Deck 3: Pricing Forwards and Futures I

Question 1

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 1

1.4853

Question 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?

A) The gold spot market is in disequilibrium.
B) The demand for gold is expected to rise over the coming year.
C) You can make arbitrage profits by selling spot and buying forward.
D) You can make arbitrage profits by selling forward and buying spot.

Answer 2

You can make arbitrage profits by selling forward and buying spot.

Question 3

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?

A) The forward price is wrong and an arbitrage is possible.
B) There may be a benefit of carry in the oil market.
C) The market is in contango.
D) Demand for oil is expected to fall in a year.

Answer 3

There may be a benefit of carry in the oil market.

Question 4

Two assets $A$ and $B$ have the same spot price today. Asset $A$ is expected to grow at 10% over the year and asset $B$ is expected to grow at 12%. Which of the following is true if there are no holding costs or benefits for either asset?

A) Asset $A$ 's one-year forward price will be less than that of asset $B$ .
B) Asset $A$ 's one-year forward price will be greater than that of asset $A$ .
C) Asset $A$ 's one-year forward price will be equal to that of asset $B$ .
D) None of the above can be ascertained with certainty, as it also depends on other factors.

Question 5

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. What is the one-year forward price of the asset?

A) $52.50
B) $55.00
C) $60.00
D) Cannot be calculated from the given information.

Question 6

A replicating portfolio for a derivative security is

A) A portfolio consisting of long and short positions in the derivative.
B) A portfolio that has the same payoffs as the derivative.
C) A portfolio that has payoffs at least as great as, and in some states greater than, the payoffs from the derivative.
D) A portfolio that combines the derivative with another derivative on the same underlying so as to make the portfolio riskless.

Question 7

An arbitrage is a strategy where
(a) You buy one asset and sell another with a view to make a profit if the one you bought appreciates and the one you sold depreciates.
(b) 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.
(c) You buy and asset with a view of selling it at a higher price.
(d) You buy an overpriced asset and sell an underpriced one.

Question 8

Counterparty risk in a futures contract is lower than in a forward contract because

A) The participants in the futures market are better funded.
B) The futures contract is marked-to-market on a daily basis.
C) The futures exchange bears the counterparty risk.
D) The forward market does not charge commissions that may be used to offset the risk of counterparty failure.

Question 9

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

Question 10

The forward price of an asset that has no holding costs or benefits is equal to

A) The compounded price of the spot asset, where the compounding takes place at the risk-free rate.
B) The compounded price of the spot asset, where the compounding takes place at a rate equal to the expected return on the asset.
C) The market's expectation of the future spot price of the asset.
D) Its current spot price.

Question 11

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

Question 12

If you wanted to double your money in the same time as in the answer to the previous question, but were using monthly compounding, what would be the rate of interest you would require?
(a) 6.0010%
(b) 6.0068%
(c) 6.0163%
(d) 6.0224%

Question 13

The presence of the delivery option in a futures contract means that

A) A futures contract may be physically settled but not a forward contract.
B) All else remaining the same, a futures contract will trade at a lower price than a forward.
C) All else remaining the same, a futures contract will trade at a higher price than a forward.
D) A futures contract mat be settled in cash or by delivery of the physical asset.

Question 14

Two assets $A$ and $B$ have the same spot price today. The price of asset $A$ is expected to grow at 10% over the next year and that of asset $B$ is expected to grow at 10% also. Asset $A$ has a standard deviation of returns of 10% over the year and asset $B$ has standard deviation of 15%. Which of the following is true if there are no holding costs or benefits?

A) Asset $A$ 's one-year forward price will be less than that of asset $B$ .
B) Asset $A$ 's one-year forward price will be greater than that of asset $A$ .
C) Asset $A$ 's one-year forward price will be equal to that of asset $B$ .
D) Any of the above may be true.

Question 15

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

Question 16

The law of one price states that

A) Similar but not identical assets will trade in the same market.
B) Similar but not identical portfolios will have the same risk.
C) Portfolios with different cashflows cannot have the same price.
D) Portfolios with identical cashflows will have the same price.

Question 17

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

Question 18

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.

Question 19

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:

A) The one-month forward prices of IBM today equals the one-month forward price a month ago
B) The one-month forward price of IBM today is greater than the one-month forward prices a month ago by $10
C) The one-month forward prices of IBM today is lower than the one-month forward price a month ago by $10
D) The one-month forward price of IBM today is $44

Question 20

Rolling over short-dated futures contracts is the same as taking one long-dated futures contract if

A) The interest rates are constant.
B) The average change in the spot price is zero over the life of the contract.
C) There is daily mark-to-market of both the short-dated and long-dated contracts.
D) The size (notional value) of the open position in the futures does not change over the horizon of the transactions.

Question 21

An investor enters into a forward contract to buy 5,000 barrels of oil at $80 a barrel in three months. Two months later, suppose that the one-month forward price of oil is $83 a barrel, and the one-month interest rate is 0%. The value of the contract the investor holds after two months is

A) $- \$ 15,000$
B) + $15,000
C) +$400,000
D) +$415,000

Question 22

An investor enters into a forward contract to purchase 100,000 shares of IBM stock in 2 months at prices of $105 per share. After one month, the investor notes that the forward price for the same contract (which now has a one-month maturity) is $103 per share. She also notes that the one-month discount factor is 0.993. The value of the forward contract held by the investor is

A) $+ \$ 198,600.00$
B) $- \$ 198,600.00$
C) $+ \$ 200,000.00$
D) $+ \$ 201,409.90$

Question 23

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?

A) Oil prices plummet a day before the maturity of the contracts
B) Oil prices skyrocket a day before the maturity of the contracts
C) Oil prices plummet a day after the firm enters the contracts
D) Oil prices skyrocket a day after the firm enters the contracts

Question 24

The replication method identifies the price of a USD/GBP forward rate as a function of

A) The expected future USD/GBP exchange rate, the GBP interest rates, and the USD interest rates
B) The spot USD/GBP exchange rate and the volatility of the spot USD/GBP exchange rate
C) The spot USD/GBP exchange rate, the GBP interest rates, and the USD interest rates
D) Only the spot USD/GBP exchange rate

Question 25

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)?

A) The forward rate is larger than the spot rate
B) The forward rate is smaller than the spot rate
C) The forward rate is equal to the spot rate
D) There is not enough information to answer this question