FNCE 443: Midterm
NAME: ID ：
DO NOT OPEN OR TURN THE EXAM BEFORE I TOLD YOU THE EXAM HAS STARTED PLEASE READ THE INSTRUCTIONS BELOW CAREFULLY BEFORE THE EXAM
· You can use books, computers, formula sheets, etc. The only thing you cannot use is help from someone else.
· You can write on this exam, or can submit an electronic version of this test.
· Always show your work: which formula you are using and what numbers you are plugging in. No credit will be given for simply stating the result.
· Please write legibly, illegible answers will receive no credit.
· There is enough space left to work out the problems. In the unlikely event that you run out of space, use the blank space at the end of the exam.
· Exams might have problems in different order or calculations using different numbers.
· Violations to the rules of the exam or to the ethic codes of the school will not be tolerated.
· Each question in the exam is worth the same. The following rubric will be used in each question:
· 5 Perfect
· 4 Perfect logic but had a numerical mistake
· 3 Almost perfect logic, but missed something important or had a numerical mistake
· 2 Important problems with the logic and numerical mistakes
· 1 Tried to do something but didn’t quite know what to do
· 0 No answer or a wrong number with no explanation
· You have 1 hours and 15 minutes to work on this exam.
· Make sure you fill out your name, signature and ID number on the exam.
Imagine that only three relevant news will arrive within this month: with a 30% probability the news will be that outcome 1 will take place, with a 40% probability the news will be that outcome 2 will take place, and with a 30% probability the news will be that outcome 3. After careful analysis, you uncover a few assets with the following payouts in one month. Payouts depend on the news as follows:
Please calculate the following for assets A, B, and C.
1. The holding period return for each possible outcome
2. The expected excess return for each asset assuming a risk-free rate of .2%
3. The variance and volatility for each asset’s excess returns, and the covariance between them
4. Assuming that the returns and volatilities of these assets remain constant month after month, what is the annual expected return, and annual volatility for each asset?
5. Assuming the monthly risk free rate is .2%, calculate the beta of each asset
6. The expected return for each asset according to the CAPM, assuming the risk-free rate is .20% per month.
7. The alpha of each asset, assuming the risk-free rate is .2% per month.
8. The systematic and idiosyncratic volatility of each asset
9. The expected payoffs for each asset (note: if you do this right you’ll get the same number for all assets)
10. The expected payoffs for each asset are identical, please explain in less than three sentences why their prices are not identical.
11. Assuming absence of arbitrage, what is the monthly risk-free rate? (If you cannot answer this question, continue assuming it is .20% for subsequent calculations.)
12. What is the highest Sharpe ratio of forming a portfolio with assets A and C?
13. Suppose you are advising someone whose risk-aversion is A=2. Assuming this investor’s preferences can be captured by the utility function U=Er-1/2*A*Variance, which assets (A, B, C and the market) should be in the investor’s optimal portfolio, and in what proportions?
14. The three possible outcomes are a recession, average growth, and a boom. Which of these is most likely to be Outcome 1? Outcome 3?
15. Bonus question: Suppose you identify another asset with the following characteristics:
What should be the price of Asset D if there is to be no arbitrage?