient markets are a result of investors trading on the unexpected portion of announcements The easier it is to trade on surprises, the more efficient markets should be Efficient markets involve random price changes because we cannot predict surprises How do you compute the expected return and standard deviation For an individual asset? For a portfolio? What is the difference between systematic and unsystematic risk? Which determines the expected return? How to estimate expected returns? 13-31 Financial Management Konan Chan 32