Derivatives Exam 1
Which of the following statements is true of the value of European (E) options, American (A) options, and Bermudan (B) options?
(a) (b) (c) (d) Answer a.
A US-based exporter anticipated receiving €100 million in six months, and took a short forward position, locking-in an exchange rate of $1.38/€. If after six months, at maturity, the exporter calculates that she has made a profit of $2 million from the hedging strategy, the spot exchange rate at maturity must be
(a) $ 0.50/€. (b) $ 1.36/€ (c) $1.40/€ (d) $ 2.00/€ Answer b.
An investor enters into a long position in 10 gold futures contracts at a futures price of $1000/oz and closes out the position at a price of $1020/oz. If one gold futures contract is for 50 ounces, what are the investor's gains or losses?
(a) $100 (b) $1,000 (c) $5,000 (d) $10,000 Answer d
The price of oil is $100 per barrel. Oil prices are expected to grow at 4% a year. The one-year risk-free rate of interest is 2% in simple terms. It costs $1 to store a barrel of oil for one year. If oil has no costs or benefits of carry, what is the theoretical one-year forward price of oil?
(a) $100.00 (b) $102.00 (c) $103.02 (d) $104.00 Answer c.
A stock has a current price of $20. The risk-free interest rate for a half-year maturity is 6% and the dividend rate is 3%. Assume continuous compounding. What is the six-month forward price of the stock?
(a) $20.30 (b) $20.61 (c) $20.92 (d) $21.24 Answer a.
Plutonium is trading at a one-year futures price of $5,000 per gram. A futures contract comprises 100 grams. The initial margin is $100,000 and the maintenance margin is $80,000. You are short one futures contract. There is a margin call when the price per gram of plutonium changes to
(a) $4,750 (b) $4,900 (c) $5,100 (d) $5,250 Answer d.
A forward contract is struck at a forward price of $40. At maturity the spot price of the asset is $45. The short forward position earns the following payoff:
(a) $5 (b) -$5 (c) $45 (d) -$45 Answer b.
The spot price of an asset is $50. The expected return on the asset is 10% a year (in simple terms) and the standard deviation of these returns is 20%. The risk-free rate of interest is 5% a year in simple terms. Assuming no costs or benefits of carry, what is the one-year forward price of the asset?
(a) $52.50 (b) $55.00 (c) $57.50 (d) $60.00 Answer a.
How many options does a callable, convertible bond contain?
(a) 0 (b) 1 (c) 2 (d) 3 Answer c. There are two options: (a) the issuer holds a call on the bond, and (b) the buyer has the right to convert the bond into equity. One may extend the idea and say that there is an additional option—the option to default held by the issuer of the convertible. If such a response is provided, then the correct answer would be 3 options, i.e., answer (d).
Eurodollar deposits follow the money-market day-count convention. Suppose a deposit is made for 92 days at a Libor rate of 4% on a notional amount of $100. The interest amount is
(a) 1.0082 (b) 1.0099 (c) 1.0101 (d) 1.0222 Answer d. The eurodollar money-market convention is Actual/360, so the interest is 100×4×92/360 = 1.0222.
The US dollar-euro spot exchange rate is $1.50/€. If the one-year simple interest rate on dollars is 1% and on euro is 2%, what is the one-year forward rate of dollars per euro?
(a) 1.4748 (b) 1.4853 (c) 1.5000 (d) 1.5149 Answer b.
How many years does it take to double your money if the continuously-compounded interest rate is 6%?
(a) 11.55 (b) 12.66 (c) 13.77 (d) 16.66 Answer a. The answer is the solution to the following equation: ln(2) / 0.06 = 11.55
State which of these statements is false
(a) A futures contract is traded on an exchange. (b) A futures contract involves counterparty credit risk. (c) A futures contract is fully customizable. (d) A futures contract may be reversed unilaterally. Answer c.
An investor enters into a forward contract to buy 4,000 barrels of oil in three months at $80 a barrel. At the maturity of the contract, the spot price of oil is $65 a barrel. The investor's payoff (gain/loss) from the forward contract is
(a) A gain of $60,000 (b) A loss of $60,000 (c) A gain of $260,000 (d) A loss of $260,000 Answer b.
A forward contract may be used for
(a) Hedging price exposure at a future date. (b) Speculating on price. (c) Locking-in a price for a future transaction. (d) All of the above. Answer d.
