ch 10 extra

Consider the multifactor APT. There are two independent economic factors, F1 and F2. The risk- free rate of return is 6%. The following information is available about two well- diversified portfolios: Portfolio A: Beta on F1 = 1.0 ; Beta on F2 = 2.0 ; E(R) = 0.19 B: Beta on F1 = 1.0 ; Beta on F2 = 0 ; E(R) = 0.12 Assuming no arbitrage opportunities exist, the risk premium on the factor F1 of the portfolio should be:

2.0(F1) + 0(F2) + 0.06 = 0.12 2(F1) = 0.06 F1 = 0.03 = 3% No arb opps implies F1 is same for Portfolio A and B. Can use Portfolio B because Beta on F2 is zero.

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 19%. The standard deviation on the factor portfolio is 12%. The beta of the well-diversified portfolio is approximately A. 1.58. B. 1.13. C. 1.25. D. 0.76.

A. 1.58 (s of well-div p) = √(B^2 * s^2 of factor p) (s of well-div p) = (B * s of factor p) 0.19 = B * 0.12 B = 1.58

Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on factor 1, and a beta of 0.86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exist? A. 9.26% B. 3% C. 4% D. 7.75%

A. 9.26% 0.176 = 1.45(0.032) + .86(F2) + 0.05 F2 = 9.26. E(r) = B1(riskP1) + B2(riskP2) + Rf

1. Consider the multifactor APT. The risk premiums on the factor 1 and factor 2 portfolios are 6% and 4%, respectively. The risk-free rate of return is 4%. Stock A has an expected return of 16% and a beta on factor-1 of 1.3. Stock A has a beta on factor-2 of A. 1.33 B. 1.05 C. 1.67 D. 2.00 E. 1.55

B. 1.05 0.16 = 1.3(0.06) + F2(0.04) + 0.04 0.12 = 0.078 + F2(0.04) 0.042 = F2(0.04) F2 = 1.05

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 18%. The standard deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately A. 0.80. B. 1.13. C. 1.25. D. 1.56.

B. 1.13 variance (s^2) of well-div. portfolio = (B^2) * (s^2 of factor portfolio) (s of well-div p) = √(B^2 * s^2 factor p) (s of well-div p) = B * (s of factor p) 0.18 = B * 0.16 B = 0.18/0.16 B = 1.125 =1.13

Consider the multifactor model APT with three factors. Portfolio A has a beta of 0.8 on factor 1, a beta of 1.1 on factor 2, and a beta of 1.25 on factor 3. The risk premiums on the factor 1, factor 2, and factor 3 are 3%, 5%, and 2%, respectively. The risk-free rate of return is3%. The expected return on portfolio A is if no arbitrage opportunities exist. A. 13.5% B. 13.4% C. 16.5% D. 23.0% E. 20.0%.

B. 13.4% 0.8(0.03) + 1.1(0.05) + 1.25(0.02) + 0.03 = 0.134 = 13.4%

Suppose you are working with two factor portfolios, portfolio 1 and portfolio 2. The portfolios have expected returns of 15% and 6%, respectively. Based on this information, what would be the expected return on well-diversified portfolio A, if A has a beta of 0.80 on the first factor and 0.50 on the second factor? The risk-free rate is 3%. A. 15.2% B. 14.1% C. 13.3% D. 10.7% E. 8.4%

B. 14.1% E(Rp) = Rf + B1(E(R1) - Rf) + B2(E(R2) - Rf) E(Rp) = 0.03 + 0.8(0.15 - 0.03) + 0.5(0.06 - 0.03) E(Rp) = 0.03 + 0.096 + 0.015 E(Rp) = 0.141 E(Rp) = 14.1%

There are three stocks: A, B, and C. You can either invest in these stocks or short sell them. There are three possible states of nature for economic growth in the upcoming year(each equally likely to occur); economic growth may be strong, moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature are given below: *Stock Return given Economic Growth Rates:* A: Strong 39%; Moderate 17%; Weak -5%; B: Strong 30%; Moderate 15%; Weak 0%; C: Strong 6%; Moderate 14%; Weak 22%; If you invested in an equally-weighted portfolio of stocks A and C, your portfolio returnwould be if economic growth was strong. A. 17.0% B. 22.5% C. 30.0% D. 30.5% E. 20.2%.

