Question

In: Finance

10. Security A has an expected rate of return of 10% and a standard deviation of...

10. Security A has an expected rate of return of 10% and a standard deviation of 16%. Security B has an expected rate of return of 8% and a standard deviation of 12%. Let A and B are perfectly negatively correlated. The expected return of a risk-free portfolio formed with A and B is

Select one:

a. 10%

b. 9.47%

c. 7.86%

d. 8.86%

Solutions

Expert Solution

Expected return of A, μ_A = 10%

Standard Deviation of A, σ_A = 16%

Expected return of B, μ_B = 8%

Standard Deviation of B, σ_B = 12%

Correlation coefficient, ρ_(A,B) = -1

Portfolio variance is given by the formula

Where w_A and w_B are weights of the assets in the portfolio

w_B = 1-w_A

For a risk free portfolio, variance = 0

Implies

Solving for w_A using solution for a quadratic equation

w_A = 0.0672 / 0.1568 = 0.428571

w_B = 1- w_A = 1- 0.428571 = 0.571429

Expected return of the risk free portfolio = w_A*μ_A + w_B*μ_B = 0.428571 * 10% + 0.571429 * 8%

= 4.2857% + 4.5714% = 8.8571%

Expected return of the risk free portfolio = 8.86%

Answer is Option d.

jeff jeffy answered 2 years ago

Next > < Previous

Related Solutions

Security X has expected return of 14% and standard deviation of 22%. Security Y has expected...

Security X has expected return of 14% and standard deviation of 22%. Security Y has expected return of 16% and standard deviation of 28%. The two securities have a correlation coefficient of -1. You wish to combine the two securities in order to construct a portfolio that has a standard deviation of zero. Which percentage of your capital should you invest in security X? (Enter your answer as a percent)

Assume a security has an expected return of .12 and a standard deviation of 0.08 a)...

Assume a security has an expected return of .12 and a standard deviation of 0.08 a) What is the expected return two standard deviation above the mean and what is the probability of a return greater that this amount? B) What is the probability of a return greater than 0.04 for a given year.

A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15....

A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6%. An investor has the following utility function: U = E(r) - (A/2)s 2 . Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset? How would I complete this on a scientific calculator? For example, you cannot put algebra into a scientific calculator. So I'll need to do it manually, is it possible...

Stock A has an expected return of 5%, and a standard deviation of returns of 10%....

Stock A has an expected return of 5%, and a standard deviation of returns of 10%. Stock B has an expected return of 15% and a standard deviation of returns of 20%. The correlation between the two stocks returns in 0.90. The standard deviation of an equally-weighted portfolio comprised of the two stocks will be: more than 15% None of the answers listed here. 15% less than 15%

A portfolio consists of 60% of Security A (expected return of 0.10 and standard deviation of...

A portfolio consists of 60% of Security A (expected return of 0.10 and standard deviation of 0.03) and 40% of Security B (expected return of 0.20 and standard deviation of 0.05) and the correlation coefficient between A and B is -0.0012. a) Calculate the expected return and standard deviation of the portfolio. b) Calculate the standard deviation of the portfolio if there was no diversification benefit.

The expected return and standard deviation of return for four securities are listed below. Which security...

The expected return and standard deviation of return for four securities are listed below. Which security is the least risky? A B C D Expected Return 15% 12% 18% 8% Standard Deviation 14% 14% 18% 10% A. Security C. B. Security A. C. Security B. D. Security D.

The expected return on stock W is 10% and its standard deviation is 15%. Expected return...

The expected return on stock W is 10% and its standard deviation is 15%. Expected return on stock V is 16% and its standard deviation is 24%. The correlation between returns of W and V is 20%. calculate expected return and standard deviation of a portfolio that invests 40% in W and 60% in V. determine the minimum variance combination of W and V and determine its expected return and standard deviation. If the risk-free rate is 4%, determine the...

suppose asset a has an expected return of 10% and a standard deviation of 20% asset...

suppose asset a has an expected return of 10% and a standard deviation of 20% asset b has an expected return of 16% and a standard deviation of 40%.if the correlation between a and b is 0.6,what are the expected return and standard deviation for a prtifolio comprised of 40% asset a

Stock ABC has an expected return of 10% and a standard deviation of returns of 5%....

Stock ABC has an expected return of 10% and a standard deviation of returns of 5%. Stock XYZ has an expected return of 12% and a standard deviation of returns of 7%. You would like to invest $3000 in stock ABC and $2000 in stock XYZ. The correlation between the two stocks is .5. The expected market return is 11% and the risk free rate is 4%. Which of the following is false? 1,The expected return of the portfolio is...

Portfolio A has an expected return of 10% per year and a standard deviation of 20%...

Portfolio A has an expected return of 10% per year and a standard deviation of 20% per year, while the risk-free asset returns 2% per year. a. What is the expected return of a portfolio consisting the risk-free asset and portfolio A that has a standard deviation of 15%? b. What is the portfolio weight on A of a portfolio consisting the risk-free asset and portfolio A that has a standard deviation of 15%? c. What is the standard deviation...

Subjects