Q&A Hero

Q: A stock index spot price is $1,350. The zero coupon interest rate is 2.6%. What is the potential arbitrage profit if the 6-month futures contract on the index is priced at $1,342? A) $8 B) $25 C) $32 D) $39

Q: A stock index spot price is $1,287. The zero coupon interest rate is 3.8%. What is the potential arbitrage profit if the 6-month futures contract on the index is priced at $1,350? A) $19.50 B) $31.50 C) $63.00 D) $39.00

Q: The spot price of a futures contract is different than the price for which an investor can buy the underlying commodity for immediate delivery. This represents an opportunity for ________. A) arbitrage B) hedging C) speculation D) loss leading

Q: The overwhelming majority of trading in futures contracts is done via ________. A) trading pits B) phone C) open outcry D) electronic networks

Q: The only money exchanged by both the long and short at the creation of a futures contract is called the ________. A) spot price B) futures price C) margin D) collateral

Q: The Student Loan Marketing Association (SLMA) has short-term student loans funded by long-term debt. To hedge out this interest rate risk, SLMA could: I. Engage in a swap to pay fixed and receive variable interest payments II. Engage in a swap to pay variable and receive fixed interest payments II. Buy T-bond futures IV. Sell T-bond futures A) I and II only B) I and IV only C) II and III only D) II and IV only

Q: A market timer now believes that the economy will soften over the rest of the year as the housing market slump continues, and she also believes that foreign investors will stop buying U.S. fixed-income securities in the large quantities that they have in the past. One way the timer could take advantage of this forecast is to ________. A) buy T-bond futures and sell stock-index futures B) sell T-bond futures and buy stock-index futures C) buy stock-index futures and buy T-bond futures D) sell stock-index futures and sell T-bond futures

Q: A bank has made long-term fixed-rate mortgages and has financed them with short-term deposits. To hedge out its interest rate risk, the bank could ________. A) sell T-bond futures B) buy T-bond futures C) buy stock-index futures D) sell stock-index futures

Q: A farmer sells futures contracts at a price of $2.75 per bushel. The spot price of corn is $2.55 at contract expiration. The farmer harvested 12,500 bushels of corn and sold futures contracts on 10,000 bushels of corn. Ignoring the transaction costs, how much did the farmer improve his cash flow by hedging sales with the futures contracts? A) $0 B) $2,000 C) $31,875 D) $33,875

Q: A farmer sells futures contracts at a price of $2.75 per bushel. The spot price of corn is $2.55 at contract expiration. The farmer harvested 12,500 bushels of corn and sold futures contracts on 10,000 bushels of corn. What are the farmer's proceeds from the sale of corn? A) $27,500 B) $31,875 C) $33,875 D) $35,950

Q: A corporation will be issuing bonds in 6 months, and the treasurer is concerned about unfavorable interest rate moves in the interim. The best way for her to hedge the risk is to ________. A) buy T-bond futures B) sell T-bond futures C) buy stock-index futures D) sell stock-index futures

Q: The price of a corn futures contract is $2.65 per bushel when the contract is issued, and the commodity spot price is $2.55. When the contract expires, the two prices are identical. What principle is represented by this price behavior? A) convergence B) margin C) basis D) volatility

Q: In order for a binomial option price to approach the Black Scholes price, ________. A) the number of subintervals must increase substantially B) the volatility must be low C) the probability of each subinterval needs to be similar to the stock's standard deviation D) the interest rate needs to increase

Q: Given a stock price of $18, an exercise price of $20, and an interest rate of 7%, what are the intrinsic values which will occur for a one-period binomial option model if the stock price goes up to $23 or down to $16? A) $3 and $0 B) $3 and −$4 C) $4 and $3 D) $4 and $2

Q: A stock with a stock and exercise price of $20 can either increase to $26 or decrease to $18 over the course of one year. In a one-period binomial option model, given an interest rate of 5% and equal probabilities, what is the likely option price? (Use annual compounding.) A) $2.36 B) $2.50 C) $2.88 D) $3.00

Q: Which combination of stock, exercise, and option prices are most likely associated with an American call option? A) stock = $60, exercise = $65, option = $5 B) stock = $65, exercise = $60, option = $5 C) stock = $65, exercise = $60, option = $7 D) stock = $60, exercise = $65, option = $7

Q: Hedge ratios for long puts are always ________. A) between −1 and 0 B) between 0 and 1 C) 1 D) greater than 1

Q: A put option has a strike price of $35 and a stock price of $38. If the put option is trading at $1.25, what is the time value embedded in the option? A) $0 B) $0.75 C) $1.25 D) $3

