Tài liệu Tài chính doanh nghiệp ( Bài tập)_ Chapter 10 doc

Chapter 10: Return and Risk: The Capital Asset Pricing Model (CAPM) 10.1 a Expected Return = (0.1)(-0.045) + (.2)(0.044) + (0.5)(0.12) + (0.2)(0.207) = 0.1057 = 10.57% The expected return on Q-mart’s stock is 10.57% b Variance (σ2) = (0.1)(-0.045 – 0.1057)2 + (0.2)(0.044 – 0.1057)2 + (0.5)(0.12 – 0.1057)2 + (0.2)(0.207 – 0.1057)2 = 0.005187 Standard Deviation (σ) = (0.005187)1/2 = 0.0720 = 7.20% The standard deviation of Q-mart’s returns is 7.20% 10.2 a Expected ReturnA = (1/3)(0.063) + (1/3)(0.105) + (1/3)(0.156) = 0.1080 = 10.80% The expected return on Stock A is 10.80% Expected ReturnB = (1/3)(-0.037) + (1/3)(0.064) + (1/3)(0.253) = 0.933 = 9.33% B The expected return on Stock B is 9.33% b VarianceA (σA2) = (1/3)(0.063 – 0.108)2 + (1/3)(0.105 – 0.108)2 + (1/3)(0.156 – 0.108)2 = 0.001446 Standard DeviationA (σA) = (0.001446)1/2 = 0.0380 = 3.80% The standard deviation of Stock A’s returns is 3.80% VarianceB (σB2) = (1/3)(-0.037 – 0.0933)2 + (1/3)(0.064 – 0.0933)2 + (1/3)(0.253 – 0.0933)2 = 0.014447 B Standard DeviationB (σB) = (0.014447)1/2 = 0.1202 = 12.02% B B The standard deviation of Stock B’s returns is 12.02% c Covariance(RA, RB) = (1/3)(0.063 – 0.108)(-0.037 – 0.0933) + (1/3)(0.105 – 0.108)(0.064 – 0.933) + (1/3)(0.156 – 0.108)(0.253 – 0.0933) = 0.004539 B The covariance between the returns of Stock A and Stock B is 0.004539 Correlation(RA,RB) = Covariance(RA, RB) / (σA * σB) B B B = 0.004539 / (0.0380 * 0.1202) = 0.9937 The correlation between the returns on Stock A and Stock B is 0.9937 10.3 a Expected ReturnHB = (0.25)(-0.02) + (0.60)(0.092) + (0.15)(0.154) = 0.0733 = 7.33% The expected return on Highbull’s stock is 7.33% Expected ReturnSB = (0.25)(0.05) + (0.60)(0.062) + (0.15)(0.074) = 0.0608 = 6.08% The expected return on Slowbear’s stock is 6.08% b VarianceA (σHB2) = (0.25)(-0.02 – 0.0733)2 + (0.60)(0.092 – 0.0733)2 + (0.15)(0.154 – 0.0733)2 = 0.003363 Standard DeviationA (σHB) = (0.003363)1/2 = 0.0580 = 5.80% The standard deviation of Highbear’s stock returns is 5.80% VarianceB (σSB2) = (0.25)(0.05 – 0.0608)2 + (0.60)(0.062 – 0.0608)2 + (0.15)(0.074 – 0.0608)2 = 0.000056 B Standard DeviationB (σB) = (0.000056)1/2 = 0.0075 = 0.75% B B The standard deviation of Slowbear’s stock returns is 0.75% c Covariance(RHB, RSB) = (0.25)(-0.02 – 0.0733)(0.05 – 0.0608) + (0.60)(0.092 – 0.0733)(0.062 – (0.0608) + (0.15)(0.154 – 0.0733)(0.074 – 0.0608) = 0.000425 The covariance between the returns on Highbull’s stock and Slowbear’s stock is 0.000425 Correlation(RA,RB) = Covariance(RA, RB) / (σA * σB) = 0.000425 / (0.0580 * 0.0075) = 0.9770 B B B The correlation between the returns on Highbull’s stock and Slowbear’s stock is 0.9770 10.4 Value of Atlas stock in the portfolio = (120 shares)($50 per share) = $6,000 Value of Babcock stock in the portfolio = (150 shares)($20 per share) = $3,000 Total Value in the portfolio = $6,000 + $3000 = $9,000 Weight of Atlas stock = $6,000 / $9,000 = 2/3 The weight of Atlas stock in the portfolio is 2/3 Weight of Babcock stock = $3,000 / $9,000 = 1/3 The weight