Solve the problem set as the last assignment you did for me.Solve the problem set as the last assignment you did for me.
Masters of Financial Economics, ADEC 73601 Dr. Danielle Zanzalari Problem Set 2 2018
Please follow the instructions listed on your syllabus regarding problem sets. I do not accept late work. Email me with any questions you have.
1. Using the VNM utility function of U(Y ) = Y 1−λ
1−λ where you could win $10,000 with probability 0.20 and lose $400 with probability 0.80 calculate the following if λ = 0.3 and Y = $2000:
a) The expected return of this lottery.
b) The relative risk aversion of this person.
c) The absolute risk aversion of this person.
d) The certainty equivalent. (Note: Follow the same set-up as the notes. Essentially you replace (E(Z)) with CE(Z), CE(Z) being the certainty equivalent.)
2. Crosby is considering investing in the following tech startups: African Water Nonprofit and Boston GoodWill to Go. Crosby has the following VNM utility function: U(Y ) = 30+Y − Y
2
200
where Y is in thousands. Crosby’s total income in $200,000 and would have to invest $50,000 in African Water Nonprofit with a probability of success of 50% and $75,000 in Boston GoodWill to Go with a 65% chance of success. If these start-ups are not successful he loses all of his money, whereas if they are successful he will retain his initial investment plus 10% and 15% return of each respective company. So,
a) Will Crosby invest in either company?
b) Would a risk neutral person make this investment?
3. What is the risk preference of investors with the following VNM utility functions?
a) U(Y ) = √ Y
b) U(Y ) = Y 2
c) U(Y ) = ln(Y )
d) U(Y ) = 10Y + 18
e) U(Y ) = Y 1−λ
1−λ
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4. Alex has a wealth of $175,000, no health insurance and worker’s compensation does not apply. Alex has a 10% chance of losing $52,000, which is the probability he breaks his leg sliding into second base in a baseball game and the amount of money it would cost for hos- pital bills, rehabilitation and loss of work for a week. His utility function is: U(Y ) = Y
0.8
0.8 .
Blue Cross Blue Shield of NYC offers the following policies and deductibles:
Insurance Premium Deductible
$4382 $1000 $4782 $500 $5502 $0 $3682 $1350
then which insurance policy (if any) will Alex choose and why?
5. Use the Condo Price excel spreadsheet, sourced from Zillow, on the mean condo prices of the top 10 cities in the U.S. to help you answer the following questions. Please use Stata, R, Matlab or Excel and submit your code along with your answers written down.
a) Using the 10 cities in the Excel spreadsheet and the assumption that house prices rise on average 7% a year and mortgage costs are 6%. Our debt to equity ratio is 4. Based on what you calculate the expected return on our levered investment to be and what you view the house price of the following year, does it make sense to buy a condo in each of these cities and in each of these years? Do not calculate this by each month. Please just use year-06 numbers (i.e. Use numbers from June each year for all problems. So, use 2010-06 to estimate the expected return on your levered investment if you sold in 2011-06. Evaluate your expected return with the actual return. Please do this for each city and for 2010-2018.)
b) Now, let’s assume that we put down 5% in our condo in Boston, Massachusetts and borrow the rest. Our borrowing costs go up 8% since we must pay PMI (an extra cost for not putting down 20% equity). If we want to ensure we make a return of 5% on our levered investment, what must our expected return on our unlevered investment be in Boston, Massachusetts for each year? Does it make sense to do a levered investment then?
c) Look at Dallas-Fort-Worth, Texas, let’s assume that we put 10% down on our condo and our borrowing costs are 5%. For what states of the world (i.e. for what unlevered return) does a levered investment not make sense?
d) Using the numbers you calculate above in part c., calculate the risk of each Dallas-Fort Worth investment assuming that the standard deviation of the unlevered investment is 2%.
e) (EXTRA CREDIT: 10 pts)Lastly, the expected return on our levered investment does not take into account the tax benefits of owning a condo (or home). How would you propose we consider the tax benefits in the home purchase leverage equation we have been discussing?
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