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TestId: 1001 For each problem, choose the answer choice that best answers the question. Name ___________________________________ 1 ____________ 13 ____________ 2 ____________ 14 ____________ 3 ____________ 15 ____________ 4 ____________ 16 ____________ 5 ____________ 17 ____________ 6 ____________ 18 ____________ 7 ____________ 19 ____________ 8 ____________ 20 ____________ 9 ____________ 21 ____________ 10 ____________ 22 ____________ 11 ____________ 23 ____________ 12 ____________ 24 ____________ 25 ____________ TestId: 1001 TestId: 1001 Question 1) I own a delta-hedged portfolio with a total gamma exposure of -50.76. I want to hedge my gamma exposure by entering into a position in a call option with a delta of 0.64 and a gamma of 0.12. I also want to make sure my portfolio remains delta-neutral. Thus, I will also make a trade in the underlying stock to retain delta-neutrality. Which of the following indicates the trades I need to make to achieve my objectives? 1) 2) 3) 4) Sell 50.76 call options, sell 640 shares Buy 423 call options, sell 270.72 shares Buy 600 call options, sell 320 shares Sell 64 call options, but 391.43 shares TestId: 1001 Question 2) A non-dividend-paying stock has a current price of $70. Over the next month, the stock price will either increase by 20% or decrease by 20%. An investor has a short position in a 1-month call with a strike price of $75. How many shares of stock must be purchased if the investor wants to create a risk-free portfolio? 1) 2) 3) 4) 0.523 -0.523 0.321 1.000 TestId: 1001 Question 3) Which of the following is NOT an assumption necessary for the Black, Scholes, Merton option pricing model to be correct? 1) 2) 3) 4) Over very short periods of time, the return of the underlying stock has a normal distribution All investors must hold the market portfolio Arbitrage opportunities do not exist The distribution of the return of the stock from present until expiration is lognormal TestId: 1001 Question 4) The implied volatility of a 2-month call option with strike price $45 on stock XYZ is 32%. The implied volaitlity of a 3-month put option with strike price $42 on the same stock is 28%. Which of the following is true? 1) There is an arbitrage opportunity that can be captured by buying the put and selling the call. 2) There is an arbitrage opportunity that can be captured by selling the put and buying the call. 3) There is no arbitrage opportunity. 4) There is an arbitrage opportunity that can be captured by buying both the call and the put. TestId: 1001 Question 5) You are using a 1-step binomial tree to calculate the price of a 2-month European put option with strike price of $24 on a non-dividend-paying stock that is currently worth $26. You calculate that a portfolio that is short one of the put options and short 0.6 shares of the stock will generate a riskless payoff of -$18 at expiration. The risk-free rate is 4%. What is the price of the put contract? 1) 2) 3) 4) $3.25 $1.18 -$3.25 $2.28 TestId: 1001 Question 6) The price of a non-dividend-paying stock is $71. The Black, Scholes, Merton price of a 12-month European put option with strike price of $69 is $4.99. The risk-free rate is 4%. What is the implied volatility of the option? When answering the question, you may use the information below. When =7% N(d1)=0.8449 N(d2)=0.8276 N(-d1)=0.1551 N(-d2)=0.1724 N'(d1)=N'(-d1)=0.2384 N'(d2)=N'(-d2)=0.2554 When =26% N(d1)=0.6531 N(d2)=0.5532 N(-d1)=0.3469 N(-d2)=0.4468 N'(d1)=N'(-d1)=0.3692 N'(d2)=N'(-d2)=0.3954 1) 2) 3) 4) When =14% N(d1)=0.7122 N(d2)=0.6627 N(-d1)=0.2878 N(-d2)=0.3373 N'(d1)=N'(-d1)=0.3411 N'(d2)=N'(-d2)=0.3653 When =30% N(d1)=0.6475 N(d2)=0.5313 N(-d1)=0.3525 N(-d2)=0.4687 N'(d1)=N'(-d1)=0.3714 N'(d2)=N'(-d2)=0.3977 14% 26% 7% 30% TestId: 1001 Question 7) Which of the following accurately describes the objectives of a principal protected note? 1) Protect the principal of the investment while also providing up-side exposure to the market 2) Take a leveraged position in the market portfolio, thus providing the possibility of extremely large gains but taking the risk of extremely large losses 3) Provide a portfolio that generates a high rate of interest but may expirience large losses if the market goes down 