of Babcock stock in the portfolio is 1/3 10.5 a The expected return on the portfolio equals: E(RP) = (WF)[E(RF)] + (WG)[E(RG)] where E(RP) = the expected return on the portfolio E(RF) = the expected return on Security F E(RG) = the expected return on Security G WF = the weight of Security F in the portfolio WG = the weight of Security G in the portfolio E(RP) = (WF)[E(RF)] + (WG)[E(RG)] = (0.30)(0.12) + (0.70)(0.18) = 0.1620 = 16.20% The expected return on a portfolio composed of 30% of Security F and 70% of Security G is 16.20% b The variance of the portfolio equals: σ2P = (WF)2(σF)2 + (WG)2(σG)2 + (2)(WF)(WG)(σF)(σG)[Correlation(RF, RG)] where σ2P WF WG σF σG RF RG = the variance of the portfolio = the weight of Security F in the portfolio = the weight of Security G in portfolio = the standard deviation of Security F = the standard deviation of Security G = the return on Security F = the return on Security G σ2P = (WF)2(σF)2 + (WG)2(σG)2 + (2)(WF)(WG)(σF)(σG)[Correlation(RF, RG)] = (0.30)2(0.09)2 + (0.70)2(0.25)2 + (2)(0.30)(0.70)(0.09)(0.25)(0.2) = 0.033244 The standard deviation of the portfolio equals: σP = (σ2P)1/2 where σP σ2P = the standard deviation of the portfolio = the variance of the portfolio σP = (σ2P)1/2 = (0.033244)1/2 = 0.1823 =18.23% If the correlation between the returns of Security F and Security G is 0.2, the standard deviation of the portfolio is 18.23% 10.6 a The expected return on the portfolio equals: E(RP) = (WA)[E(RA)] + (WB)[E(RB)] B where B E(RP) = the expected return on the portfolio E(RA) = the expected return on Stock A E(RB) = the expected return on Stock B WA = the weight of Stock A in the portfolio WB = the weight of Stock B in the portfolio B E(RP) = (WA)[E(RA)] + (WB)[E(RB)] = (0.40)(0.15) + (0.60)(0.25) = 0.21 = 21% B B The expected return on a portfolio composed of 40% stock A and 60% stock B is 21% The variance of the portfolio equals: σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] B where σ2P WA WB σA σB RA RB B B B B B = the variance of the portfolio = the weight of Stock A in the portfolio = the weight of Stock B in the portfolio = the standard deviation of Stock A = the standard deviation of Stock B = the return on Stock A = the return on Stock B σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] = (0.40)2(0.10)2 + (0.60)2(0.20)2 + (2)(0.40)(0.60)(0.10)(0.20)(0.5) = 0.0208 B B B B B The standard deviation of the portfolio equals: σP = (σ2P)1/2 where σP = the standard deviation of the portfolio σ2P = the variance of the portfolio σP = (0.0208)1/2 = 0.1442 =14.42% If the correlation between the returns on Stock A and Stock B is 0.5, the standard deviation of the portfolio is 14.42% b σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] = (0.40)2(0.10)2 + (0.60)2(0.20)2 + (2)(0.40)(0.60)(0.10)(0.20)(-0.5) = 0.0112 B B B B B σP = (0.0112)1/2 = 0.1058 =10.58% If the correlation between the returns on Stock A and Stock B is -0.5, the standard deviation of the portfolio is 10.58% 10.7 c As Stock A and Stock B become more negatively correlated, the standard deviation of the portfolio decreases a