Consider an investor with preferences over the mean and variance of the returns on his or...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider an investor with preferences over the mean and variance of the returns on his or her portfolio that are described by the utility function U(@P,0})=HP- · (4) ², where a higher value of A corresponds to a larger aversion to risk. Suppose that this investor is able to form a portfolio from a risk-free asset with return rf and a risky asset with expected return equal top, and a standard deviation of its return equal to or. In this context, the risky asset may simply be the only risky asset available to the investor or it can be the tangency portfolio that represents the optimal combination of many individual risky assets. Either way, our analysis from class showed that the relationship between up and op for the portfolio that combines the risk-free asset with the risky asset is linear: + (#₁ = 71) Or - Tf Or HP = Tf+ By substituting this constraint into the investor's utility function, his or her problem can be solved as one of choosing op to maximize Tf+ op. Op- - ( 4 ) %. Use the first-order condition for this problem to solve for the optimal choice of op. Our analysis from class also showed that the portfolio formed from the risk-free and risky asset that has a return with standard deviation op allocates the fraction op of wealth to the risk asset and the remaining fraction 1- w to the risk-free asset. Use this expression, together with your solution for the optimal choice of op from question 3, above, to find the investors' optimal choice of w. How does the optimal share of the risky asset depend on the investor's risk aversion, as measured by the parameter A from the utility function? How does the optimal share of the risky asset depend on r-rf, the risk premium defined as the expected return on the risky asset minus the risk-free return? Consider an investor with preferences over the mean and variance of the returns on his or her portfolio that are described by the utility function U(@P,0})=HP- · (4) ², where a higher value of A corresponds to a larger aversion to risk. Suppose that this investor is able to form a portfolio from a risk-free asset with return rf and a risky asset with expected return equal top, and a standard deviation of its return equal to or. In this context, the risky asset may simply be the only risky asset available to the investor or it can be the tangency portfolio that represents the optimal combination of many individual risky assets. Either way, our analysis from class showed that the relationship between up and op for the portfolio that combines the risk-free asset with the risky asset is linear: + (#₁ = 71) Or - Tf Or HP = Tf+ By substituting this constraint into the investor's utility function, his or her problem can be solved as one of choosing op to maximize Tf+ op. Op- - ( 4 ) %. Use the first-order condition for this problem to solve for the optimal choice of op. Our analysis from class also showed that the portfolio formed from the risk-free and risky asset that has a return with standard deviation op allocates the fraction op of wealth to the risk asset and the remaining fraction 1- w to the risk-free asset. Use this expression, together with your solution for the optimal choice of op from question 3, above, to find the investors' optimal choice of w. How does the optimal share of the risky asset depend on the investor's risk aversion, as measured by the parameter A from the utility function? How does the optimal share of the risky asset depend on r-rf, the risk premium defined as the expected return on the risky asset minus the risk-free return?
Expert Answer:
Answer rating: 100% (QA)
Answer To find the optimal choice of P we need to maximize the utility function UP P2 P A2 P2 subject to the constraint P rf r rfr P Lets differentiate the utility function with respect to P and set i... View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
Students also viewed these finance questions
-
Generally speaking, what is appealing about vbloggers? What make a vblog go viral? Who is the target audience /target customer segments for $21,000 Emirates Airlines travel ticket for a 7+ hour...
-
1. If you repeat the dice game several times, or perhaps in a class, you might find that Red occasionally comes out the winner. Seeing that all of the others lose with Red, how might it be that some...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Assume that Polaris manufactures and sells 60,000 units of a product at $ 11,000 per unit in domestic markets. It costs $ 6,000 per unit to manufacture ($ 4,000 variable cost per unit, $ 2,000 fixed...
-
Discuss the relative advantages of globalization versus regionalization/localization.
-
Midwest Home Furnishings Corporation (MHFC) manufactures a variety of house wares for the consumer market in the midwest. The company's three major product lines are cooking utensils, tableware, and...
-
In a laboratory test of a new automobile engine design carried out at the Colorado School of Mines, the emission rate (in milligrams per second) of oxides of nitrogen was measured for 32 engines at...
-
Calvin uses fraud to induce Maria to promise to pay money in return for goods he has delivered to her. Has a contract been formed? If so, what kind? What are the rights of Calvin and Maria?
-
What is the fundamental challenge buyers face when purchasing under all unit discounts, compared to when they purchase under incremental discounts?
-
In March 2013 the management team of Londonderry Air (LA) met to discuss a proposal to purchase five shorthaul aircraft at a total cost of $25 million. There was general enthusiasm for the...
-
On 31 December 2017 Real Estate Company issued K300, 000 of 10% bonds. The bonds are due on January 1, 2023, with interest payable each July 1 and January 1. The bonds are issued to yield 8%...
-
Veronica has come in to speak to you as she requires support to help her get through the current situation that she is in. Veronica has recently lost custody of her two (2) children in a nasty...
-
Kamala Harris has been described as the first black VicePresident as well as the first Asian Vice President. Her fatherwas an immigrant to the US from Jamaica, and her mother immigratedto the US from...
-
1. For the year ended February 28, 2016, Pynel Company, the 90% owned acquired subsidiary of Shally Corporation declared a dividend of P125,000 and had net income of P375,000. Also for that year,...
-
Suppose a seven-year, $1,000 bond with a 7.6% coupon rate and semiannual coupons is trading with a yield to maturity of 6.63%. a. Is this bond currently trading at a discount, at par, or at a...
-
On this day we learned about " Why voting matters " they talked about the different barriers people may have such as transportation ( How do we get voters to the poles and back to their desire...
-
Alpha + Beta = pi/4. Prove: (1+tan(alpha)) (1+tan(beta)) = 2
-
A bubble-point liquid feed is to be distilled as shown in Figure. Use the Edmister group method to estimate the mole-fraction compositions of the distillate and bottoms. Assume initial overhead and...
-
Children, Parents, Baby Booms and Baby Busts: Economists often think of parents and children trading with one another across time. When children are young, parents take care of children; but when...
-
This exercise reviews some concepts from earlier chapters on consumer theory in preparation for exercise 19.5. A. Consider an individual saver who earns income now but does not expect to earn income...
-
In exercise 22.2, we showed how an efficient equilibrium with a complete set of insurance markets can be re-established with truthful signaling of information by consumers. We now illustrate that...
-
Assume that Boardmaster sold skateboards to a department store for \($35,000\) cash. How would this transaction affect Boardmasters accounting equation? a. Increase both assets and stockholders...
-
Generally Accepted Accounting Principles (GAAP) are created by the a. Securities and Exchange Commission (SEC). b. Financial Accounting Standards Board (FASB). C. Institute of Management Accountants...
-
Boardmaster is famous for custom skateboards. At the end of a recent year, Boardmasters total assets added up to \($622\) million, and stockholders equity was \($487\) million. How much did...
Study smarter with the SolutionInn App