Q: The option smirk in the Black-Scholes option model indicates that ________. A) implied volatility changes unpredictably as the exercise price rises B) stock prices may fall by a larger amount than the model assumes C) stock prices evolve continuously in today's actively traded markets D) stocks with lower exercise prices are more likely to pay dividends

Q: A stock priced at $65 has a standard deviation of 30%. Three-month calls and puts with an exercise price of $60 are available. The calls have a premium of $7.27, and the puts cost $1.10. The risk-free rate is 5%. Since the theoretical value of the put is $1.525, you believe the puts are undervalued. If you want to construct a riskless arbitrage to exploit the mispriced puts, you should ________. A) buy the call and sell the put B) write the call and buy the put C) write the call and buy the put and buy the stock and borrow the present value of the exercise price D) buy the call and buy the put and short the stock and lend the present value of the exercise price

Q: Suppose you purchase a call and write a put on the same stock with the same exercise price and expiration. If prices are at equilibrium, the value of this portfolio is ________. A) S0 − Xe−rt B) S0 − X C) S0 + Xe−rt D) S0 + X

Q: What aspect of the time value of money does the factor of e represent in the Black-Scholes option value formula? A) annual compounding B) compounding at the expiration time frame C) continuous compounding D) daily compounding

Q: A call option has an exercise price of $35 and a stock price of $36.50. If the call option is trading at $2.25, what is the time value embedded in the option? A) $0 B) $0.75 C) $1.50 D) $2.25

Q: A call option has an exercise price of $30 and a stock price of $34. If the call option is trading for $5.25, what is the intrinsic value of the option? A) $0 B) $1.25 C) $4 D) $5.25

Q: The intrinsic value of an out-of-the-money call option ________. A) is negative B) is positive C) is zero D) cannot be determined

Q: Calculate the price of a European call option using the Black Scholes model and the following data: stock price = $56.80, exercise price = $55, time to expiration = 15 days, risk-free rate = 2.5%, standard deviation = 22%, dividend yield = 8%. A) $1.49 B) $1.79 C) $2.19 D) $2.29

Q: The fact that American put values may not equal the price implied by put-call parity is attributable to the possibility of what event? A) changes in the dividend B) early exercise C) interest rate declines D) interest rate rises

Q: The time value of a call option is likely to decline most rapidly ________ days before expiration? A) 10 B) 30 C) 60 D) 90

Q: What combination of variables is likely to lead to the lowest time value? A) short time to expiration and low volatility B) long time to expiration and high volatility C) short time to expiration and high volatility D) long time to expiration and low volatility

Q: You calculate the Black-Scholes value of a call option as $3.50 for a stock that does not pay dividends, but the actual call price is $3.75. The most likely explanation for the discrepancy is that either the option is ________ or the volatility you input into the model is too ________. A) overvalued and should be written; low B) undervalued and should be written; low C) overvalued and should be purchased; high D) undervalued and should be purchased; high

Q: You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co. What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = $50? A) share of stock and $25 in bills B) 1 share of stock and $50 in bills C) share of stock and $26.19 in bills D) 1 share of stock and $25 in bills

Q: You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co. What would have been the cost of a protective put portfolio? A) $48.81 B) $51.19 C) $52.38 D) $53.38

Q: You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co. Suppose the desired put options with X = 50 were traded. How much would it cost to purchase? A) $1.19 B) $2.38 C) $5 D) $3.33

Q: A call option on Juniper Corp. stock with an exercise price of $75 and an expiration date 1 year from now is worth $3 today. A put option on Juniper Corp. stock with an exercise price of $75 and an expiration date 1 year from now is worth $2.50 today. The risk-free rate of return is 8%, and Juniper Corp. pays no dividends. The stock should be worth ________ today. A) $69.73 B) $71.69 C) $73.12 D) $77.25

Q: The stock price of Harper Corp. is $33 today. The risk-free rate of return is 6%, and Harper Corp. pays no dividends. A put option on Harper Corp. stock with an exercise price of $30 and an expiration date 73 days from now is worth $0.95 today. A call option on Harper Corp. stock with an exercise price of $30 and the same expiration date should be worth ________ today. A) $2.25 B) $3.14 C) $3.99 D) $4.31

Q: The stock price of Atlantis Corp. is $43 today. The risk-free rate of return is 10%, and Atlantis Corp. pays no dividends. A call option on Atlantis Corp. stock with an exercise price of $40 and an expiration date 6 months from now is worth $5 today. A put option on Atlantis Corp. stock with an exercise price of $40 and an expiration date 6 months from now should be worth ________ today. A) $0.05 B) $0.14 C) $2 D) $3.95

Q: You are considering purchasing a put option on a stock with a current price of $33. The exercise price is $35, and the price of the corresponding call option is $2.25. According to the put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until expiration, the value of the put should be ________. A) $2.25 B) $3.91 C) $4.05 D) $5.52

