Question 1

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

Accepted Answer

The theoretical one-year forward price of oil can be calculated as follows:
Forward price = Spot price x (1 + risk-free rate - storage cost) x (1 + expected growth rate)
Forward price = $100 x (1.02 - 0.01) x (1.04) = $103.02

Therefore, the best choice is C, as it matches the calculated theoretical one-year forward price of oil.

Question 2

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.

Accepted Answer

The current spot price of oil is $100, and the forward price is $98. This suggests that the market is in contango, meaning that the forward price is below the spot price. However, since the cost of carry (storage + financing cost) is $3 ($1 for storage and 2% of $100 for financing), the effective forward price is $101, which is above the spot price. This suggests that investors could benefit from a carry trade in the oil market by buying spot oil, storing it for a year, and selling it forward at a profit. The fact that the expected growth rate of oil prices is 4% per year also supports the idea of a benefit of carry, as the cost of carry is lower than the expected price appreciation. Therefore, the correct answer is B.

Question 3

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.

Accepted Answer

If futures prices and interest rate movements are positively correlated, the futures prices will be higher than forward prices because the higher interest rate will increase the cost of carry for futures. If they are negatively correlated, futures prices will be lower than forward prices because lower interest rates will reduce the cost of carry for futures. If they are uncorrelated, futures and forward prices will coincide because the cost of carry will be the same for both. Therefore, all of the above statements are true.

Question 4

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.

Accepted Answer

The forward price of an asset is determined by its spot price and the expected growth rate, not by the standard deviation of returns. Since both assets have the same spot price and expected growth rate, their one-year forward prices will be equal.

Question 5

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

Accepted Answer

The answer is the solution to the following equation:  $$2 = e ^ { 0.06 t } , \quad t = \ln ( 2 ) / 0.06 = 11.55 \text { years. }$$

Question 6

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%

Accepted Answer

The correct answer is C because the rate of interest required to double your money in the same time as in the answer to the previous question, but using monthly compounding, is 6.0163%.

Question 7

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.

Accepted Answer

The forward price of an asset is the spot price multiplied by the growth factor. Since both assets have the same spot price and asset B is expected to grow at a higher rate, the forward price of asset B will be higher than that of asset A.

Question 8

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.

Accepted Answer

Arbitrage involves taking advantage of discrepancies in prices between two or more assets or markets to make profit with no or minimal risk. Choice B correctly describes an arbitrage strategy by ensuring cash flows are non-negative at all points in time, and at least one positive cash flow. Choices A, C, and D do not entail a risk-free profit-making opportunity as arbitrage does.

Question 9

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.

Accepted Answer

The forward price should be $1020 ($1000 * 1.02) due to the risk-free rate. Since the forward price is $103, it's undervalued, allowing arbitrage by selling forward and buying spot.

Question 10

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.

Accepted Answer

(No cost/benefits of carry information is provided. )

Question 11

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.

Accepted Answer

If interest rates are constant, the cost of carry is predictable, making the rolling of short-dated contracts equivalent to holding a long-dated contract.

Question 12

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

Accepted Answer

The answer of A stock has a current price of...

Question 13

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

Accepted Answer

The correct answer is A.The one-year forward price of the asset is $52.50. This is because the forward price is equal to the spot price plus the expected return on the asset minus the risk-free rate of interest. In this case, the spot price is $50, the expected return on the asset is 10%, and the risk-free rate of interest is 5%. Therefore, the forward price is $50 + 10% - 5% = $52.50.

Question 14

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.

Accepted Answer

The answer of The presence of the delivery option in...

Question 15

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.

Accepted Answer

The law of one price states that portfolios with identical cashflows will have the same price. This concept is the foundation of the theory of arbitrage, which involves taking advantage of differences in prices of identical assets or portfolios to earn risk-free profits. Therefore, option D is the best choice as it correctly defines the law of one price. The other options are not accurate descriptions of this financial concept.

Question 16

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.

Accepted Answer

The forward price of an asset with 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. This is because the forward price reflects the cost of carrying the asset forward in time, which, in the absence of holding costs or benefits, is determined by the opportunity cost of not investing at the risk-free rate.

Question 17

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

Accepted Answer

The one-month forward price of IBM is determined by the current stock price, the interest rate, and the expected future stock price. Since the stock price has remained the same, the only difference is the change in volatility. However, volatility does not affect the forward price of the stock. Therefore, the one-month forward prices of IBM today equals the one-month forward price a month ago.

Question 18

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

Accepted Answer

To find the one-year forward rate of dollars per euro, we need to use the interest rate parity formula:

F/S = (1 + Rd) / (1 + Rf)

Where F is the forward exchange rate, S is the spot exchange rate, Rd is the domestic interest rate (1% for dollars), and Rf is the foreign interest rate (2% for euros).

Plugging in the numbers, we get:

F/1.50 = (1 + 0.01) / (1 + 0.02)
F/1.50 = 1.01 / 1.02
F = 1.01 / 1.02 * 1.50
F = 1.4853

Therefore, the one-year forward rate of dollars per euro is 1.4853, which corresponds to choice B.

Question 19

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.

Accepted Answer

A replicating portfolio is a portfolio that replicates the payoffs of a derivative security. Therefore, the best choice is B, which states that a replicating portfolio has the same payoffs as the derivative. Choices A, C, and D do not accurately define a replicating portfolio.

Question 20

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.

Accepted Answer

The answer of Counterparty risk in a futures contract is...

Quiz 3: Pricing Forwards and Futures I

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?

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?

The relationship of forwards and futures is best represented by the following statement(s)

How many years does it take to double your money if the continuously-compounded interest rate is 6%?

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?

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?

An arbitrage is a strategy where

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?

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?

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

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?

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?

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

The law of one price states that

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

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 replicating portfolio for a derivative security is

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