4) Generate large gains if the stock market experiences a large loss or a large gain with losses only occuring when the level of the stock market does not change very much. TestId: 1001 Question 8) The 3-month futures price for a currency is $18.18. The volatility of the exchange rate is 12%. The U.S. dollar risk-free rate is 5%. According to Black's model, what is the price of a 3-month European futures put option on the currency with a strike price of $18.10? When answering this question, you may use the information below. N(d1)=0.5412 N(d2)=0.5173 N(-d1)=0.4588 N(-d2)=0.4827 N'(d1)=N'(-d1)=0.3968 N'(d2)=N'(-d2)=0.3986 1) 2) 3) 4) $0.28 $1.32 $0.39 $0.98 TestId: 1001 Question 9) You are using a 2-step binomial tree to price a 6-month option on a stock that pays no dividends. The current price of the stock is $35 and the volatility of the stock is 40%. If the stock has two up moves (one at each step of the tree) what will the stock price be at expiration? 1) 2) 3) 4) $33.58 $73.68 $52.21 $48.92 TestId: 1001 Question 10) You are calculating the price of an option on a foreign currency using a binomial tree. The risk-free rate of return on U.S. dollars is 4% per year and the risk-free rate of return on the foreign currency is also 4% per year. Each step in your binomial tree covers a 3-month period. The volatility of the exchange rate is 15%. What is the risk-neutral probability that, in any given step in the tree, the exchange rate increases from the previous step? 1) 2) 3) 4) 57% 53% 48% 42% TestId: 1001 Question 11) The 12-month forward price on a stock is currently $53. Which of the following portfolios will generate the exact same payoff in 12 months as a short 12-month forward position? When answering this question, assume that the options and bonds used to create to the portfolio have expiration and maturity in 12 months. 1) Buy a put option with a strike price of $55, sell a call option with a strike price of $55, and sell $2 face value worth of risk-free bonds. 2) Sell a call option with a strike price of $53 and buy $53 face value worth of bonds. 3) Buy a put option with a strike price of $50 and buy a call option with a strike price of $50 4) Buy a call option with a strike price of $55, sell a put option with a strike price of $55, and buy $2 face value worth of risk-free bonds. TestId: 1001 Question 12) You are short a call option on a futures contract. The strike price of the call is 2114. At the time the option expires, the underlying futures price is 2130. What is the payoff, from your point of view, of the call option? 1) 2) 3) 4) -$32 $0 -$16 $32 TestId: 1001 Question 13) The current 6-month futures price for an equity index is 1883. The price of a 6-month European futures call contract with a strike price 1900 is $88.31. The risk-free rate is 3%. What is the price of a 6-month European futures put contract with a strike price of 1900? 1) 2) 3) 4) $105.06 $88.31 $103.91 $17.00 TestId: 1001 Question 14) Which of the following creates a strangle trading strategy? When answering this question, assume all of the options have the same expiration and same underlying security. 1) 2) 3) 4) Buy 2 puts with a strike price of $48 Sell a call with a strike price of $50 and buy a call with a strike price of $55 Buy a put with a strike price of $40 and but a call with a strike price of $50 Buy a call with a strike price of $45 and sell a call with a strike price of $50 TestId: 1001 Question 15) In 3 months my firm will buy a factory in Australia for 30 million Australian dollars (AUD). The current exchange rate is $0.75 per AUD. Which of the following AUD option positions will ensure that the effective exchange rate that I pay in 3 months when I buy the factory is between $0.70 and $0.80 per AUD? 1) 2) 3) 4) Long 3-month call with strike $0.70 and long 3-month put with strike $0.80 Long 3-month put with strike $0.70 and long 3-month call with strike $0.80 Long 3-month range forward with strikes $0.70 and $0.80 Short 3-month range forward with strikes $0.70 and $0.80 TestId: 1001 Question 16) The price of a 1-month European call option on the S&P 500 index with a strike price of 2030 is $39.49. The price of a 1-month European put option on the S&P 500 index with a strike price of 2030 is $22.92. The risk-free rate is 1% and the dividend yield of the S&P 500 index is 3%. What is the current level of the S&P 500 index? 