Q: According to the put-call parity theorem, the payoffs associated with ownership of a call option can be replicated by ________. A) shorting the underlying stock, borrowing the present value of the exercise price, and writing a put on the same underlying stock and with the same exercise price B) buying the underlying stock, borrowing the present value of the exercise price, and buying a put on the same underlying stock and with the same exercise price C) buying the underlying stock, borrowing the present value of the exercise price, and writing a put on the same underlying stock and with the same exercise price D) shorting the underlying stock, lending the present value of the exercise price, and buying a put on the same underlying stock and with the same exercise price

Q: You are considering purchasing a call option with a strike price of $35. The price of the underlying stock is currently $27. Without any further information, you would expect the hedge ratio for this option to be ________. A) negative and near 0 B) negative and near −1 C) positive and near 0 D) positive and near 1

Q: You find the option prices for three June call options on the same stock. The 95 call has an implied volatility of 25%, the 100 call has an implied volatility of 25%, and the 105 call has an implied volatility of 30%. If you believe this represents a mispricing situation. you may want to ________. A) buy the 105 call and write the 100 call B) buy the 105 call and write the 95 call C) buy either the 95 or the 100 call and write the 105 call D) write the 105 call and write either the 95 or the 100 call

Q: Which one of the following will increase the value of a put option? A) a decrease in the exercise price B) a decrease in time to expiration of the put C) an increase in the volatility of the underlying stock D) an increase in stock price

Q: If you have an extremely "bullish" outlook on the stock market, you could attempt to maximize your rate of return by ________. A) purchasing out-of-the-money call options B) purchasing at-the-money bull spreads C) purchasing in-the-money call options D) purchasing at-the-money call options

Q: If a stock price increases, the price of a put option on the stock will ________ and the price of a call option on the stock will ________. A) decrease; decrease B) decrease; increase C) increase; decrease D) increase; increase

Q: A hedge ratio of 0.70 implies that a hedged portfolio should consist of ________. A) long 0.70 calls for each short stock B) long 0.70 shares for each long call C) long 0.70 shares for each short call D) short 0.70 calls for each long stock

Q: A one-dollar increase in a stock's price would result in ________ in the call option's value of ________ than one dollar. A) a decrease; less B) a decrease; more C) an increase; less D) an increase; more

Q: A higher-dividend payout policy will have a ________ impact on the value of a put and a ________ impact on the value of a call. A) negative; negative B) negative; positive C) positive; negative D) positive; positive

Q: Hedge ratios for long call positions are ________, and hedge ratios for long put positions are ________. A) negative; negative B) negative; positive C) positive; negative D) positive; positive

Q: The delta of a call option on a stock is always ________. A) negative and less than −1 B) between −1 and 1 C) positive D) positive but less than 1

Q: The price of a stock put option is ________ correlated with the stock price and ________ correlated with the exercise price. A) negatively; negatively B) negatively; positively C) positively; negatively D) positively; positively

Q: The delta of a put option on a stock is always ________. A) between 0 and −1 B) between −1 and 1 C) positive but less than 1 D) greater than 1

Q: The practice of using options or dynamic hedging strategies to provide protection against investment losses while maintaining upside potential is called ________. A) trading on gamma B) index optioning C) portfolio insurance D) index arbitrage

Q: Of the variables in the Black-Scholes OPM, the ________ is not directly observable. A) price of the underlying asset B) risk-free rate of interest C) time to expiration D) variance of the underlying asset return

Q: Research conducted by Rubinstein (1994) suggests that ________ command a disproportionately high time value. A) out-of-the-money call options B) out-of-the-money put options C) in-the-money call options D) in-the-money put options

Q: Research suggests that the performance of the Black-Scholes option-pricing model has ________. A) improved in recent years B) remained about the same over time C) been deficient for stocks with high dividend payouts D) varied widely over the years since 1973

Q: In the Black-Scholes model, as the stock's price increases, the values of N(d1) and N(d2) will ________ for a call and ________ for a put option. A) increase; decrease B) increase; increase C) decrease; increase D) decrease; decrease

Q: In the Black-Scholes model, if an option is not likely to be exercised, both N(d1) and N(d2) will be close to ________. If the option is definitely likely to be exercised, N(d1) and N(d2) will be close to ________. A) 1; 0 B) 0; 1 C) −1; 1 D) 1; −1

Q: In a binomial option model with three subintervals, the probability that the stock price moves up every possible time is ________. A) 25% B) 15.5% C) 12.5% D) 8%

Q: The Black-Scholes hedge ratio for a long put option is equal to ________. A) N(d1) B) N(d2) C) N(d1) − 1 D) N(d2) − 1

