The universe of available securities includes two risky stocks A and B, and a risk-free asset....
The universe of available securities includes two risky stocks A and B, and a risk-free asset. The data for the universe are as follows:
| Assets | Expected Return | Standard Deviation |
|---|---|---|
| Stock A | 6% | 25% |
| Stock B | 12% | 42% |
| Risk free | 5% | 0 |
The correlation coefficient between A and B is -0.2.
The investor maximizes a utility function
U=E(r)−σ2
(i.e. she has a coefficient of risk aversion equal to 2).
Assume that to maximize his utility when there is no available risk-free asset, an investor invest w in stock A and 1-w in stock B.
a) What is the value of w?
Further assume that this investor has A=5 and the above risky portfolio in a) containing A and B is the OPTIMAL risky portfolio. The investor wants to maximize his utility when using both risky assets and risk-free asset. How much will he invest in stocks A and B and in risk free assets?
Weight in stock A?
Weight in stock B?
Weight in risk-free asset?
Homework Answers
Add Answer to:
The universe of available securities includes two risky stocks A
and B, and a risk-free asset....
2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A...
2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A and B, have mean-variance utility functions (with different risk aversion coef- ficients). Let P denote investor A's optimal portfolio of risky and risk-free assets and let Q denote investor B's optimal portfolio of risky and risk-free assets. P and Q have expected returns and standard deviations given by P Q E[R] St. Dev. 0.2 0.45 0.1 0.25 (a) What is the risk-free interest rate...
1. The universe of available securities includes two risky stock funds, A and B and T-bills....
1. The universe of available securities includes two risky stock funds, A and B and T-bills. The data for the universe are as follows: Expected Return Standard Deviation 109 20 Tbilis The correlation coefficient between funds A and B is -0.2. a. Find the optimal risky portfolio, P. and its expected return and standard deviation b. Find the slope of the CAL supported by T-bills and portfolio P. c. How much will an investor with 4-5 invest in funds A...
1. The universe of available securities includes two risky stock funds, A and B, and T-blls....
1. The universe of available securities includes two risky stock funds, A and B, and T-blls. The data for the universe are as follows Expected Return Standard Deviation A 10% 20% В 30 60 T-bills The correlation coefficient between funds A and B is -0.2. a. Find the optimal risky portfolio, P, and its expected return and standard deviation. b. Find the slope of the CAL supported by T-bills and portfolio P c. How much will an investor with A...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure r...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure rate of return rj, the risky asset has a random rate of return r. Suppose the utility function of an investor is U(x) =--. The initial wealth is wo, the dollar amount invested in the risky asset is θ. r is normally distributed with mean μ and variance σ2. Based on the maximum utility framework, find the optimal investment strategy 6. (25...
Mary has access to risky stocks A and B. But she has no access to risk-free...
Mary has access to risky stocks A and B. But she has no access to risk-free T-bills. The two assets have the following characteristics: Stock A: Expected return= 12.5% per annum, Standard deviation=14% per annum Stock B: Expected return = 5% per annum. Standard deviation=8% per annum The correlation coefficient between retum on stock A and return on stock B is 0.10 Mary's utility function U = E(R)- Ao and her coefficient of risk aversion is equal to 3 a)...
Mary has access to risky stocks A and B. But she has no access to risk-free...
Mary has access to risky stocks A and B. But she has no access to risk-free T-bills. The two assets have the following characteristics: Stock A: Expected return= 12.5% per annum, Standard deviation=14% per annum Stock B: Expected return = 5% per annum. Standard deviation=8% per annum The correlation coefficient between retum on stock A and return on stock B is 0.10 Mary's utility function U = E(R)- Ao and her coefficient of risk aversion is equal to 3 a)...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure rate of return rj, the risky asset has a random rate of return r. Suppose the utility function of an investor is U(x) =--. The initial wealth is wo, the dollar amount invested in the risky asset is θ. r is normally distributed with mean μ and variance σ2. Based on the maximum utility framework, find the optimal investment strategy 6. (25...
(a) Suppose that there are many stocks in the security market and that the characteristics of...
(a) Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows Stock A B Expected Return Standard Deviation 10% 5% 15% 10% Correlation =-1 Suppose that it is possible to borrow at the risk-free rate, If. What must be the value of the risk-free rate? Explain. HINT!!! The stocks are perfectly negatively correlated. (b) Calculate the expected return and standard deviation of an equally weighted portfolio of...
Tom has $10,000. He can invest the money in (1) a corporate bond, (2) a stock,...
Tom has $10,000. He can invest the money in (1) a corporate bond, (2) a stock, and (3) the risk-free T-bill. The table below provides these assets’ expected returns and standard deviations: Bond (D) Stock (E) T-Bill (F) Expected Return 5% 10% 2% Standard Deviation 10% 20% 0 The coefficient of correlation between the corporate bond and the stock (ρDE) is 30%. Tom has a risk aversion coefficient of A=5. To construct the optimal portfolio with two risky assets and...