Value of Macrosoft stock in the portfolio = (100 shares)($80 per share) = $8,000 Value of Intelligence stock in the portfolio = (300 shares)($40 per share) = $12,000 Total Value in the portfolio = $8,000 + $12,000 = $20,000 Weight of Macrosoft stock = $8,000 / $20,000 = 0.40 Weight of Intelligence stock = $12,000 / $20,000 = 0.60 The expected return on the portfolio equals: E(RP) = (WMAC)[E(RMAC)] + (WI)[E(RI)] where E(RP) = the expected return on the portfolio E(RMAC) = the expected return on Macrosoft stock E(RI) = the expected return on Intelligence Stock WMAC = the weight of Macrosoft stock in the portfolio WI = the weight of Intelligence stock in the portfolio E(RP) = (WMAC)[E(RMAC)] + (WI)[E(RM)] = (0.40)(0.15) + (0.60)(0.20) = 0.18 = 18% The expected return on her portfolio is 18% The variance of the portfolio equals: σ2P = (WMAC)2(σMAC)2 + (WI)2(σI)2 + (2)(WMAC)(WI)(σMAC)(σI)[Correlation(RMAC, RI)] where σ2P WMAC WI σMAC σI RMAC RI = the variance of the portfolio = the weight of Macrosoft stock in the portfolio = the weight of Intelligence stock in the portfolio = the standard deviation of Macrosoft stock = the standard deviation of Intelligence stock = the return on Macrosoft stock = the return on Intelligence stock σ2P = (WMAC)2(σMAC)2 + (WI)2(σI)2 + (2)(WMAC)(WI)(σMAC)(σI)[Correlation(RMAC, RI)] = (0.40)2(0.08)2 + (0.60)2(0.20)2 + (2)(0.40)(0.60)(0.08)(0.20)(0.38) = 0.018342 The standard deviation of the portfolio equals: σP = (σ2P)1/2 where σP = the standard deviation of the portfolio σ2P = the variance of the portfolio σP = (0.018342)1/2 = 0.1354 =13.54% The standard deviation of her portfolio is 13.54% b Janet started with 300 shares of Intelligence stock After selling 200 shares, she has 100 shares left Value of Macrosoft stock in the portfolio = (100 shares)($80 per share) = $8,000 Value of Intelligence stock in the portfolio = (100 shares)($40 per share) = $4,000 Total Value in the portfolio = $8,000 + $4,000 = $12,000 Weight of Macrosoft stock = $8,000 / $12,000 = 2/3 Weight of Intelligence stock = $4,000 / $12,000 = 1/3 E(RP) = (WMAC)[E(RMAC)] + (WI)[E(RI)] = (2/3)(0.15) + (1/3)(0.20) = 0.1667 = 16.67% The expected return on her portfolio is 16.67% σ2P = (WMAC)2(σMAC)2 + (WI)2(σI)2 + (2)(WMAC)(WI)(σMAC)(σI)[Correlation(RMAC, RI)] = (2/3)2(0.08)2 + (1/3)2(0.20)2 + (2)(2/3)(1/3)(0.08)(0.20)(0.38) = 0.009991 σP = (0.009991)1/2 = 0.1000 =10.00% The standard deviation of her portfolio is 10.00% 10.8 a Expected ReturnA = (0.20)(0.07) + (0.50)(0.07) + (0.30)(0.07) = 0.07 = 7% The expected return on Stock A is 7% VarianceA (σA2) = (0.20)(0.07 – 0.07)2 + (0.50)(0.07 – 0.07)2 + (0.30)(0.07 – 0.07)2 =0 The variance of the returns on Stock A is Standard DeviationA (σA) = (0)1/2 = 0.00 = 0% The standard deviation of the returns on Stock A is 0% Expected ReturnB = (0.20)(-0.05) + (0.50)(0.10) + (0.30)(0.25) = 0.1150 = 11.50% B The expected return on Stock B is 11.50% VarianceB (σB2) = (0.20)(-0.05 – 0.1150)2 + (0.50)(0.10 – 0.1150)2 + (0.30)(0.25 – 0.1150)2 = 0.011025 B The variance of the returns on Stock B is 0.011025 Standard DeviationB (σB) = (0.011025)1/2 = 0.1050 =10.50% B B The standard deviation of the returns on Stock B is 10.50% b Covariance(RA, RB) = (0.20)(0.07 – 0.07)(-0.05 – 0.1150) + (0.50)(0.07 – 0.07)(0.10 – 0.1150) (0.30)(0.07 – 0.07)(0.25 – 0.1150) =0 B The covariance between the returns on Stock A and Stock B is Correlation(RA,RB) = Covariance(RA, RB) / (σA * σB) = / (0 * 0.1050) =0 B B B The correlation between the returns on Stock A and Stock B is c The expected return on the portfolio equals: E(RP) = (WA)[E(RA)] + (WB)[E(RB)] B where E(RP) E(RA) E(RB) WA WB B B = the expected return on the portfolio = the expected return on Stock A = the expected return on Stock B = the weight of Stock A in the portfolio = the weight of Stock B in the portfolio E(RP) = (WA)[E(RA)] + (WB)[E(RB)] = (1/2)(0.07) + (1/2)(0.115) = 0.0925 B B = 9.25% The expected return of an equally weighted portfolio is 9.25% σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] B where σ2P WA WB σA σB RA RB B B B B = the variance of the portfolio = the weight of Stock A in the portfolio = the weight of Stock B in the portfolio = the standard deviation of Stock A = the standard deviation of Stock B = the return on Stock A = the return Stock B σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] = (1/2)2(0)2 + (1/2)2(0.105)2 + (2)(1/2)(1/2)(0)(0.105)(0) = 0.002756 B B B B B The standard deviation of the portfolio equals: σP = (σ2P)1/2 σP = the standard deviation of the portfolio σ2P = the variance of the portfolio where σP = (0.002756)1/2 = 0.0525 =5.25% The standard deviation of the returns on an equally weighted portfolio is 5.25% 10.9 a The expected return on the portfolio equals: E(RP) = (WA)[E(RA)] + (WB)[E(RB)] B where E(RP) E(RA) E(RB) WA WB B B = the expected return on the portfolio = the expected return on Stock A = the expected return on Stock B = the weight of Stock A in the portfolio = the weight of Stock B in the portfolio E(RP) = (WA)[E(RA)] + (WB)[E(RB)] = (0.30)(0.10) + (0.70)(0.20) = 0.17 = 17% B B The expected return on the portfolio is 17% The variance of a portfolio equals: σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] B where σ2P WA B B B = the variance of the portfolio = the weight of Stock A in the portfolio B WB σA σB RA RB = the weight of Stock B in the portfolio = the standard deviation of Stock A = the standard deviation of Stock B = the return on Stock A = the return on Stock B σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] = (0.30)2(0.05)2 + (0.70)2(0.15)2 + (2)(0.30)(0.70)(0.05)(0.15)(0) = 0.01125 B B B B B The standard deviation of the portfolio equals: σP = (σ2P)1/2 where σP = the standard deviation of the portfolio σ2P = the variance of the portfolio σP = (0.01125)1/2 = 0.1061 = 10.61% The standard deviation of the portfolio is 10.61% b E(RP) = (WA)[E(RA)] + (WB)[E(RB)] = (0.90)(0.10) + (0.10)(0.20) = 0.11 = 11% B B The expected return on the portfolio is 11% σ2P = (WA)2(σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(σA)(σB)[Correlation(RA, RB)] = (0.90)2(0.05)2 + (0.10)2(0.15)2 + (2)(0.90)(0.10)(0.05)(0.15)(0) = 0.00225 B B B B B σP = (0.00225)1/2 = 0.0474 = 4.74% The standard deviation of the portfolio is 4.74% c No, you would not hold 100% of Stock A because the portfolio in part b has a higher expected return and lower standard deviation than Stock A You may or may not hold 100% of Stock B, depending on your risk preference If you have a low level of risk-aversion, you may prefer to hold 100% Stock B because of its higher expected return If you have a high level of risk-aversion, however, you may prefer to hold a portfolio containing both Stock A and Stock B since the portfolio will have a lower standard deviation, and hence, less risk, than holding Stock B alone 10.10 The expected return on the portfolio must be less than or equal to the expected return on the asset with the highest expected return It cannot be greater than this asset’s expected return because all assets with lower expected returns will pull down the value of the weighted average expected return Similarly, the expected return on any portfolio must be greater than or equal to the expected return on the asset with the lowest expected return The portfolio’s expected return cannot be below the lowest expected return among all the assets in the portfolio because assets with higher expected returns will pull up the value of the weighted average expected return 10.11 a Expected ReturnA = (0.40)(0.03) + (0.60)(0.15) = 0.1020 = 10.20% The expected return on Security A is 10.20% VarianceA (σA2) = (0.40)(0.03 – 0.102)2 + (0.60)(0.15 – 0.102)2 = 0.003456 Standard DeviationA (σA) = (0.003456)1/2 = 0.0588 = 5.88% The standard deviation of the returns on Security A is 5.88% Expected ReturnB = (0.40)(0.065) + (0.60)(0.065) = 0.0650 = 6.50% B The expected return on Security B is 6.50% VarianceB (σB2) = (0.40)(0.065 – 0.065)2 + (0.60)(0.065 – 0.065)2 =0 B Standard DeviationB (σB) = (0)1/2 = 0.00 = 0% B B The standard deviation of the returns on Security B is 0% b Total Value of her portfolio = $2,500 + $3,500 = $6,000 Weight of Security A = $2,500 / $6,000 = 5/12 Weight of Security B = $3,500 / $6,000 = 7/12 E(RP) = (WA)[E(RA)] + (WB)[E(RB)] B where E(RP) E(RA) E(RB) WA WB B B = the expected return on the portfolio = the expected return on Security A = the expected return on Security B = the weight of Security A in the portfolio = the weight of Security B in the portfolio E(RP) = (WA)[E(RA)] + (WB)[E(RB)] = (5/12)(0.102) + (7/12)(0.065) = 0.0804 = 8.04% B B ... σ2P = (WA) 2(? ?A)2 + (WB) 2(? ?B)2 + (2 )(WA)(WB )(? ?A )(? ?B)[Correlation(RA, RB)] = (0 .40) 2(0 .10) 2 + (0 .60) 2(0 .20)2 + (2 )(0 .40 )(0 .60 )(0 .10 )(0 .20 )(- 0.5) = 0.0112 B B B B B σP = (0 .0112)1/2 = 0 .105 8 =10. 58%... = the return on Stock B σ2P = (WA) 2(? ?A)2 + (WB) 2(? ?B)2 + (2 )(WA)(WB )(? ?A )(? ?B)[Correlation(RA, RB)] = (0 .40) 2(0 .10) 2 + (0 .60) 2(0 .20)2 + (2 )(0 .40 )(0 .60 )(0 .10 )(0 .20 )(0 .5) = 0.0208 B B B B B The standard... Stock A = the return Stock B σ2P = (WA) 2(? ?A)2 + (WB) 2(? ?B)2 + (2 )(WA)(WB )(? ?A )(? ?B)[Correlation(RA, RB)] = (1 /2) 2(0 )2 + (1 /2) 2(0 .105 )2 + (2 )(1 /2 )(1 /2 )(0 )(0 .105 )(0 ) = 0.002756 B B B B B The standard