Question 1

Consider the following probability distribution for stocks A and B:  If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and standard deviation

Accepted Answer

E(R_P) = 0.35(13%) + 0.65(8.4%) = 10.01%; s_P = [(0.35)²(2.45%)² + (0.65)²(1.66)² + 2(0.35)(0.65)(2.45)(1.66)(0.590)]^1/2 = 1.7%.

Question 2

Theoretically, the standard deviation of a portfolio can be reduced to what level
 Explain.Realistically, is it possible to reduce the standard deviation to this level
 Explain.

Accepted Answer

The answer of Theoretically, the standard deviation of a portfolio...

Question 3

Consider the following probability distribution for stocks C and D:  If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected rate of return and standard deviation

Accepted Answer

E(R_P) = 0.25(4.4%) + 0.75(9.5%) = 8.225%; s_P = [(0.25)²(10.35)² + (0.75)²(12.93)² + 2(0.25)(0.75)(10.35)(12.93)(-0.50)]^1/2 = 8.70%.

Question 4

Security X has expected return of 7% and standard deviation of 14%.Security Y has expected return of 11% and standard deviation of 22%.If the two securities have a correlation coefficient of -0.45, what is their covariance

Accepted Answer

Cov(r_X, r_Y) = (-.45)(.14)(.22) = -.01386.

Question 5

Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%.B has an expected rate of return of 9% and a standard deviation of 14%.The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

E(R_P) = 0.45(12%) + 0.55(9%) = 10.35%.

Question 6

Security M has expected return of 17% and standard deviation of 32%.Security S has expected return of 13% and standard deviation of 19%.If the two securities have a correlation coefficient of 0.78, what is their covariance

Accepted Answer

Cov(r_X, r_Y) = (.78)(.32)(.19) = .0474.

Question 7

Consider two perfectly negatively correlated risky securities A and B.A has an expected rate of return of 12% and a standard deviation of 17%.B has an expected rate of return of 9% and a standard deviation of 14%. The weights of A and B in the global minimum variance portfolio are _____ and _____, respectively.

Accepted Answer

w_A = 14/(17 + 14) = 0.45; w_B = 1 - 0.45 = 0.55.

Question 8

Consider two perfectly negatively correlated risky securities, K and L.K has an expected rate of return of 13% and a standard deviation of 19%.L has an expected rate of return of 10% and a standard deviation of 16%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Accepted Answer

E(R_P) = 0.46(13%) + 0.54(10%) = 11.38%.

Question 9

State Markowitz's mean-variance criterion.Give some numerical examples of how the criterion would be applied.

Accepted Answer

The answer of State Markowitz's mean-variance criterion.Give some numerical examples...

Question 10

Draw a graph of a typical efficient frontier.Explain why the efficient frontier is shaped the way it is.

Accepted Answer

The answer of Draw a graph of a typical efficient...

Question 11

Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance.

Accepted Answer

The answer of Discuss how the investor can use the...

Question 12

Consider the following probability distribution for stocks C and D:  The coefficient of correlation between C and D is

Accepted Answer

Cov_C,D = 0.30(7% - 4.4%)(-9% - 9.5%) + 0.50(11% - 4.4%)(14% - 9.5%) + 0.20(-16% - 4.4%)(26% - 9.5%) = -66.9; ρ_A,B = -66.90/[(10.35)(12.93)] = -0.50.

Question 13

Consider the following probability distribution for stocks C and D:  The standard deviations of stocks C and D are _____ and _____, respectively.

Accepted Answer

s_C = [0.30(7% - 4.4%)² + 0.5(11% - 4.4%)² + 0.20(-16% - 4.4%)²]^1/2 = 10.35%; s_D = [0.30(-9% - 9.5%)² + 0.50(14% - 9.5%)² + 0.20(26% - 9.5%)²]^1/2 = 12.93%.

Question 14

Consider the following probability distribution for stocks C and D:  The expected rates of return of stocks C and D are _____ and _____, respectively.