The relationship of forwards and futures is best represented by the following statement(s)
(a) If futures price movements and interest rate movements are positively correlated, then futures prices will be higher than forward prices. (b) If futures price movements and interest rate movements are negatively correlated, then futures prices will be lower than forward prices. (c) If futures price movements and interest rate movements are uncorrelated, then futures and forward prices will coincide. (d) All of the above. Answer d
If the market is in backwardation
(a) Spot prices are less than forward prices. (b) Futures prices are less than forward prices. (c) Spot prices are less than futures prices. (d) None of the above. Answer d.
Which of the following features distinguish futures markets from forwards markets?
(a) Standardization of contracts. (b) The use of margin accounts to manage risk. (c) Ease in reversing positions. (d) All of the above. Answer d.
"Basis" risk may arise in a hedging situation if
(a) The expiry date of the futures contract and the date on which the hedge is unwound do not coincide. (b) The futures contract used for hedging relates to a commodity that is somewhat different than that being hedged. (c) A disconnect between spot and futures markets causes the failure of the convergence of futures to spot at expiry of the futures contract. (d) All of the above. Answer d. While (c) is not mentioned explicitly in the text, it evidently causes uncertainty in the cash flows of the hedged position.
Which of the following securities is not a derivative?
A bond issued by a BBB-rated corporate firm
Which of the following statements is true of forward contracts?
A forward contract is customizable and traded over-the-counter.
A calendar spread futures position comprises
A long position in a futures contract of one maturity and a short position in another futures contract of a different maturity.
A replicating portfolio for a derivative security is
A portfolio that has the same payoffs as the derivative.
Which of the following types of orders does not involve specifying a price limit or trigger price as part of the order?
A spread order
Two stocks, A and B, have expected returns for one year of and respectively. The stocks have identical prices of $100 each, do not pay dividends, and the one-year risk-free rate of return is 2% in simple terms. The one-year forward prices of the two stocks are:
A; 102; B: 102
The presence of the delivery option in a futures contract means that
All else remaining the same, a futures contract will trade at a lower price than a forward
Which option gives the right to sell an asset at any time prior to or at maturity?
American put
3. A derivative security derives its value from an "underlying" security that is
Any other security
Using a linear regression of changes in spot asset prices on changes in futures asset prices, the minimum-variance hedge ratio may be obtained
As the slope coefficient in the regression.
Two assets and have the same spot price today. Asset is expected to grow at 10% over the year and asset is expected to grow at 12%. Which of the following is true if there are no holding costs or benefits for either asset?
Asset 's one-year forward price will be equal to that of asset .
Two assets and have the same spot price today. The price of asset is expected to grow at 10% over the next year and that of asset is expected to grow at 10% also. Asset has a standard deviation of returns of 10% over the year and asset has standard deviation of 15%. Which of the following is true if there are no holding costs or benefits?
Asset 's one-year forward price will be equal to that of asset .
If the futures contract used to hedge a spot position is marked-to-market daily, then the minimum-variance hedge ratio formula computed ignoring daily resettlement is, in absolute terms,
Biased upwards.
You borrow money at Libor with a floating-rate note for one year with two semi-annual payments. What position do you need to add to this note to fix the cost of borrowing for the entire year?
Buy a 6x12 FRA.
Ignoring convenience yields, the theoretical futures price for a commodity with a positive cost of carry should typically exhibit
Contango.
For commodity forwards and futures, which of the following statements is valid?
Convenience yields may lead to the market being in backwardation.
For a futures contract on an asset to be successful compared to the alternative of forward contracts, which of the following features would help?
Counterparty credit risk is high
1. Which class of derivatives have been blamed most widely for causing the financial crisis of 2008?
Credit Derivatives
Eurodollar deposits are
Dollar denominated deposits made in banks in Europe
Bonds A and B both have a duration of exactly one year. An equally-weighted portfolio of these bonds will have a duration of
Equal to one year because the average duration is still one year.
March what futures are trading at $4.20 a bushel and May wheat futures are trading at $4.35 a bushel. You expect the spread between May and March futures prices to widen. To speculate on this view, you would
Go long May futures and short March futures.
September corn futures are currently trading at $3.80 a bushel while the spot price of corn is $3.65 a bushel, so the "basis" (the futures price minus the spot price) is $0.15 a bushel. If you expect the basis to weaken (i.e., to fall) significantly in the next few days, you can speculate on your view by
Going long spot corn and short September futures
Consider hedging an exposure with (i) a futures contract, or (ii) an option with a strike price close to the futures price. The hedge with the futures contract
Has no upfront cost
The cheapest-to-deliver option
Hurts the holder of the long position in the futures contract.
You are hedging a spot position with futures. If the spot asset is more volatile than the corresponding futures, the minimum-variance hedge ratio is
Indeterminate, given the information available
Which of the following statements about index futures is false?
Index futures are rarely shorted because it is very difficult to borrow all the stocks in the index in the correct proportions in order to effect the short.
The most widely traded futures are of the following type
Interest Rate
Backwardation becomes more likely when, ceteris paribus,
Interest rates decline
Consider futures on a stock market index. Which of the following scenarios is most likely to increase the futures-spot basis?
Interest rates increase and dividend yields decline.
The tailed hedge ratio becomes lower in comparison to the untailed one when
Interest rates rise and hedge maturity increases.
2. Which class of derivatives accounts for the largest dollar share in the world market in terms of notional amount outstanding?
Interest-Rate Derivatives
The payoff of the FRA has the following property
It is concave in the Libor rate.
You go short oil 10 futures contracts on NYMEX when the futures price of oil is $79 a barrel and close out your position three days later at a futures price of $83 a barrel. One futures contract is for 1,000 barrels. Ignoring interest on the margin account, the futures trading has resulted in a
Loss of $40,000
If the minimum-variance hedge ratio is +1, then which of the following is true?
Neither (a) nor (b) is necessarily true.
The tailed minimum-variance hedge ratio becomes lower in comparison to the untailed one when
Nominal interest rates rise and hedge maturity increases.
A firm enters into a one-year forward contract to buy refined oil. To hedge itself, the firm simultaneously sells one-year futures contracts on crude oil. In which of the following scenarios might the firm come under cash flows pressure related to these contracts?
Oil prices skyrocket a day after the firm enters the contracts
The law of one price states that
Portfolios with identical cashflows will have the same price.
An embedded option is one where the security contains features that are option-like. Which of the following is not an example of a security with an embedded option?
Preferred stock.
If the implied repo rate is lower than the borrowing rate and the lending rate for the same maturity, what strategy would you adopt to undertake an arbitrage?
Sell the asset spot, buy it forward, lend at rate .
Using the spot and forward markets to borrow at the implied repo rate entails
Selling the spot asset and buying it forward.
ABC Inc. has to borrow money to undertake a seasonal business expansion in six months time. They will need additional working capital funding for six months and wish to hedge themselves against a rise in interest rates in six month's time. They should
Take a long position in a 6×12 FRA.
Forward pricing by replication depends on the following assumption:
That the underlying is a traded asset which is storable.
Futures contracts are more likely to be cash-settled when
The asset underlying the contract is too costly to deliver physically
The forward price of an asset that has no holding costs or benefits is equal to
The compounded price of the spot asset, where the compounding takes place at the risk-free rate
When the futures-spot basis weakens
The difference between futures and spot prices drops.
Ceteris paribus, as interest rates rise, which of these statements is most likely to be true?
The duration of bonds falls.
If there is a convenience yield, then the following is true of the forward price:
The forward price is lower than it would be with no convenience yield.
Consider that the one-year Euro interest rate is greater than the US one-year interest rate. How does the one-year forward exchange rate (USD per EUR) compare to the spot exchange rate (USD per EUR)?
The forward rate is smaller than the spot rate
Counterparty risk in a futures contract is lower than in a forward contract because
The futures exchange bears the counterparty risk.
When a counterparty to a futures contract fails to perform under the contract,
The futures exchange bears the loss,
The following is not a point of difference between futures and forwards
The futures payoff depends on the spot price of the asset at contract maturity
The volatility of a stock index falls sharply, the index drops in value, and its expected return increases. Assuming all else (dividend yield, interest rates, etc.) are constant, which of the following is true?
The futures price decreases because of the drop in the level of the index.
The convexity bias between FRAs and eurodollar futures implies that
The futures results in greater cash inflows or lower cash outflows than the FRA.
The tailed hedge ratio (which takes into account daily resettlement of the futures contract) is smaller than the untailed one in absolute value. Which of these statements is true in relation to this mathematical fact?
The interest earned or lost on the daily mark-to-market gains and losses increases the volatility of the changes in value of the hedging futures position, thereby reducing the hedge ratio.
