Chapter13 •Return, Risk, and the Security Market Line McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights Chapter 13 – Index of Sample Problems • • • • • • • • Slide # 02 - 03 Slide # 04 - 05 Slide # 06 - 07 Slide # 08 - 18 Slide # 19 - 22 Slide # 23 - 26 Slide # 27 - 32 Slide # 33 - 35 Expected return of individual stock Standard deviation of individual stock Portfolio weights Portfolio expected return Portfolio standard deviation Portfolio beta Capital asset pricing model Reward-to-risk ratio 2: Expected return of individual stock You own 500 shares of ABC, Inc This stock has the following expected returns given the various possible states of the economy State of Economy Boom Normal Recession Probability of State of Economy 20 70 10 What is your expected return on this stock? Rate of Return if State Occurs 28% 12% -40% 3: Expected return of individual stock E r = (.20 × 28) + (.70 × 12) + (.10 × −.40) = 056 + 084 − 04 = 10 = 10% 4: Standard deviation of individual stock A stock has returns of 6.8%, 9.2%, -4.3% and 18.7% over the last four years, respectively What is the standard deviation of this stock assuming the returns are normally distributed? 5: Standard deviation of individual stock (.068 − 076) + (.092 − 076) + (−.043 − 076) + (.187 − 076) σ= −1 = 000064 + 000256 + 014161 + 012321 026802 = = 008934 = 0945 = 9.45% 068 + 092 − 043 + 187 304 = = 076 Er = 6: Portfolio weights You own 50 shares of Stock A and 200 shares of stock B Stock A sells for $30 a share and stock B sells for $22 a share What are the portfolio weights for each stock? 7: Portfolio weights Stock A B Number of Shares 50 200 Price per Share $30 $22 Totals Total Value $1,500 $4,400 $5,900 Portfolio Weight 25.4% 74.6% 100.0% 8: Portfolio expected return You have $3,600 invested in stock A and $5,400 invested in stock B Stock A has an expected return of 11% and stock B has an expected return of 7% What is the expected return of your portfolio? 9: Portfolio expected return Stock Expected Return Amount Invested A 11% $3,600 B 7% $5,400 Totals $9,000 Portfolio Weight 40% 60% 100% E r = (.40 × 11) + (.60 × 07) = 044 + 042 = 086 = 8.6% 22: Portfolio standard deviation State of Probability of Economy State of Economy Boom 10 Normal 70 Recession 20 Portfolio expected return = 0562 Expected Return if State Occurs 125 081 -.065 σ portfolio = 10 × (.125 − 0562) + 70 × (.081 − 0562) + 20 × (−.065 − 0562) = 10 × 004733 + 70 × 000615 + 20 × 014689 = 000473 + 000431 + 002938 = 003842 = 061984 = 6.20% 23: Portfolio beta Your portfolio consists of the following stocks: Stock A B C D Portfolio Weight 20% 30% 40% 10% What is the beta of your portfolio? Beta 76 1.89 1.05 34 24: Portfolio beta β portfolio = (.20 × 76) + (.30 ×1.89) + (.40 ×1.05) + (.10 × 34) = 152 + 567 + 42 + 034 = 1.173 = 1.17 (rounded) 25: Portfolio beta You want to create a portfolio that has a risk level equal to the overall market Your portfolio will consist of the following securities: Security Stock A Treasury bills Portfolio Weight ? ? What the portfolio weights need to be? Beta 1.4 ? 26: Portfolio beta β portfolio = ( w A × β A ) + ( w B × β B ) 1.0 = [ w A ×1.4] + [(1 − w A ) × 0] 1.0 = 1.4w A + w A = 7143 w A = 71.43% Weight of Stock A Weight of Treasury bills = 100% - 71.43% = 71.43% = 28.57% 27: Capital asset pricing model You own shares of Big Burgers, Inc This stock has a beta of 1.24 U.S Treasury bills are returning 3.4% The return on the market is 11.4% What is the expected return on Big Burgers, Inc.? 28: Capital asset pricing model E r = rf + β × (rm − rf ) = 034 + [1.24 × (.114 − 034)] = 034 + [1.24 × 08] = 034 + 0992 = 1332 = 13.32% 29: Capital asset pricing model You own shares of International Coffees The expected return on this stock is 16% The risk-free rate is 3% and the market risk premium is 7% What is the beta of the International Coffees stock? 30: Capital asset pricing model E r = rf + β × (rm − rf ) 16 = 03 + ( β × 07) 13 = 07 β β = 1.857 31: Capital asset pricing model A stock has a beta of 86 and an expected return of 13.5% The riskfree rate is 4% What is the expected return on the market? 32: Capital asset pricing model E r = rf + β × (rm − rf ) 135 = 04 + 86 × (rm − 04) 135 = 04 + 86rm − 0344 1294 = 86rm rm = 1505 rm = 15.05% 33: Reward-to-risk ratio Stock A B C Beta 42 1.23 89 Expected Return 6.6% 11.8% 9.8% Are these stocks correctly priced if the risk-free rate is 3% and the market risk premium is 8%? 34: Reward-to-risk ratio E r = r f + β × (rm + rf ) E r A = 03 + (.42 × 08) = 0636 E r B = 03 + (1.23 × 08) = 1284 E r C = 03 + (.89 × 08) = 1012 35: Reward-to-risk ratio Stock Expected Return CAPM Return Stock Pricing A B C 6.6% 11.8% 9.8% 6.36% 12.84% 10.12% underpriced overpriced overpriced Chapter13 •End of Chapter 13 McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights ... own 500 shares of ABC, Inc This stock has the following expected returns given the various possible states of the economy State of Economy Boom Normal Recession Probability of State of Economy 20... State of Economy Boom Normal Recession Probability of Rate of Return if State Occurs State of Economy Stock A Stock B Stock C 20 17% 13% 40% 50 8% 6% 13% 30 -12% -5% -50% Your portfolio consists of. .. State of Economy Boom 14% Normal 9% Recession -5% Probability of Rate of Return if State Occurs State of Economy Stock A Stock B Stock C 10 24% 5% 70 11% 6% 20 -30% 7% Your portfolio consists of