FIN 411 Midterm Practice Exam
The price of a stock on February 1 is $84. A trader buys 200 put options on the stock with a strike price of $90 when the option price is $10. The options are exercised when the stock price is $85. The trader's net profit or loss is A.Loss of $1,000 B.Loss of $2,000 C.Gain of $200 D.Gain of $1000
A. Loss of $1000 The payoff is 90−85 or $5 per option. For 200 options the payoff is therefore 5×200 or $1000. However the options cost 10×200 or $2000. There is therefore a net loss of $1000.
Which of the following creates a bull spread? A.Buy a low strike price call and sell a high strike price call B.Buy a high strike price call and sell a low strike price call C.Buy a low strike price call and sell a high strike price put D.Buy a low strike price put and sell a high strike price call
Answer: A A bull spread is created by buying a low strike call and selling a high strike call. Alternatively, it can be created by buying a low strike put and selling a high strike put.
A company knows it will have to pay a certain amount of a foreign currency to one of its suppliers in the future. Which of the following is true A.A forward contract can be used to lock in the exchange rate B.A forward contract will always give a better outcome than an option C.An option will always give a better outcome than a forward contract D.An option can be used to lock in the exchange rate
Answer: A A forward contract ensures that the effective exchange rate will equal the current forward exchange rate. An option provides insurance that the exchange rate will not be worse than a certain level, but requires an upfront premium. Options sometimes give a better outcome and sometimes give a worse outcome than forwards.
How can a straddle be created? A.Buy one call and one put with the same strike price and same expiration date B.Buy one call and one put with different strike prices and same expiration date C.Buy one call and two puts with the same strike price and expiration date D.Buy two calls and one put with the same strike price and expiration date
Answer: A A straddle consists of one call and one put where the strike price and time to maturity are the same. It has a V-shaped payoff.
The frequency with which futures margin accounts are adjusted for gains and losses is A.Daily B.Weekly C.Monthly D.Quarterly
Answer: A In futures contracts margin accounts are adjusted for gains or losses daily.
Which of the following must post margin? A.The seller of an option B.The buyer of an option C.The seller and the buyer of an option D.Neither the seller nor the buyer of an option
Answer: A The seller of the option must post margin as a guarantee that the payoff on the option (if there is one) will be made. The buyer of the option usually pays for the option upfront and so no margin is required.
When volatility increases with all else remaining the same, which of the following is true? A.Both calls and puts increase in value B.Both calls and puts decrease in value C.Calls increase in value while puts decrease in value D.Puts increase in value while calls decrease in value
Answer: A Volatility increases the likelihood of a high payoff from either a call or a put option. The payoff can never be negative. It follows that as volatility increases the value of all options increase.
A company enters into a long futures contract to buy 1,000 units of a commodity for $60 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin account? A. $58 B. $62 C. $64 D. $66
Answer: B Amounts in the margin account in excess of the initial margin can be withdrawn. Each $1 increase in the futures price leads to a gain of $1000. When the futures price increases by $2 the gain will be $2000 and this can be withdrawn. The futures price is currently $60. The answer is therefore $62.
As the convenience yield increases, which of the following is true? A.The one-year futures price as a percentage of the spot price increases B.The one-year futures price as a percentage of the spot price decreases C.The one-year futures price as a percentage of the spot price stays the same D.Any of the above can happen
Answer: B As the convenience yield increases, the futures price declines relative to the spot price. This is because the convenience of owning the asset (as opposed to having a futures contract) becomes more important.
Which of the following increases basis risk? A. A large difference between the futures prices when the hedge is put in place and when it is closed out B.Dissimilarity between the underlying asset of the futures contract and the hedger's exposure C.A reduction in the time between the date when the futures contract is closed and its delivery month D.None of the above
Answer: B Basis is the difference between futures and spot at the time the hedge is closed out. This increases as the time between the date when the futures contract is put in place and the delivery month increases. (C is not therefore correct). It also increases as the asset underlying the futures contract becomes more different from the asset being hedged. (B is therefore correct.)
A trader has a portfolio worth $5 million that mirrors the performance of a stock index. The stock index is currently 1,250. Futures contracts trade on the index with one contract being on 250 times the index. To remove market risk from the portfolio the trader should A. Buy 16 contracts B.Sell 16 contracts C.Buy 20 contracts D.Sell 20 contracts
Answer: B One futures contract protects a portfolio worth 1250×250. The number of contract required is therefore 5,000,000/(1250×250)=16. To remove market risk we need to gain on the contracts when the market declines. A short futures position is therefore required.
An investor shorts 100 shares when the share price is $50 and closes out the position six months later when the share price is $43. The shares pay a dividend of $3 per share during the six months. How much does the investor gain? A. $1,000 B. $400 C. $700 D. $300
Answer: B The investor gains $7 per share because he or she sells at $50 and buys at $43. However, the investor has to pay the $3 per share dividend. The net profit is therefore 7−3 or $4 per share. 100 shares are involved. The total gain is therefore $400.
The price of a stock, which pays no dividends, is $30 and the strike price of a one-year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A.$5.00 B.$5.98 C.$4.98 D.$3.98
Answer: B The lower bound in S0 − Ke-rT. In this case it is 30 - 25e-0.04×1 = $5.98.
