## FNCE 443: Midterm

**NAME:**** **** ** **ID ：**** **

**SIGNATURE: **** **

**DO NOT OPEN OR TURN THE EXAM BEFORE I TOLD YOU THE EXAM HAS STARTED PLEASE READ THE INSTRUCTIONS BELOW CAREFULLY BEFORE THE EXAM**

**INSTRUCTIONS:**

· 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.

** GOOD LUCK!**

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

*volatility for each asset?*

*annual***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?

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