Suppose there is one risky asset and one risk free asset. Derive the optimal weights for...
Suppose there is one risky asset and one risk free asset. Derive the optimal weights for a mean-variance optimizer to hold of each.
Homework Answers
OPtimal Weight = The weight should be made in each Asset
Expected Risk = Risk of Risky Asset * Weight of that Risky Asset
Weight in Risky Asset = Max risk that can beared / Risk of Risky Asset
Weight in Risk Free Asset = 1 - Weight in Risky Asset.
Pls comment, f any further assistance is required.
Add Answer to:
Suppose there is one risky asset and one risk free asset. Derive
the optimal weights for...
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...
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...
Exercise 2. Suppose that there is one risk free asset with return rf and one risky...
Exercise 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ~ N(u,02). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that E[r] – rf OCARA = AO2 Hint: Use the fact that if a random variable x is distributed normally with mean Mx and variance...
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...
Find the weights for the optimal risky portfolio. Assuming risk-free rate is 3%. E(rs) =10% E(rB...
Find the weights for the optimal risky portfolio. Assuming risk-free rate is 3%. E(rs) =10% E(rB )= 5% σs = 15% σB = 6% PBS = 0.3
Which one of the following measures the amount of systematic risk present in a particular risky asset relative to that in an average risky asset?
Which one of the following measures the amount of systematic risk present in a particular risky asset relative to that in an average risky asset? 1) Standard deviation 2) Squared deviation 3) Beta coefficient 4) Mean 5) Variance
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...
There is one risk-free asset that pays a return of rF=0.005. There are 3 risky assets:...
There is one risk-free asset that pays a return of rF=0.005. There are 3 risky assets: A, B and C. The expected returns of the risky assets are: μA=0.01, μB=0.02, μC=0.03. The variances are: σ2A=0.00001, σ2B=0.0004, σ2C=0.0036. The covariances are: σAB=0.0002, σAC=0, σBC=-0.0002. Combining A,B and C, we create four risky portofolios, called 1,2,3 and 4. The shares of assets A, B and C in portfolio 1 are: w1A=0.6, w1B=0.2 and w1C=0.2. Similarly, the share in portfolio 2 are: w2A=0.2,...
Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%...
Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%. The optimal risky portfolio, i.e., the portfolio with the highest Sharpe ratio, is given below: A BC Stock A Stock B Risk-free asset 2 Expected return 0.062 0.075 0.03 3 Variance 0.1521 0.0484 4 Standard deviation 0.39 0.22 5 Covariance 0.02574 D Optimal risky portfolio 8 Weights 9 Expected return 10 Variance 11 Standard deviation 12...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
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...
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...
Exercise 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ~ N(u,02). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that E[r] – rf OCARA = AO2 Hint: Use the fact that if a random variable x is distributed normally with mean Mx and variance...
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...
Which one of the following measures the amount of systematic risk present in a particular risky asset relative to that in an average risky asset? 1) Standard deviation 2) Squared deviation 3) Beta coefficient 4) Mean 5) Variance
Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%. The optimal risky portfolio, i.e., the portfolio with the highest Sharpe ratio, is given below: A BC Stock A Stock B Risk-free asset 2 Expected return 0.062 0.075 0.03 3 Variance 0.1521 0.0484 4 Standard deviation 0.39 0.22 5 Covariance 0.02574 D Optimal risky portfolio 8 Weights 9 Expected return 10 Variance 11 Standard deviation 12...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago