Derivatives

__________________________ is the minimum amount which must remain in a margin account a. Maintenance margin b. Variation margin c. Initial margin d. None of the above

A. Maintenance margin

The spot price of a commodity is $70 per unit. Forward prices for 3, 6, 9, and 12 months are $70.70, $71.41, $72.13, and $72.86. Is this an example of contango or backwardation?

Contango

True or False: As the current price of the underlying moves away from the strike (in either direction) the delta of a call option approaches 1.

False

True or False: Strangles are financial positions designed to hedge against decreasing prices of the underlying asset

False

True or False: The delta of a call option is the same as the delta of a put

False

True or False: You believe that the volatility of a stock is higher than indicated by market prices for options on that stock. You want to speculate on that belief by buying and/or selling at-the-money options. You should buy a strangle.

False

True or False: The payoff of the call bull spread is equal to the payoff of the put bull spread

False. The profits are equal

True or False: Consider two call options with the same strike but different time to maturity: 0.5 years and 2 weeks. The delta of the call option with 2 weeks to maturity goes to zero or one faster than the delta of the option with 6 months to maturity.

True

True or False: If the stock moves according to the binomial model, the delta-hedge portfolio is approximately self-financing

True

True or False: Option position in the aggregate sum to zero

True

True or False: The "vega" of an option goes to zero as the stock price moves away from the strike.

True

True or False: The delta of an in-the-money option increases toward 1 as the time to maturity goes toward zero

True

True or False: The gamma of a put is the same as the gamma of a call

True

True or False: The profit diagram and the payoff diagram for long positions in a forward contract are identical.

True

True or False: The Γ of ITM or OTM options falls toward zero as the time to maturity approaches zero.

True

True or False: There are always trade-offs in designing a position. It is always possible to lower the cost of a position by reducing its payoff.

True

True or False: When compared to longer maturity options, the gamma for shorter maturity options is steeper around the strike and it falls away to zero much faster

True

True or False: When there is just one day to maturity the "theta" of an ATM option is more negative because you have more to lose over the next day than you would if there was a one year to maturity

True

Maryam bakes batches of cupcakes for a cupcake convention. She buys forward 21 pounds of raspberries from a local farmer at the forward price of $5.60/lb. She projects to bake 336 cupcakes and sell each for $3. The total aggregate non-raspberry costs of baking the cupcakes are $200. If the market price of raspberries on the day of the cupcake convention is $5.40, what is Maryam's profit? a. $690.40 b. $490.40 c. $808.00 d. $894.60 e. None of the above

a. $690.40

Which of the following is true: If I'm willing to buy oil forward contracts from you... a. I must think that oil prices are going to go way up. b. I just need the oil, and I want to get rid of the uncertainty. c. None of those

a. I must think that oil prices are going to go way up b. I just need the oil, and I want to get rid of the uncertainty

Suppose the market-marker wishes to hedge a long forward position. a. the market-maker offsets this risk with a reverse cash-and-carry that entails short-selling the index and entering into a long forward position b. the market maker offsets this risk with a cash-and-carry which entails creating a synthetic long forward position c. the market-maker offsets this risk with a cash-and-carry that entails short-selling the index and entering into a long forward position d. the market-maker offsets this risk with a cash-and-carry which entails creating a synthetic short forward position

a. The market-maker offsets this risk with a reverse cash-and-carry that entails short-selling the index and entering into a long forward position

Assume that the spot price of oil is$30 a barrel and that market participants expect the price of oil to be $27 in three months. In order to entice investors into the market, the futures price is set at $25, which is a discount to the expected future spot price. Now suppose that at the time the contract expires, oil is trading at the expected price of $26. What is the profit of the investor, and the breakdown of the profit into premium and price change? a. The profit is $1, and it can be broken into a $2 premium and a -$1 price change b. The profit is $1, and it can be broken into a -$1 premium, and a $2 price change c. The profit is $1, and it can be broken into a $0 premium, and $1 price change d. The profit is $1, and it can be broken into $1 premium and , $0 price change e. The profit is $2, and it can be broken into a $2 premium and $0 price change f. The profit is $2 and it can be broken into $0 premium and a $2 price change

a. The profit is $1 and it can be broken into a $2 premium and a -$1 price change

The payoffs for financial derivatives can be linked to which of the following (more than one answer)... a. a commodity b. the volatility of the stock market c. previously issued securities, such as bonds or stocks d. a specific currency like the British Pound e. None of the above

a. a commodity b. the volatility of the stock market c. previously issues securities, such as bonds or stocks d. a specific currency like the British Pound

Consider the following payoff curve. Which of the following positions has the above payoff? a. a put bull spread b. a call bull spread c. a put bear spread d. a call bear spread e. none of the above

a. a put bull spread

To speculate on high volatility, we... a. buy a straddle b. short a straddle c. buy a butterfly spread d. sell an OTM option e. None of the above

a. buy a sraddle

In Figure 1, with the expiration price of 120, the best return is obtained by a. buying futures b. buying a call option c. selling futures d. buying a put option e. none of the above

a. buying futures

To speculate on low volatility, we... a. a long butterfly spread b. sell a butterfly spread c. buy a straddle d. buy a call option e. none of the above

a. long a butterfly spread

As the underlying stock price moves, the delta of a position changes. In order to remain delta-neutral, it is necessary to revise the position over time. Assume you are long a call option and you want to delta-hedge. According to "gamma", when the stock goes down, delta-hedging prescribes an additional... a. purchase of stock shares b. sale of stock shares

a. purchase of stock shares

You are the producer of goods. You want to hedge your long position. You should... a. take a long collar position b. take a short collar position c. buy a forward d. None of the above

a. take a long collar position

If you're selling me oil forward contract, you might want to do it because a. You've got a lot of oil and you want to lock in a price for selling that oil, say, six months from now b. you have some asymmetric (or private) information that oil prices are going to go down c. None of the above

a. you've got a lot of oil and you want to lock in a price for selling that oil, say, six months from now b. you have some asymmetric (or private) information that oil price are going to go down

We want to speculate on the stock price increasing. Consider buying a 40-strike call with 3 months to expiration for a premium of $2.78. You also sell a 45-strike call for a premium of 0.97. The interest rate is 8%. What is the total profit at expiration if the stock price at expiration is $47.5? a. 3.15 b.3.2 c.5 d.0

a.3.15

The premium on a 1000-strike, 2 month European call option on the market index is $20. After 2 months the market index spot price is 1075. If the risk-free interest rate equals 0.5% (discretely compounded) per month, what is the long-call profit. a. 54.90 b.54.8 c. 75 d. none of the above

b. 54.8 (St-K) - FV0,t[Vc,0] (1075-1000) - 20(1.005^2

For a non-dividend-paying stock index, the current price is 1,100 and the 6-month forward price is 1150. Assume the price of the stock index in 6 months will be 1210. Which of the following is true regarding the forward positions in the stock index? a. Long position gains 50 b. Long position gains 60 c. Long position gains 110 d. Short position gains 60 e. Short positions gains 110

b. Long position gains 60. S(T)-F = 1210 - 1150 = 60

Consider the following payoff curve. Which of the following positions has the above payoff? a. a straddle b. a strangle c. a box spread d. a long collar e. none of the above

b. a strangle

Recall that a buyer of a commodity has an inherent short position in that asset. If they decide to use European calls to hedge they should: a. write the call option b. buy the call option

b. buy the call option

Determine which of the following positions has or have an unlimited loss potential from adverse movement in the underlying asset regardless of the initial premium received (i) Short 1 forward contract (ii) Short 1 call option (iii) Short 1 put option a. None b. i and ii c. i and iii d. ii and iii e. every option is correct

b. i and ii

You are the buyer of goods. You want to hedge your (inherent) short position. You should... a. take a long collar position b. take a short collar position c. buy a put option d. None of the above

b. take a short collar position

A call option gives the seller.... a. the right to sell the underlying security b. the obligation to sell the underlying security c. the right to buy the underlying security d. the obligation to buy the underlying security