B. 22.5% Strong Econ Growth: A: 39% return C: 6% return 0.5(0.39) + 0.5(0.06) = 0.225 = 22.5%

Consider the one-factor APT. Assume that two portfolios, A and B, are well diversified. The betas of portfolios A and B are 1.0 and 1.5, respectively. The expected returns on portfolios A and B are 19% and 24%, respectively. Assuming no arbitrage opportunities exist,the risk-free rate of return must be A. 4.0%. B. 9.0%. C. 14.0%. D. 16.5%. E. 3.5%

B. 9.0% A: 1.0(F) + Rf = 0.19 B: 1.5(F) + Rf = 0.24 SUBTRACT: (B - A) to find F, then sub for Rf • 0.5(F) + 0 = 0.05 • F = 0.1 = 10% B: 1.5(0.1) + Rf = 0.24 0.15 + Rf = 0.24 Rf = 0.09 = 9%

Consider the single factor APT. Portfolio A has a beta of 0.5 and an expected return of 12%. Portfolio B has a beta of 0.4 and an expected return of 13%. The risk-free rate of return is 5%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio and a long position in portfolio. A. A; A B. A; B C. B; A D. B; B E. A, B

B. A; B Portfolio A: 0.12 = 0.5(F) + 0.05 0.07 = 0.5(F) F = 0.14 F = 14% Portfolio B: 0.13 = 0.4(F) + 0.05 0.08 = 0.4(F) F = 0.2 F = 20% 20% > 14% FB > FA Long B, Short A

Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor, and portfolio B has a beta of 2.0 on the factor. The expected returns on portfolios A and B are 11% and 17%, respectively. Assume that the risk-free rate is 6%, and that arbitrage opportunities exist. Suppose you invested $100,000 in the risk-free asset, $100,000 in portfolio B, and sold short $200,000 of portfolio A. Your expected profit from this strategy would be A. - $1,000. B. $0. C. $1,000. D. $2,000. E. -$2,000

C. $1,000. arb opps exist: F's can be diff (but don't actually have to calculate F's) A: 1.0(Fa) + 0.06 = *0.11* • -$200,000(0.11) = -$22,000 B: 2.0(Fb) + 0.06 = *0.17* • $100,000(0.17) = $17,000 Rf: 6% return • $100,000(0.06) = $6,000 17,000 + 6,000 - 22,000 = 1,000

Consider the single factor APT. Portfolios A and B have expected returns of 14% and 18%, respectively. The risk-free rate of return is 7%. Portfolio A has a beta of 0.7. If arbitrage opportunities are ruled out, portfolio B must have a beta of A. 0.45. B. 1.00. C. 1.10. D. 1.22. E. None of the options are correct.

C. 1.10 A: 0.7(F) + 0.07 = 0.14 0.7(F) = 0.07 F = 0.1 no arb opps --- F will be same for portfolio A and B B: B(0.1) + 0.07 = 0.18 B(0.1) = 0.11 B = 1.1

Consider the multifactor APT. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 3%, respectively. The risk-free rate of return is 10%. Stock A has an expected return of 19% and a beta on factor 1 of 0.8. Stock A has a beta on factor 2 of A. 1.33. B. 1.50. C. 1.67. D. 2.00. E. 2.0.

C. 1.67 (0.8)0.05 + (B2)0.03 + 0.1 = 0.19 0.14 + (B2)0.03 = 0.19 (B2)0.03 = 0.05 B2 = 1.67

Consider the multifactor model APT with two factors. Portfolio A has a beta of 0.75 on factor 1 and a beta of 1.25 on factor 2. The risk premiums on the factor-1 and factor-2 portfolios are 1% and 7%, respectively. The risk-free rate of return is 7%. What is the expected returnon portfolio A if no arbitrage opportunities exist? A. 13.5% B. 15.0% C. 16.5% D. 23.0% E. 10.4%

C. 16.5% 0.75(0.01) + 1.25(0.07) + 0.07 = 0.165 = 16.5%

Consider the multifactor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 6%, respectively. Stock A has a beta of 1.2 on factor-1, and a beta of 0.7 on factor-2. The expected return on stock A is 17%. If no arbitrage opportunities exist, the risk-free rate of return is: A. 6.0%. B. 6.5%. C. 6.8%. D. 7.4%. 2.5%.

C. 6.8% 1.2(0.05) + 0.7(0.06) + Rf = 0.17 0.102 + Rf = 0.17 Rf = 0.068 = 6.8%

Consider the one-factor APT. The variance of returns on the factor portfolio is 6%. The beta of a well-diversified portfolio on the factor is 1.1. The variance of returns on the well- diversified portfolio is approximately A. 3.6% B. 6.0% C. 7.3% D. 10.1%

C. 7.3% variance (s^2) of well-div. portfolio = (B^2) * (s^2 of factor portfolio) = ((1.1)^2) * (0.06) = 7.26%.

Consider a single factor APT. Portfolio A has a beta of 1.0 and an expected return of 16%. Portfolio B has a beta of 0.8 and an expected return of 12%. The risk-free rate of return is 6%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _______ and a long position in portfolio _______. A. A; A B. A; B C. B; A D. B; B E. A; the riskless asset

C. B ; A (short B, long A) Portfolio A: 0.16 = 1.0(F) + 0.06 0.1/1.0 = F F = 0.1 = 10% Portfolio B: 0.12 = 0.8F + 0.06 0.06/0.8 = F F = 0.075 = 7.5% 10% > 7.5% ( F is risk premium ) A > B Long A, Short B

Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _______ and a long position in portfolio _____ A. A; A B. A; B C. B; A D. B; B

C. B; A Portfolio A .13 = 0.2F + 0.1 0.03/0.2 = F F = 0.15 = 15% Portfolio B 0.15 = 0.4F + 0.1 0.05/0.4 = F F = 0.125 = 12.5% 15% > 12.5% ( F is risk premium ) A > B Short B, Long A

There are three stocks: A, B, and C. You can either invest in these stocks or short sell them. There are three possible states of nature for economic growth in the upcoming year(each equally likely to occur); economic growth may be strong, moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature are given below: *Stock Return given Economic Growth Rates:* A: Strong 39%; Moderate 17%; Weak -5%; B: Strong 30%; Moderate 15%; Weak 0%; C: Strong 6%; Moderate 14%; Weak 22%; If you invested in an equally-weighted portfolio of stocks B and C, your portfolio returnwould be if economic growth was weak. A. -2.5% B. 0.5% C. 3.0% D. 11.0% E. -1.0%

D. 11.0% Weak: B: 0% return C: 22% return 0.5(0) + 0.5(0.22) = 0.11 = 11%

Consider the one-factor APT. The variance of returns on the factor portfolio is 9%. The beta of a well-diversified portfolio on the factor is 1.25. The variance of returns on the well-diversified portfolio is approximately A. 3.6%. B. 6.0%. C. 7.3%. D. 14.1%. E. 10.2%

D. 14.1%. variance (s^2) of well-div. portfolio = (B^2) * (s^2 of factor portfolio) s^2 wdp = 1.25^2 * 0.09 s^2 wdp = 1.5625 * 0.09 s^2 wdp = 0.140625 s^2 wdp = 14.1%

There are three stocks: A, B, and C. You can either invest in these stocks or short sell them. There are three possible states of nature for economic growth in the upcoming year(each equally likely to occur); economic growth may be strong, moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature are given below: *Stock Return given Economic Growth Rates:* A: Strong 39%; Moderate 17%; Weak -5%; B: Strong 30%; Moderate 15%; Weak 0%; C: Strong 6%; Moderate 14%; Weak 22%; If you invested in an equally-weighted portfolio of stocks A and B, your portfolio return would be if economic growth were moderate. A. 3.0% B. 14.5% C. 15.5% D. 16.0% E. 10.0%.

D. 16.0% Moderate Econ growth: A: return 17% B: return 15% 0.5(0.17) + 0.5(0.15) = 0.16 = 16%

Consider the multi-factor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1, and a beta of 0.8 on factor 2. The risk premium on the factor-1 portfolio is 3%. The risk-free rate of return is 6%. What is the risk-premium on factor 2 if no arbitrage opportunities exist? A. 2% B. 3% C. 4% D. 7.75% E. 5%

D. 7.75% A: 0.164 = 1.4(0.03) + 0.8(F) + 0.06 0.104 = 0.042 + 0.8F 0.062 = 0.8F F = 0.0775 = 7.75%

Which of the following factors might affect stock returns? A. the business cycle B. interest rate fluctuations C. inflation rates D. All of the options.

D. All of the options

Consider the single-factor APT. Stocks A and B have expected returns of 15% and 18%, respectively. The risk-free rate of return is 6%. Stock B has a beta of 1.0. If arbitrage opportunities are ruled out, stock A has a beta of A. 0.67. B. 1.00. C. 1.30. D. 1.69. E. 0.75.

E. 0.75. B: 0.18 = 1.0F + 0.06 F = 0.12 no arbitrage opps, so F will be equal for A & B A: 0.15 = B(0.12) + 0.06 0.09 = B(0.12) B = 0.075

1. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium on the first factor portfolio is 4%, and the risk premium on the secondfactor portfolio is 3%. If portfolio A has a beta of 1.2 on the first factor and .8 on the second factor, what is its expected return? A. 7.0% B. 8.0% C. 9.2% D. 13.0% E. 13.2%

E. 13.2% 1.2(0.04) + 0.8(0.03) + 0.06 = 0.132 = 13.2%

In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has an average value of σ(ei) equal to 20% and 40 securities? A. 12.5% B. 625% C. 0.5% D. 3.54% E. 3.16%

E. 3.16% Ip^2 = 1/ (#sec^2) * (#sec * ave.σ(ei)^2) Ip^2 = (1/40^2) • (40 * 20%^2)) Ip = √[ (1/1600) • (40 * 0.2^2)) ] Ip = √[ (1/1600) • (40 * 0.04)) ] Ip = √[ (1/1600) • (1.6) ] Ip = √[ (1/1600) • (1.6) ] Ip = √[ 0.001 ] Ip = 0.0361 Ip = 3.16% unlikely