衍生工具试题Questions

FINA 0301/2322:DerivativesReview questions,Fall,20131.Which of the positions can result in the following profit diagram?ProfitStock priced d d d d d d d d d d(a)Buy one low strike call,sell two high-strike calls.(b)Buy one high strike call,sell two low strike calls.(c)Buy two strike call,sell three 1050-strike calls.(d)Buy three strike call,sell five 1050-strike calls.Answer:A2.Which of the following phrases is used to describe an option where the strike price is approximately equal to the asset price?(a)At-the-money(b)In-the-money(c)Over-the-money(d)Out-of-the-moneyAnswer:A3.Assume that you purchase 100shares of Jiffy,mon stock at the bid-ask prices of $32.00-$32.50.When you sell the bid-ask prices are $32.50-$33.00.If you pay a commission rate of 0.5%,what is your profit or loss?(a)$0(b)$16.25loss(c)$32.50gain(d)$32.50lossAnswer:D(32.50−32.50)×100+(32.50+32.50)×100×0.5%=32.504.A put option was purchased1year ago.The Exercise price on the underlying asset is$40.If thecurrent price of the asset is$36.45and the future value of the original option premium is$1.62, what is the put profit,if any today?(a)$1.62(b)$1.93(c)$3.55(d)$5.17Answer:B(40−36.45)−1.62=1.935.A strategy consists of buying a market index product at the spot price of$830and longing a puton the index with a strike of$830.If the put premium is$18.00and interest rates are0.5%per month,what is the profit or loss from the long index position by itself at expiration(in6months) if the market index is$810.(a)$45.21loss(b)$21.22loss(c)$18.00gain(d)$24.25gainAnswer:A810−830×1.0056=−45.216.At the6-month point,what is the breakeven index price for a strategy of longing the market indexat a price of830?Effective interest rates are0.5%per month.(a)$802.12(b)$830.00(c)$855.21(d)$866.32Answer:C,you break even when your cost equals your payoff830×1.0056=855.217.The$830strike put premium is$18.00and the call premium is$42.47.The$850strike putpremium is$25.45and the$850strike call is selling for$30.51.What is the maximum profit that an investor can obtain from a strategy employing a long830call and a short850call over6 months?Interest rates are0.5%per month.(c)$6.10(d)$12.32Answer:B,think about the diagram of the bull spread–you achieve maximum profit when the price goes up,and they buyer of the high strike call exercises.Of course you exercise your low strick call as well.Therefore,figure out your payoff,subtract your cost for the options(850−830)−(42.47−30.51)×1.0056=7.688.What is the break even point that an investor can obtain from a6-month strategy employing along830call and a short850call?Interest rates are0.5%per month.(a)$832.82(b)$842.32(c)$852.22(d)$862.92Answer:B,to break even,you must receive some money by exercising the830-call to cover the cost for the options.Figure out your payoffS T−E,then subtract your cost for the options.Set S T=x,(x−830)−(42.47−30.51)×1.0056=0x=842.329.A strategy consists of longing a put on the market index with a strike of850and shorting a calloption on the market index with a strike price of850.The put premium is$25.45and the call premium is$30.51.Interest rates are0.5%per month.What is the breakeven price of the market index for this strategy at expiration(in6months)?(a)$802.12(b)$830.00(c)$855.21(d)$866.32Answer:C,the payoffto the same strike price long put is Max[E−S T,0],and short call is–Max[0, S T−E].Combined,it is just E−S T.This is your payoff.To breakeven,set S T=x,and let payoffequal your cost for the options,850−x−(25.45−30.51)×1.0056=0x=855.2110.Farmer Jayne bought a$1.70strike put option for$0.11and sold a$1.75strike call option fora premium of$0.14.Her total costs are$1.65per bushel and interest rates are4.0%over thisperiod.What is thefloor in her strategy assuming a20,000-bushel crop?