The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price? A. $19.67 B. $35.84 C. $45.15 D. $40.50
Answer: B The present value of the income is 2e-0.1×1+2e-0.1×2= $3.447. The three year forward price is obtained by subtracting the present value of the income from the current stock price and then grossing up the result for three years at the risk-free rate. It is (30−3.447)e0.1×3 = $35.84.
A company can invest funds for five years at LIBOR minus 30 basis points. The five-year swap rate is 3%. What fixed rate of interest can the company earn by using the swap? A.2.4% B.2.7% C.3.0% D.3.3%
Answer: B When the company invests at LIBOR minus 0.3% and then enters into a swap where it pays LIBOR and receives 3% it earns 2.7% per annum. Note that it is the bid rate that will apply to the swap.
15.Clearing houses are A.Never used in futures markets and sometimes used in OTC markets B.Used in OTC markets, but not in futures markets C.Always used in futures markets and sometimes used in OTC markets D.Always used in both futures markets and OTC markets
Answer: C Clearing houses are always used by exchanges trading futures. Increasingly, OTC products are cleared through CCPs, which are a type of clearing house.
The six-month zero rate is 8% per annum with semiannual compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate? A.8.02% B.8.52% C.9.02% D.9.52%
Answer: C If the rate is R we must have97= 3/1.04+103e^-R*1ore^-R= (97-3/1.04)/103 =0.9137so that R = ln(1/0.9137) = 0.0902 or 9.02%.
An investor has exchange-traded put options to sell 100 shares for $20. There is a 2 for 1 stock split. Which of the following is the position of the investor after the stock split? A.Put options to sell 100 shares for $20 B.Put options to sell 100 shares for $10 C.Put options to sell 200 shares for $10 D.Put options to sell 200 shares for $20
Answer: C When there is a stock split the number of shares increases and the strike price decreases. In this case, because it is a 2 for 1 stock split, the number of shares doubles and the strike price halves.
Which of the following is a use of a currency swap? A.To exchange an investment in one currency for an investment in another currency B.To exchange borrowing in one currency for borrowings in another currency C.To take advantage situations where the tax rates in two countries are different D.All of the above
Answer: D
The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50? A.$9.91 B.$7.00 C.$6.00 D.$2.09
Answer: D Put-call parity is c+Ke-rT=p+S0. In this case K=50, S0=51, r=0.06, T=1, and c=6. It follows thatp=6+50e-0.06×1−51 = 2.09
Which of the following describes an interest rate swap? A.The exchange of a fixed rate bond for a floating rate bond B.A portfolio of forward rate agreements C.An agreement to exchange interest at a fixed rate for interest at a floating rate D.All of the above
Answer: D The answer is D because all of A, B, and C are true for an interest rate swap.
A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)? A.$100 B.$200 C.$300 D.$400
Answer: D The butterfly spread involves buying 100 options with strike prices $60 and $70 and selling 200 options with strike price $65. The maximum gain is when the stock price equals the middle strike price, $65. The payoffs from the options are then, $500, 0, and 0, respectively. The total payoff is $500. The cost of setting up the butterfly spread is 11×100+18×100−14×200 = $100. The gain is 500−100 or $400.
A short forward contract that was negotiated some time ago will expire in three months and has a delivery price of $40. The current forward price for three-month forward contract is $42. The three month risk-free interest rate (with continuous compounding) is 8%. What is the value of the short forward contract? A. +$2.00 B. −$2.00 C. +$1.96 D. −$1.96
Answer: D The contract gives one the obligation to sell for $40 when a forward price negotiated today would give one the obligation to sell for $42. The value of the contract is the present value of −$2 or −2e-0.08×0.25 = −$1.96.
The two-year zero rate is 6% and the three-year zero rate is 6.5%. What is the forward rate for the third year? All rates are continuously compounded. A.6.75% B.7.0% C.7.25% D.7.5%
Answer: D The forward rate for the third year is (3×0.065−2×0.06)/(3−2) = 0.075 or 7.5%
The price of a stock is $64. A trader buys 1 put option contract on the stock with a strike price of $60 when the option price is $10. When does the trader make a profit? A.When the stock price is below $60 B.When the stock price is below $64 C.When the stock price is below $54 D.When the stock price is below $50
Answer: D The payoff must be more than the $10 paid for the option. The stock price must therefore be below $50.
On March 1 the price of a commodity is $1,000 and the December futures price is $1,015. On November 1 the price is $980 and the December futures price is $981. A producer of the commodity entered into a December futures contracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity? A. $1,016 B. $1,001 C.$981 D.$1,014
Answer: D The producer of the commodity takes a short futures position. The gain on the futures is 1015−981 or $34. The effective price realized is therefore 980+34 or $1014. This can also be calculated as the March 1 futures price (=1015) plus the November 1 basis (=−1).
The yield curve is flat at 6% per annum. What is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years? All rates are compounded semiannually. A.$9.12 B.$9.02 C.$8.88 D.$8.63
Answer: D The value of the FRA is the value of receiving an extra 0.5×(0.08−0.06)×1000 = $10 in 2.5 years. This is 10/(1.035) = $8.63
A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9? A.Long 192 contracts B.Short 192 contracts C.Long 48 contracts D.Short 48 contracts
Answer: D To reduce the beta by 0.3 we need to short 0.3×36,000,000/(900×250) or 48 contracts.
