Securities CH 7

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% The coefficient of correlation between A and B is?

A. .46 covA,B = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% - 7.7%) + 0.2(12% - 13.2%)(6% - 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) + 0.2(15% - 13.2%)(8% - 7.7%) = 0.76; rA,B = 0.76/[(1.1)(1.5)] = 0.46.

Which of the following statement(s) is(are) false regarding the selection of a portfolio from those that lie on the capital allocation line? I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors. II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors. III) Investors choose the portfolio that maximizes their expected utility.

A. I only

Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz? Portfolio: W, X, Y, Z Exp Ret: 9%, 5%, 15%, 12% St. Dev: 21%, 7%, 36%, 15%

A. Only portfolio W cannot lie on the efficient frontier.

The individual investor's optimal portfolio is designated by:

A. The point of tangency with the indifference curve and the capital allocation line.

The risk that can be diversified away is?

A. firm specific risk

The expected return of a portfolio of risky securities?

A. is a weighted average of the securities' returns.

Systematic risk is also referred to as?

A. market risk, nondiversifiable risk

The separation property refers to the conclusion that?

A. the determination of the best risky portfolio is objective and the choice of the best complete portfolio is subjective.

The efficient frontier of risky assets is?

A. the portion of the investment opportunity set that lies above the global minimum variance portfolio.

Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of 5%, what is the slope of the best feasible CAL?

B. 0.27 Slope = (12 - 5)/26 = .2692

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% The variances of return of stocks A and B are _____ and _____, respectively.

B. 2.2%; 1.2 % varA = [0.1(10% - 13.2%)2 + 0.2(13% - 13.2%)2 + 0.2(12% - 13.2%)2 + 0.3(14% - 13.2%)2 + 0.2(15% - 13.2%)2] = 2.16%; varB = [0.1(8% - 7.7%)2 + 0.2(7% - 7.7%)2 + 0.2(6% - 7.7%)2 + 0.3(9% - 7.7%)2 + 0.2(8% - 7.7%)2] = 1.21%.

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard deviation?

B. 9.9%; 1.1% E(RP) = 0.4(13.2%) + 0.6(7.7%) = 9.9%; sP = [(0.4)2(1.5)2 + (0.6)2(1.1)2 + 2(0.4)(0.6)(1.5)(1.1)(0.46)]1/2 = 1.1%.

The measure of risk in a Markowitz efficient frontier is:

B. Standard deviation of returns

Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum variance portfolio has a standard deviation that is always?

B. equal to zero

Efficient portfolios of N risky securities are portfolios that?

B. have the highest rates of return for a given level of risk

The unsystematic risk of a specific security?

B. results from factors unique to the firm

In words, the covariance considers the probability of each scenario happening and the interaction between?

B. securities' returns relative to their mean returns.

Nondiversifiable risk is also referred to as?

B. systematic risk, market risk

Market risk is also referred to as?

B. systematic risk, nondiversifiable risk

Portfolio theory as described by Markowitz is most concerned with?

B. the effect of diversification on portfolio risk

When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio?

B. the portfolio standard deviation will be less than the weighted average of the individual security standard deviations.

In a two-security minimum variance portfolio where the correlation between securities is greater than -1.0 ?

B. the security with the higher standard deviation will be weighted less heavily.

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% The expected rates of return of stocks A and B are _____ and _____, respectively.

C. 13.2%; 7.7% E(RA) = 0.1(10%) + 0.2(13%) + 0.2(12%) + 0.3(14%) + 0.2(15%) = 13.2%; E(RB) = 0.1(8%) + 0.2(7%) + 0.2(6%) + 0.3(9%) + 0.2(8%) = 7.7%.

Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

C. 8.9% E(RP) = 0.43(10%) + 0.57(8%) = 8.86%.

Which of the following statement(s) is(are) true regarding the variance of a portfolio of two risky securities? I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance. II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance. III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.

C. III only

Which of the following is not a source of systematic risk?

C. Personnel changes

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% Which of the following portfolio(s) is (are) on the efficient frontier?

C. The portfolio with 26 percent in A and 74 percent in B.

The variance of a portfolio of risky securities?

C. is the weighted sum of the securities' variances and covariances

The capital allocation line provided by a risk-free security and N risky securities is?

C. the line tangent to the efficient frontier of risky securities drawn from the risk-free rate

The standard deviation of a portfolio of risky securities is?

C. the square root of the weighted sum of the securities' variances and covariances.

The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is?

D. -1.0

For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks?

D. -1.00

Security X has expected return of 12% and standard deviation of 18%. Security Y has expected return of 15% and standard deviation of 26%. If the two securities have a correlation coefficient of 0.7, what is their covariance?

