# PracticeFinalWithAnswers - Practice Final Exam (with...

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Practice Final Exam (with answers) Financial Instruments Professor Robert Novy-Marx Fall 2006 1. (25 points) SHORT QUESTIONS (a) (5 points) Suppose that Apple and Dell have been producing the same type of MP3 players over the last year. As a consequence of being exposed to the same type of risk (= whether consumers like these MP3 players), the stock returns of these two companies have become more correlated with each other. How does this aﬀect the price of call options on Apple and Dell? Explain your answer. Answer : This question is a popular interview question. Since this only aﬀects correlation and not the volatility of returns, nothing happens to option prices. (b) (5 points) True or False An American call option on a foreign currency should never be exercised before maturity. Explain your answer. Answer : False. Foreign currency can be thought of as an asset that pays continuous dividend at the rate, r foreign . So an Amer- ican call on it can be thought of as that on a dividend paying stock. Thus if r foreign is high enough it may be optimal to exer- cise it early. 1

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(c) (5 points) True or False. Since the price of a stock is expected to increase over time, the stock can be used to Theta-hedge (i.e., neutralize the Θ of) an option on the stock. Explain your answer. Answer : False. The Θ of the stock is zero, so it cannot neutralize any nonzero Θ of a call. The reason that the stock’s Θ is zero is because the Greeks are partial derivatives and we are holding changes in the stock price constant (since that would be delta). Perhaps more intuitively, the theta of a call only represents the sensitivity of option value as time changes, ceteris paribus . Since the stock price is expected to rise, on average, over time, the value of a call option, as a leveraged position on the stock, is also expected to rise, on average, over time. (d) (5 points) You trade Dell options. For normal business days, you know that an estimate of 30% (annualized) volatility works well for pricing Dell options. For days of earnings announcements, however, you found out that you need to adjust this estimate. From your experience, you need to double the normal volatility estimate for days with earnings announcements. Suppose that you want to price an option with the Black-Scholes formula that will expire in 5 days. Tomorrow is an earnings announcement. What (annualized) volatility number do you want to use? Answer: This question is from problem set 6, Q2. σ = ± 4 × 0 . 3 2 +1 × 0 . 6 2 5 =0 . 3795 2
(e) (5 points) In the context of foreign exchange derivatives, Fnd the risk-neutral probability that we would have to use to price, say, an American call on the British pound based on a Binomial Tree.

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## This note was uploaded on 08/14/2009 for the course BUS 35100 taught by Professor Novy-marx during the Winter '07 term at CHIC.

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PracticeFinalWithAnswers - Practice Final Exam (with...

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