1) 2) 3) 4) 2,030 2,040 2,050 2,025 TestId: 1001 Question 17) What is the delta of a 3-month European put option with a strike price of $42 on a non-dividend-paying stock with current price of $45 and a volatility of 19%? The risk-free rate is 2%. When answering this question you may use the information below. N(d1)=0.7957 N(d2)=0.7677 N(-d1)=0.2043 N(-d2)=0.2323 N'(d1)=N'(-d1)=0.2835 N'(d2)=N'(-d2)=0.3053 1) 2) 3) 4) -0.538 0.310 0.937 -0.204 TestId: 1001 Question 18) Which of the following is true if all of the assumptions of the Black-Scholes-Merton model are true? When answering this question, assume all options in question are European options written on the same underlying asset. 1) No two options can have the same implied volatility. 2) For any given strike price, the implied volatility of all options must be the same, but the implied volatility may be different for different strike prices. 3) The implied volatility of all options, regardless of expiration and strike, is the same. 4) For any given expiration date, the implied volatility of all options must be the same, but for different expirations the implied volatility may be different. TestId: 1001 Question 19) I have purchased a 1-month straddle portfolio using options with a strike price of $70. I paid $3.26 for the call option and $2.91 for the put option used to form the straddle. At expiration in 1 month, the price of the stock is $67.45. What is my profit from the trade? Note: A negative number in the answer represents a loss. 1) 2) 3) 4) -$8.72 -$3.62 $8.72 $2.45 TestId: 1001 Question 20) The 4-month futures price for an equity index is $4391. The risk-free rate is 2%. Which of the following is the lowest possible price for a 4-month European futures put option on the index with a strike price of $4425? 1) 2) 3) 4) $41.91 $29.59 $35.71 $33.77 TestId: 1001 Question 21) I own a portfolio of options on the Euro. The total delta of the option portfolio is -201,398. The risk-free rate on the Euro is 2.041%. The risk-free rate on the U.S. dollar is 5%. If I want to delta-hedge my option portfolio using 2-year Euro futures contracts, what position must I take? Round your answer to the nearest integer. 1) 2) 3) 4) Long 209,789 futures Long 189,825 futures Short 1,398,182 futures Short 201,398 futures TestId: 1001 Question 22) A stock currently worth $45 pays no dividends and has a volatility of 17%. According to the Black, Scholes, Merton option pricing model, what is the value of a 6-month European call option with a strike price of $46 on this stock. The risk-free rate is 5%. When answering this question you may use the information below. N(d1)=0.534 N(d2)=0.4861 N(-d1)=0.466 N(-d2)=0.5139 N'(d1)=N'(-d1)=0.3975 N'(d2)=N'(-d2)=0.3987 1) 2) 3) 4) $3.18 $2.22 $4.31 $7.52 TestId: 1001 Question 23) You just bought a 6-month European call option with a strike price of $22 on a non-dividend-paying stock. The current spot price of the stock is $23, the volatility of the stock is 42% and the risk-free rate is 4%. The vega of the option is 6.07. If the volatility of the stock increases to 44% and everything else stays the same, what will be your profits? 1) 2) 3) 4) $6.0700 -$0.2183 $0.2593 $0.1214 TestId: 1001 Question 24) You are using a binomial tree to value a call option on a future contract. At a given node in the tree, if the futures price has an up move, the futures price will be $1233.94 and the call price will be $228.16. If the futures price has a down move, the futures price will be $866.46 and the call price will be $15.12. What is the value of at this node of the tree? 1) 2) 3) 4) 0.50 0.63 0.41 0.58 TestId: 1001 Question 25) The U.S. dollar risk-free rate of return is 3%. The current exchange rate between the U.S. dollar and the Brittish pound is $1.50 per pound. The price of a 6-month European call option on the pound with strike price of $1.50 is $0.1220. The price of a 6-month European put option on the pound with strike price of $1.50 is $0.1350. What is the implied risk-free rate on the pound? 1) 2) 3) 4) 1.28% 4.77% 3.00% 3.75% 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 2 3 2 3 4 2 1 3 3 3 1 3 1 3 3 3 4 3 2 4 2 2 4 4 2