Rolling over short-dated futures contracts is the same as taking one long-dated futures contract if
The interest rates are constant
A "stack-and-roll" strategy makes profits from the "roll" part when
The market is in backwardation
A price tick is
The minimum amount by which the price can move
Which of the following statements is true when comparing the payoffs at maturity of a long forward contract with a long position in a call option, assuming the strike price of the option is the same as the delivery price in the forward contract?
The minimum payoff of the option exceeds that of the forward contract.
If changes in spot and futures prices are uncorrelated, then
The minimum variance hedge ratio is zero.
If the minimum-variance hedge ratio is , then which of the following statements is true?
The minimum-variance hedge for a long spot exposure is a short futures exposure of the same size
You are hedging a spot position with futures. If the spot asset is less volatile than the futures, and there is basis risk, which of the following is surely false:
The minimum-variance hedge ratio is greater than 1
A month ago, the price of an IBM stock was $110 and its volatility was 28%. Today, its price is still $110 but its volatility has gone up to 40%. If the one-month interest rate has not changed over the last month and IBM stock does not pay any dividends (i.e., there are no costs or benefits of carry,) then
The one-month forward prices of IBM today equals the one-month forward price a month ago
Which of the following statements about forwards is false?
The payoff at maturity from a long forward contract is always non-negative (either positive or zero).
An option gives the buyer
The right but not the obligation to undertake the trade specified in the contract at maturity
The replication method identifies the price of a USD/GBP forward rate as a function of
The spot USD/GBP exchange rate, the GBP interest rates, and the USD interest rates
At maturity of the forward contract, the following is true of the spot price and delivery price locked-in using the forward contract:
The spot price can be greater, equal to, or less than the delivery price.
In the absence of arbitrage, the futures price at maturity should equal
The spot price of the underlying asset at that point.
Suppose you want to hedge a futures contract A with another futures contract B. You calculate the minimum-variance hedge ratio ignoring daily resettlement (for example, by regressing daily changes in Contract A's prices on daily changes in Contract B's prices). Suppose, however, that both contracts are marked-to-market daily. Which of the following statements is always true?
The tailed hedge ratio is equal to the untailed one
Commodity forward contracts differ from financial forwards in the following manner:
The underlying asset in a commodity forward is an asset that may be used in production and that gets consumed in the process
You are long a forward on the S&P 500 index that you entered into two months ago and has a month left to maturity. If the one-month rate of interest increases, then, ceteris paribus,
The value of your forward contract is unaffected since the delivery price on your contract was already locked in two months ago
If changes in spot and futures prices are perfectly correlated over the horizon of a hedge, then
The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero
If changes in spot and futures prices have a correlation of , then
The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero
The level of margining in a futures contract takes as an important input
The volatility of the asset underlying the futures contract.
When the correlation between two assets is exactly , which of the following statements is true?
There is no basis risk in hedging.
The risk-free interest rate drops but the futures on a stock market index rises. Which of the following statements is the most accurate?
There is not enough information in the question to identify if there is an arbitrage or not
The price of oil is $100 per barrel. Oil prices are expected to grow at 4% a year. The one-year risk-free rate of interest is 2% in simple terms. It costs $1 to store a barrel of oil for one year. If you observe a one-year forward price of oil of $98, what inference could you draw?
There may be a benefit of carry in the oil market.
The spot price trades at a bid/ask quote of 100-101 (you can buy at 101 and sell at 100). The one-year forward trades at 99-101.90 (you can buy forward at 101.90 and sell forward at 99). If the simple interest rate for one year is 2%, which of the following statements is most accurate?
You can execute an arbitrage by selling spot, buying forward, and investing the proceeds of the spot sale at 2%.
The spot price of gold is $1000 per oz. The one-year risk-free rate is 2% in simple terms. There are no costs or benefits of holding gold. If the one-year forward price of gold is $103, what can you say about the market?
You can make arbitrage profits by selling forward and buying spot
The spot price trades at the following bid/ask quote: 100-101 (i.e., you can buy at 101 and sell at 100). The one-year forward trades at 102-103 (you can buy forward at 103 or sell forward at 102). If the simple interest rate for one year is 2%, which of the following statements is most accurate?
You cannot execute an arbitrage at these prices.
An arbitrage is a strategy where
You construct a series of trades that lead to non-negative cash flows at all points in time and at least one positive cash flow
All else being equal, a bond with a higher coupon has a duration that is ________ than that of a bond with a lower coupon
greater than.