2. Consider a market with only two risky stocks, A and B, and one risk-free asset....
2. Consider a market with only two risky stocks, A and B, and one risk-free asset. We have the following information about the stocks. Stock A Stock B Number of shares in the market 600 400 Price per share $2.00 $2.50 Expected rate of return 20% Standard dev.of return 12% Furthermore, the correlation coefficient between the returns of stocks A and B is PABWe assume that the returns are annual, and that the assumptions of CAPM hold. (a) (4 points)...
2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A and B, have mean-variance utility functions (with different risk aversion coef- ficients). Let P denote investor A's optimal portfolio of risky and risk-free assets and let Q denote investor B's optimal portfolio of risky and risk-free assets. P and Q have expected returns and standard deviations given by P Q E[R] St. Dev. 0.2 0.45 0.1 0.25 (a) What is the risk-free interest rate...
1. The universe of available securities includes two risky stock funds, A and B and T-bills. The data for the universe are as follows: Expected Return Standard Deviation 109 20 Tbilis The correlation coefficient between funds A and B is -0.2. a. Find the optimal risky portfolio, P. and its expected return and standard deviation b. Find the slope of the CAL supported by T-bills and portfolio P. c. How much will an investor with 4-5 invest in funds A...
1. The universe of available securities includes two risky stock funds, A and B, and T-blls. The data for the universe are as follows Expected Return Standard Deviation A 10% 20% В 30 60 T-bills The correlation coefficient between funds A and B is -0.2. a. Find the optimal risky portfolio, P, and its expected return and standard deviation. b. Find the slope of the CAL supported by T-bills and portfolio P c. How much will an investor with A...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure rate of return rj, the risky asset has a random rate of return r. Suppose the utility function of an investor is U(x) =--. The initial wealth is wo, the dollar amount invested in the risky asset is θ. r is normally distributed with mean μ and variance σ2. Based on the maximum utility framework, find the optimal investment strategy 6. (25...
Mary has access to risky stocks A and B. But she has no access to risk-free T-bills. The two assets have the following characteristics: Stock A: Expected return= 12.5% per annum, Standard deviation=14% per annum Stock B: Expected return = 5% per annum. Standard deviation=8% per annum The correlation coefficient between retum on stock A and return on stock B is 0.10 Mary's utility function U = E(R)- Ao and her coefficient of risk aversion is equal to 3 a)...
Mary has access to risky stocks A and B. But she has no access to risk-free T-bills. The two assets have the following characteristics: Stock A: Expected return= 12.5% per annum, Standard deviation=14% per annum Stock B: Expected return = 5% per annum. Standard deviation=8% per annum The correlation coefficient between retum on stock A and return on stock B is 0.10 Mary's utility function U = E(R)- Ao and her coefficient of risk aversion is equal to 3 a)...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure rate of return rj, the risky asset has a random rate of return r. Suppose the utility function of an investor is U(x) =--. The initial wealth is wo, the dollar amount invested in the risky asset is θ. r is normally distributed with mean μ and variance σ2. Based on the maximum utility framework, find the optimal investment strategy 6. (25...
(a) Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows Stock A B Expected Return Standard Deviation 10% 5% 15% 10% Correlation =-1 Suppose that it is possible to borrow at the risk-free rate, If. What must be the value of the risk-free rate? Explain. HINT!!! The stocks are perfectly negatively correlated. (b) Calculate the expected return and standard deviation of an equally weighted portfolio of...
2. Consider a market with only two risky stocks, A and B, and one risk-free asset. We have the following information about the stocks. Stock A Stock B Number of shares in the market 600 400 Price per share $2.00 $2.50 Expected rate of return 20% Standard dev.of return 12% Furthermore, the correlation coefficient between the returns of stocks A and B is PABWe assume that the returns are annual, and that the assumptions of CAPM hold. (a) (4 points)...
Most questions answered within 3 hours.
-
A) A one-way ANOVA test:
is a left-tailed test
is a right-tailed test
is a two-tailed...
asked 2 hours ago -
A mixture of nitrogen and carbon
dioxide gases, in a 9.86 L flask at
40 °C,...
asked 3 hours ago -
11) What would be the pH of 100.0 mL of a solution that is 0.040
M...
asked 2 hours ago -
A largely aquatic division of Kingdom Fungi, rarely harmful to
humans, often found as mold/mildew, &...
asked 2 hours ago -
just another way of saying good target marketing and
understanding customer needs? Why or why not?
asked 4 hours ago -
Consider the quantum number sets listed below.
What is the name of the smallest element for...
asked 5 hours ago -
In python,write a function nameSet(first, last) that takes a
person's first and last names as input,...
asked 8 hours ago -
How do you think we should value management? Specifically how
might we try to determine MRPL...
asked 7 hours ago -
Suppose the Central Bank of Turkey starts to pay
interest on reserves. Under what circumstances this...
asked 8 hours ago -
For Bergson the concept of Being contains less reality than does
the concept of Becoming. True...
asked 9 hours ago -
What is the hydroxide ion concentration, [OH-], in a solution
with a hydronium ion concentration, [H3O+]...
asked 8 hours ago -
What species is the reducing agent in the following
equation?
Mg(s) + 2HCl (aq) --> MgCl2(aq)...
asked 9 hours ago