Q: The Black-Scholes hedge ratio for a long call option is equal to ________. A) N(d1) B) N(d2) C) N(d1) − 1 D) N(d2) − 1

Q: When the returns of an option and stock are perfectly correlated as in a two-state binomial option model, the hedge ratio must be equal to the ratio of ________. A) the range of the option outcomes to the range of the stock outcomes B) the range of the stock outcomes to the range of the option outcomes C) the standard deviation of the option returns to the standard deviation of the stock returns D) the standard deviation of the stock returns to the standard deviation of the option returns

Q: According to the Black-Scholes option-pricing model, two options on the same stock but with different exercise prices should always have the same ________. A) price B) expected return C) implied volatility D) maximum loss

Q: A high dividend payout will ________ the value of a call option and ________ the value of a put option. A) increase; decrease B) increase; increase C) decrease; increase D) decrease; decrease

Q: Strike prices of options are adjusted for ________ but not for ________. A) dividends; stock splits B) stock splits; cash dividends C) exercise of warrants; stock splits D) stock price movements; stock dividends

Q: A longer time to maturity will unambiguously increase the value of a call option because: I. The longer maturity time reduces the effect of a dividend on call price. II. With a longer time to maturity the present value of the exercise price falls. III. With a longer time to maturity the range of possible stock prices at expiration increases. A) I only B) I and II only C) II and III only D) I, II, and III

Q: Which of the following is a true statement? A) The actual value of a call option is greater than its intrinsic value prior to expiration. B) The intrinsic value of a call option is always greater than its time value prior to expiration. C) The intrinsic value of a call option is always positive prior to expiration. D) The intrinsic value of a call option is greater than its actual value prior to expiration.

Q: Hedge ratios for long calls are always ________. A) between −1 and 0 B) between 0 and 1 C) 1 D) greater than 1

Q: If you know that a call option will be profitably exercised, then the Black-Scholes model price will simplify to ________. A) S0 − X B) X − S0 C) S0 − PV(X) D) PV(X) − S0

Q: The delta of an option is ________. A) the change in the dollar value of an option for a dollar change in the price of the underlying asset B) the change in the dollar value of the underlying asset for a dollar change in the call price C) the percentage change in the value of an option for a 1% change in the value of the underlying asset D) the percentage change in the value of the underlying asset for a 1% change in the value of the call

Q: Perfect dynamic hedging requires ________. A) a smaller capital outlay than static hedging B) less commission expense than static hedging C) daily rebalancing D) continuous rebalancing

Q: The value of a put option increases with all of the following except ________. A) stock price B) time to maturity C) volatility D) dividend yield

Q: The value of a call option increases with all of the following except ________. A) stock price B) time to maturity C) volatility D) dividend yield

Q: The divergence between an option's intrinsic value and its market value is usually greatest when ________. A) the option is deep in the money B) the option is approximately at the money C) the option is far out of the money D) time to expiration is very low

Q: The intrinsic value of a call option is equal to ________. A) the stock price minus the exercise price B) the exercise price minus the stock price C) the stock price minus the exercise price plus any expected dividends D) the exercise price minus the stock price plus any expected dividends

Q: Before expiration, the time value of an out-of-the-money stock option is ________. A) equal to the stock price minus the exercise price B) equal to zero C) negative D) positive

Q: The percentage change in the call option price divided by the percentage change in the stock price is the ________ of the option. A) delta B) elasticity C) gamma D) theta

Q: Investor A bought a call option, and investor B bought a put option. All else equal, if the underlying stock price volatility increases, the value of investor A's position will ________ and the value of investor B's position will ________. A) increase; increase B) increase; decrease C) decrease; increase D) decrease; decrease

Q: Investor A bought a call option, and investor B bought a put option. All else equal, if the interest rate increases, the value of investor A's position will ________ and the value of investor B's position will ________. A) increase; increase B) increase; decrease C) decrease; increase D) decrease; decrease

Q: Investor A bought a call option that expires in 6 months. Investor B wrote a put option with a 9-month maturity. All else equal, as the time to expiration approaches, the value of investor A's position will ________ and the value of investor B's position will ________. A) increase; increase B) increase; decrease C) decrease; increase D) decrease; decrease

Q: A stock with a current market price of $50 and a strike price of $45 has an associated put option priced at $3.50. This put has an intrinsic value of ________ and a time value of ________. A) $3.50; $0 B) $5; $3.50 C) $3.50; $5 D) $0; $3.50

Q: A stock with a current market price of $50 and a strike price of $45 has an associated call option priced at $6.50. This call has an intrinsic value of ________ and a time value of ________. A) $5; $1.50 B) $1.50; $5 C) $0; $6.50 D) $6.50; $0