D. 0.033 Cov(rX, rY) = (.7)(.18)(.26) = .0327

Given an optimal risky portfolio with expected return of 6% and standard deviation of 23% and a risk free rate of 3%, what is the slope of the best feasible CAL?

D. 0.13 Slope = (6 - 3)/23 = .1304

Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. The weights of A and B in the global minimum variance portfolio are _____ and _____, respectively.

D. 0.43; 0.57 wA = 12/(16 + 12) = 0.4286; wB = 1 - 0.4286 = 0.5714.

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% The standard deviations of return of stocks A and B are _____ and _____, respectively.

D. 1.5%; 1.1% sA = [0.1(10% - 13.2%)2 + 0.2(13% - 13.2%)2 + 0.2(12% - 13.2%)2 + 0.3(14% - 13.2%)2 + 0.2(15% - 13.2%)2]1/2 = 1.5%; sB = [0.1(8% - 7.7%)2 + 0.2(7% - 7.7%)2 + 0.2(6% - 7.7%)2 + 0.3(9% - 7.7%)2 + 0.2(8% - 7.7%)2]1/2 = 1.1%.

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% The expected rate of return and standard deviation of the global minimum variance portfolio, G, are __________ and __________, respectively.

D. 8.97%; 1.05% E(RG) = 0.23(13.2%) + 0.77(7.7%) = 8.965%; sG = [(0.23)2(1.5)2 + (0.77)2(1.1)2 + (2)(0.23)(0.77)(1.5)(1.1)(0.46)]1/2 = 1.05%.

Which of the following statement(s) is(are) false regarding the variance of a portfolio of two risky securities? I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance. II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance. III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.

D. I and II

The risk that can be diversified away in a portfolio is referred to as ___________. I) diversifiable risk II) unique risk III) systematic risk IV) firm-specific risk

D. I, II, and IV

The risk that cannot be diversified away is?

D. Market risk

Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz? Portfolio: A, B, C, D Exp Ret: 10%, 5%, 15%, 12% St. Dev: 12%, 7%, 20%, 25%

D. Only portfolio D cannot lie on the efficient frontier.

Which statement about portfolio diversification is correct?

D. Typically, as more securities are added to a portfolio, total risk would be expected to decrease at a decreasing rate.

Unique risk is also referred to as?

D. diversifiable risk, firm-specific risk.

Firm-specific risk is also referred to as?

D. diversifiable risk, unique risk.

Nonsystematic risk is also referred to as?

D. diversifiable risk, unique risk.

As the number of securities in a portfolio is increased, what happens to the average portfolio standard deviation?

D. it decreases at a decreasing rate

The line representing all combinations of portfolio expected returns and standard deviations that can be constructed from two available assets is called the?

D. portfolio opportunity set

Other things equal, diversification is most effective when?

D. securities' returns are negatively correlated.

The standard deviation of a two-asset portfolio is a linear function of the assets' weights when?

D. the assets have a correlation coefficient equal to one

Diversifiable risk is also referred to as?

D. unique risk, firm-specific risk.

Consider the following probability distribution for stocks A and B: State: 1, 2, 3, 4, 5 Probability: .10, .20, .20, .30, .20 Return on A: 10%, 13%, 12%, 14%, 15% Return on B: 8%, 7%, 6%, 9%, 8% Let G be the global minimum variance portfolio. The weights of A and B in G are __________ and __________, respectively?

E. 0.23; 0.77 wA = [(1.1)2 - (1.5)(1.1)(0.46)]/[(1.5)2 + (1.1)2 - (2)(1.5)(1.1)(0.46) = 0.23; wB = 1 - 0.23 = 0.77.

Given an optimal risky portfolio with expected return of 13% and standard deviation of 26% and a risk free rate of 5%, what is the slope of the best feasible CAL?

E. 0.31 Slope = (13 - 5)/26 = .31

Given an optimal risky portfolio with expected return of 20% and standard deviation of 24% and a risk free rate of 7%, what is the slope of the best feasible CAL?

E. 0.54 Slope = (20 - 7)/24 = .5417

When borrowing and lending at a risk-free rate are allowed, which capital allocation line (CAL) should the investor choose to combine with the efficient frontier? I) The one with the highest reward-to-variability ratio. II) The one that will maximize his utility. III) The one with the steepest slope. IV) The one with the lowest slope.

E. I, II, and III

Which of the following statement(s) is(are) true regarding the selection of a portfolio from those that lie on the capital allocation line? I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors. II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors. III) Investors choose the portfolio that maximizes their expected utility.

E. II and III

An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the capital allocation line must:

E. borrow some money at the risk-free rate and invest in the optimal risky portfolio and invest only in risky securities

A statistic that measures how the returns of two risky assets move together is?

E. covariance and correlation

A two-asset portfolio with a standard deviation of zero can be formed when?

E. the assets have a correlation coefficient equal to negative one.