(c)$2,624(d)$3,624Answer:B,if the selling price goes down,you can always exercise your put option.Figure out your payoff,then subtract your cost for the options(1.70−1.65)×20,000−(0.11−0.14)×20,000×1.04=1,62411.The annualized dividend yield on the S&P500Index is1.40%.The continuously compoundedinterest rate is6.4%.If the9-month forward price is$925.28and the index is priced at$950.46, what is the profit/loss from a cash-and-carry strategy?(a)$25.18loss(b)$25.18gain(c)$61.50loss(d)$61.50gainAnswer:C925.28−950.46×e(0.064−0.014)×.75=−61.5012.Consider an investment infive S&P500Index futures contracts at a price of$924.80.Theinitial margin requirement is15.0%and the maintenance margin is10.0%.If the continuously compounded interest rate is5.0%what will the futures price need to be for a margin call to occur 2weeks from now?Assume no settlement within the2weeks(52weeks for a year).(a)$852.64(b)$872.79(c)$878.29(d)$905.25Answer:C15%×924.80×e0.05/26+(F1,T−924.80)<924.80×10%F1,T<878.2913.Continuously compounding interest rates on the U.S.dollar are6.5%and euro rates are5.5%.The dollar per euro spot rate is0.950.What is the arbitrage profit on a required$1million Euro contract if the forward rate is0.980dollars per Euro and the exchange occurs in one year?(a)$10,000(b)$21,600(c)$28,000Answer:B,you can quicklyfind out which outcome is better1,000,000×0.980×e0.055−0.950×e0.065=21,600The question is only about profit.Ask yourself,the complete description of the strategy should be,borrow what currency,lend what else currency today,andfinally,long or short a forward contract?14.The annual risk free interest rate is4.0%.Today’s the spot price for corn is212cents/bushel,in12months the forward price is203cents/bushel.What is the approximate annualized lease rate on the12-month corn forward contract?(a)0.00%(b)2.25%(c)4.50%(d)8.34%Answer:Dδ=0.04−ln(203/212)15.What phrase might be used to describe the initial transaction a short seller initiates when shortingan equity security?(a)Buy(b)Sell(c)Borrow(d)CoveringAnswer:C16.A currency dealer has good credit and can borrow either$1,000,000or e800,000for one year.The one-year continuously compounding interest rate in the U.S.is i$=1.98%and in the euro zone the one-year continuously compounding interest rate is i e=5.83%.The one-year forward exchange rate is$1.20=e1.00.What must be the spot rate to eliminate arbitrage opportunities?(a)$1.2471=e1.00(b)$1.20=e1.00(c)$1.1547=e1.00(d)none of the aboveAnswer:A,e0.0198=1.02;e0.0583=1.061.2x0×1.06=1.02x0=1.21.02×1.06=1.247117.Corn call options with a$1.75strike price per bushel are trading for a$0.14premium.FarmerJayne decides to hedge her20,000bushels of corn by selling short call options.Six-month interest rates are4.0%and she plans to close her position in6months.What is the total premium she will earn on her short position in6months?(a)$2,800(b)$2,912(c)$800(d)$1,600Answer:B20000×0.14×1.04=291218.Suppose that the annual interest rate is4.88percent in the United States and3.44percent inGermany,and that the spot exchange rate is$1.12/e and the forward exchange rate,with one-year maturity,is$1.16/e.Assume that an arbitrager can borrow up to$1,000,000.If an astute traderfinds an arbitrage,what is the dollar profit in one year?(a)$10,690(b)$15,000(c)$46,207(d)$21,964.29Answer:De0.0488=1.05;e0.0344=1.035$21,964.29=−$1,000,000×(1.05)+$1,000,000×1.161.12×(1.035)19.Assume now U.S.dollar denominated interest rate is3.0%,and Yen denominated interest rate is4.0%.Today’s spot rate is1Yen equals0.01U.S.dollar.If you want to conduct carry trade,youshould borrow,lend today,and in the future.(a)Yen;U.S.dollar;short Yen(b)Yen;U.S.dollar;long Yen(c)U.S.dollar;Yen;short Yen(d)U.S.dollar;Yen;long YenAnswer:C20.When interest rate parity does not hold we should take(a)cash in advance(b)covered interest arbitrage(c)quasi arbitrage(d)fixed income arbitrageAnswer:B。