b. the obligation to sell the underlying security

An American investor wants to hold 100 euros six months from today. You are given the following: - the spot exchange rate is $1.12 per euro - the continuously compounded risk-free interest rate on the euro is 3% - the continuously compounded risk-free interest rate on the USD is 1.25% If the investor does not want to bear the exchange rate risk; what is the forward price the investor can lock in today? a. 108.69 b. 110.33 c. 111,02 d. 112 e. none of the above

c. 111.02 100 * x^(0.0125-0.03) * 1.12

Consider the general case in which : - C stands for the total aggregate fixed and variable costs of production per unit of good - F stands for the forward price per unit of good What is the price S* per unit of good at which the profit of a producer who hedges using a forward contract equals the profit of the producer who does not hedge at all? a. S* = 0 b. S* = C c. S* = F d. There is no price for which the profit of a producer who hedges using a forward contract equals the profit of the producer who does not hedge at all. e. None of the above.

c. S* = F

Consider the Following Payoff Curve. Which of the following positions has the above payoff? a. a long butterfly spread b. a short butterfly spread c. a ratio spread d. a short straddle e. none of the above

c. a ratio spread

Futures contracts are more successful than interest rate forward contracts because they... a. are less liquid b. have greater default risk c. are more liquid d. have an interest rate tied to the discount rate e. None of the above

c. are more liquid

Financial Derivatives include... a. stocks b. bonds c. futures d. none of the above

c. futures

Suppose you have a diversified portfolio of large cap stocks worth $5 million. However, you don't have any confidence that the market is going to stay where it is (the index is at 1000 points), so you want to hedge some of that risk. In particular you would like to reduce your exposure by 25%. How could you use S&P 500 futures to implement this hedge? a. sell 4 futures b. buy 4 futures c. sell 5 futures d. buy 5 futures

c. sell 5 futures

Suppose that copper costs $3 today and the continuously compounded convenience yield for copper is 5%. The continuously compounded interest rate is 10%. The copper price in 1 year is uncertain and copper can be stored costlessly. What is the No Arbitrage 1-year forward price? a. 3.316 b. 3.486 c. 3.150 d. 3.154

d. 3.154 F(0,T) = S0 * (e^(r-y)*T) 3 * e^(0.1-0.5)*1

Determine which parameter is not present in the Black Scholes formula: a. interest rate b. time-to-maturity c. volatility d. drift

d. drift

Stock XYZ has a current price of 100. The forward price for delivery of this stock in 1 year is 110. Unless otherwise indicated, the stock pays no dividends and the annual discretely compounded risk-free rate is 10%. Determine which of the following statements is FALSE: a. The time-1 profit diagram and time-1 payoff diagram for the long positions in this forward contract are identical b. The time-1 profit for a long position in this forward contract is exactly opposite to the time-1 profit for the corresponding short forward position. c. There is no comparative advantage (in terms of higher profit) to investing in the stock vs. investing in the forward. d. if the 10% interest rate was continuously compounded instead of discretely compounded, then it would be more beneficial (in terms of higher profit) to invest in the stock than from being long in the stock e. If there was a dividend of $3 paid in 6 months from now, then it would be more beneficial to invest in the stock rather than the forward contract

d. if the 10% interest rate was continuously compounded instead of discretely compounded, then it would be more beneficial (in terms of higher profit) to invest in the stock than from being long in the stock

An investor purchases XYZ at $57 and writes 60 out-of-the money calls at $1.70. The options have 60 days until they expire. What will be this investor's return if the price of the underlying stock remains unchanged? a. 0% b. -3.07% c. 2.9% d. 3.07% e. 18.68%

e. 18.68%

Which of the following positions has the same cash flows as a short stock (assume no dividends for simplicity). a. Long forward and long zero-coupon price b. Long forward and short forward c. Long forward and short zero-coupon d. Long zero-coupon bond and short forward e. short forward and short zero-coupon bond f. none of those

e. Short forward and short zero-coupon bond

By hedging a portfolio, a bank manager... a. reduces interest rate risk b. increases re-investment risk c. increases exchange rate risk d. none of the above

reduces interest rate risk