4. (The asset-market economy) Suppose there are two assets available to investors: a risk-free asset with...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
4. (The asset-market economy) Suppose there are two assets available to investors: a risk-free asset with a price of p1 = 1 and that pays Ry with certainty at date 1, and a risky asset with a price of p2 = 1 and that pays R at date 1, where R is normally distributed with mean R and variance o2. An expected utility maximizer with von Neumann-Morgenstern utility function u(c) =-e- and date 0 wealth of w holds a portfolio of these two assets. For simplicity, we will allow consumption at date 1 to take negative values. (a) Calculate the investor's expected utility if she holds a proportion of her date 0 wealth in the risky asset. Hint: If y is normally distributed with mean p and variance 2 then Ele-ae-au+fa²d² (b) What level of a maximizes her expected utility? (c) How does her portfolio change as her Arrow-Pratt measure of absolute risk aversion increases? (d) Now suppose that the investor also has normally-distributed labor income L at date 1, with mean L, variance 02, and covariance with the risky asset's payoff equal to pare. That is, her date 1 consumption equals the sum of her portfolio payoff and her labor income. Derive the expected utility maximizing portfolio z and discuss how it is affected by labor income. 4. (The asset-market economy) Suppose there are two assets available to investors: a risk-free asset with a price of p1 = 1 and that pays Ry with certainty at date 1, and a risky asset with a price of p2 = 1 and that pays R at date 1, where R is normally distributed with mean R and variance o2. An expected utility maximizer with von Neumann-Morgenstern utility function u(c) =-e- and date 0 wealth of w holds a portfolio of these two assets. For simplicity, we will allow consumption at date 1 to take negative values. (a) Calculate the investor's expected utility if she holds a proportion of her date 0 wealth in the risky asset. Hint: If y is normally distributed with mean p and variance 2 then Ele-ae-au+fa²d² (b) What level of a maximizes her expected utility? (c) How does her portfolio change as her Arrow-Pratt measure of absolute risk aversion increases? (d) Now suppose that the investor also has normally-distributed labor income L at date 1, with mean L, variance 02, and covariance with the risky asset's payoff equal to pare. That is, her date 1 consumption equals the sum of her portfolio payoff and her labor income. Derive the expected utility maximizing portfolio z and discuss how it is affected by labor income.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these finance questions
-
How does marginal cost change as output increases (a) initially and (b) eventually?
-
Suppose the random variable X is normally distributed with mean and standard deviation . If Y is a linear function of X -that is, Y = a + bX, where a and b are constants-then V is also normally...
-
A variable is normally distributed with mean 6 and standard deviation 2. Find the percentage of all possible values of the variable that a. Lie between 1 and 7. b. Exceed 5. c. Are less than 4.
-
Mary Sue owns 600 shares of QRS Moving Company. QRS pays a quarterly dividend of $0.50 per share. What is the total annual dividend that Mary Sue will receive?
-
Which of the following is an example of a variable cost? a. Insurance premium for fire insurance on the factory building b. The salary of the company president c. Wood used to make custom tables d....
-
Can a gay person wear a button saying "Support Gay Rights" at the workplace?
-
\(5,355,324\) Use divisibility rules to determine if each of the following is divisible by 12 .
-
The activities described by the following table are given for the Howard Corporation in Kansas: a) Draw the appropriate AON PERT diagram for J. C. Howards management team. b) Find the critical path....
-
I need help finding income from operations and net income for this problem. I just need to know how to find it for the current year. It's the empty box above 240,000 and the empty box below 240,000...
-
Condensed financial data of Sheffield Corp. follow. Sheffield Corp. Comparative Balance Sheets December 31 Assets Cash Accounts receivable Inventory. Prepaid expenses Long-term investments Plant...
-
Between the years 2045 and 2050, Scotland will start to send a sample return probe to Vesta. The sample needs to be collected from the south pole of Vesta. The problem will need to rendezvous with...
-
What is the function of the international monetary system?
-
Suppose that on January 1, the price of one hundred yen was 80 and PPP held. Over the year, the Japanese inflation rate was 5 percent, and the U.S. inflation rate was 10 percent. If the exchange rate...
-
Following are the proportions of the United States population that is female for five age groups. a. Is this a relative frequency table? Explain why or why not? b. Would it be appropriate to...
-
What connections exist between the current account and the capital account?
-
What were the key accomplishments of the Bretton Woods conference?
-
Reword and remove "this": The researcher's function is defined as a collector of data and a designer who molds the data into its ultimate structure. This entails ensuring that the research process is...
-
Data 9.2 on page 540 introduces the dataset Cereal, which includes information on the number of grams of fiber in a serving for 30 different breakfast cereals. The cereals come from three different...
-
In Chile, bus drivers have at times been paid based on the number of riders they pick up. Discuss the likely differences in driver behavior under this plan compared to a plan in which drivers are...
-
Describe three situations (not including the examples given in the text) in which people use rules of thumb to make complex decisions. What rules do they tend to use? Do those rules strike you as...
-
The production function of a firm that uses labor (L) and capital (K) to produce its output is The price of labor is $4 per unit and the price of capital is $5 per unit. If its level of capital is...
-
Listed below are ten separate situations. For each item indicates whether the difference is (1) temporary creating a deferred tax asset or a deferred tax liability or (2) permanent. Item 1. Pension...
-
Fox Corporation purchased a machine on January 1,2020 , that cost \(\$ 40,000\). The machine had an estimated service life of five years and no residual value. Fox uses straight-line depreciation for...
-
Wittco Company reports pretax GAAP income in 2020, its first year of operations, of \(\$ 100,000\). Temporary differences in the GAAP basis and tax basis of assets arose in 2020 from the following...
Study smarter with the SolutionInn App