Accepted Answer

E(R_C) = 0.30(7%) + 0.5(11%) + 0.20(-16%) = 4.4%; E(R_D) = 0.30(-9%) + 0.5(14%) + 0.20(26%) = 9.5%.

Question 15

Given an optimal risky portfolio with expected return of 16% and standard deviation of 20% and a risk-free rate of 4%, what is the slope of the best feasible CAL

Accepted Answer

Slope = (16 - 4)/20 = .6.

Question 16

Consider the following probability distribution for stocks A and B:  The coefficient of correlation between A and B is

Accepted Answer

cov_A,B = 0.15(8% - 13%)(8% - 8.4%) + 0.2(13% - 13%)(7% - 8.4%) + 0.15(12% - 13%)(6% - 8.4%) + 0.3(14% - 13%)(9% - 8.4%) + 0.2(16% - 13%)(11% - 8.4%) = 2.40; ρ_A,B = 2.40/[(2.45)(1.66)] = 0.590.

Question 17

Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of 3%, what is the slope of the best feasible CAL

Accepted Answer

Slope = (12 - 3)/26 = .346.

Question 18

Consider two perfectly negatively correlated risky securities, K and L.K has an expected rate of return of 13% and a standard deviation of 19%.L has an expected rate of return of 10% and a standard deviation of 16%. The weights of K and L in the global minimum variance portfolio are _____ and _____, respectively.

Accepted Answer

w_K = 1 - 0.54 = 0.46; w_L = 19/(19 + 16) = 0.54.

Question 19

Security X has expected return of 9% and standard deviation of 18%.Security Y has expected return of 12% and standard deviation of 21%.If the two securities have a correlation coefficient of -0.4, what is their covariance

Accepted Answer

Cov(r_X, r_Y) = (-.4)(.18)(.21) = -0.0151.

Question 20

Security X has expected return of 14% and standard deviation of 22%.Security Y has expected return of 16% and standard deviation of 28%.If the two securities have a correlation coefficient of 0.8, what is their covariance

Accepted Answer

Cov(r_X, r_Y) = (.8)(.22)(.28) = .04928.

Quiz 7: Optimal Risky Portfolios

Consider the following probability distribution for stocks A and B: If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and standard deviation

Theoretically, the standard deviation of a portfolio can be reduced to what level Explain.Realistically, is it possible to reduce the standard deviation to this level Explain.

Consider the following probability distribution for stocks C and D: If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected rate of return and standard deviation

Security X has expected return of 7% and standard deviation of 14%.Security Y has expected return of 11% and standard deviation of 22%.If the two securities have a correlation coefficient of -0.45, what is their covariance

Security M has expected return of 17% and standard deviation of 32%.Security S has expected return of 13% and standard deviation of 19%.If the two securities have a correlation coefficient of 0.78, what is their covariance

State Markowitz's mean-variance criterion.Give some numerical examples of how the criterion would be applied.

Draw a graph of a typical efficient frontier.Explain why the efficient frontier is shaped the way it is.

Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance.

Consider the following probability distribution for stocks C and D: The coefficient of correlation between C and D is

Consider the following probability distribution for stocks C and D: The standard deviations of stocks C and D are _ and _, respectively.

Consider the following probability distribution for stocks C and D: The expected rates of return of stocks C and D are _ and _, respectively.

Given an optimal risky portfolio with expected return of 16% and standard deviation of 20% and a risk-free rate of 4%, what is the slope of the best feasible CAL

Consider the following probability distribution for stocks A and B: The coefficient of correlation between A and B is

Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of 3%, what is the slope of the best feasible CAL

Security X has expected return of 9% and standard deviation of 18%.Security Y has expected return of 12% and standard deviation of 21%.If the two securities have a correlation coefficient of -0.4, what is their covariance

Security X has expected return of 14% and standard deviation of 22%.Security Y has expected return of 16% and standard deviation of 28%.If the two securities have a correlation coefficient of 0.8, what is their covariance