Deck 5: Hedging With Futures Forwards

Question 1

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

A)Greater than 1.
B)Exactly equal to 1.
C)Less than 1.
D)Indeterminate,given the information available.

Answer 1

ANSWER : D

depends also on the correlation between the changes in spot and futures,and no information is provided on this quantity.

Question 2

The tailed hedge ratio becomes lower in comparison to the untailed one when

A)Interest rates rise and hedge maturity increases.
B)Interest rates rise and hedge maturity decreases.
C)Interest rates fall and hedge maturity increases.
D)Interest rates fall and hedge maturity decreases.

Answer 2

Interest rates rise and hedge maturity increases.

Question 3

You own an equity portfolio that has a value of $10,000 and a beta of 1.2.The futures price per contract is currently $1,000.How many futures contracts do you need to sell to bring your equity portfolio's beta to a value of 1?

A)0.5
B)1.0
C)1.5
D)2.0

Answer 3

D

Question 4

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:

A)The minimum-variance hedge ratio is greater than 1.
B)The minimum-variance hedge ratio is less than or equal to 1.
C)The minimum-variance hedge ratio is negative.
D)The minimum-variance hedge ratio is not equal to 1.

Question 5

What must be the daily interest rate (expressed in continuously-compounded and annualized terms)for the tailed hedge ratio to be 90% of the untailed one for a one-year hedge? Assume a hedging horizon of 365 days.

A)10%
B)15%
C)20%
D)25%

Question 6

The change in spot prices has a standard deviation of $1.The change in futures prices has a standard deviation of $1.25.The correlation of spot and futures prices is 1.If the daily risk free interest rate is $R = 1.000055$ (corresponding to a continuously-compounded rate of 2% per year),then what is the tailed hedge ratio for a spot position hedged by a 30-day futures contract?

A)0.7889
B)0.7922
C)0.7994
D)0.8000

Question 7

When the correlation between two assets is exactly $- 1$ ,which of the following statements is true?

A)The hedge ratio is positive.
B)The hedge ratio is zero.
C)The variance of the hedged position is maximized.
D)There is no basis risk in hedging.

Question 8

A US-based corporation has decided to make an investment in Norwegian Kroner of NOK 500 Million (NOK = Norwegian Kroner)in 3 months.The company wishes to hedge changes in the the US dollar-NOK exchange rate using forward contracts on either the euro (EUR)or the Swiss Franc (CHF).The company makes the following estimates: -If EUR forwards are used: The standard deviation of quarterly changes in the USD/NOK spot exchange rate is 0.005,the standard deviation of quarterly changes in the USD/EUR forward rate is 0.025,and the correlation between the changes is 0.90.
-If CHF forwards are used: The standard deviation of quarterly changes in the USD/NOK spot exchange rate is 0.005,the standard deviation of quarterly changes in the USD/CHF forward rate is 0.020,and the correlation between the changes is 0.80.
The current USD/NOK spot rate is 0.160 (i.e. ,USD 0.160 per NOK),the current 3-month USD/EUR forward rate is 1.36,and the current 3-month USD/CHF forward rate is 1.04.
If the company wishes to carry out a minimum-variance hedge,which currency should it use for this purpose?

A)CHF,because the forward exchange rate of near 1 makes it "more" like the USD.
B)EUR,because Norwegian trade with the eurozone countries far exceeds its trade with Switzerland.
C)EUR,because of the higher correlation of 0.90.
D)CHF,because of the lower correlation of 0.80.

Question 9

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?

A)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.
B)The volatility of interest rates makes the correlation of spot and futures lower,and enhances basis risk between the spot and futures markets.
C)If nominal interest rates were constant,the tailed and untailed hedge ratios would be the same.
D)If real interest rates were constant,the tailed and untailed hedge ratios would be the same.

Question 10

The correlation between changes in price of a spot asset and futures asset is 99%.The standard deviation of changes in spot prices is $2,and that of futures prices is $3.What is the standard deviation of a position that is long 5 units of the spot asset and is hedged by shorting 4 units of futures?

A)1.5
B)2.0
C)2.5
D)3.0

Question 11

If the minimum-variance hedge ratio is $- 1$ ,then which of the following statements is true?

A)Changes in spot and futures prices are perfectly negatively correlated.
B)The standard deviations of spot and futures price changes are the same.
C)The minimum-variance hedge for a long spot exposure is a short futures exposure of the same size.
D)All of the above.

Question 12

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?

A)The tailed hedge ratio is lower than the untailed one.
B)The tailed hedge ratio is equal to the untailed one.
C)The tailed hedge ratio is greater than the untailed one.
D)None of the above is always true.

Question 13

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,

A)Biased downwards.
B)Unbiased.
C)Biased upwards.
D)Biased downwards only if interest rates are nonzero.

Question 14

If changes in spot and futures prices are perfectly correlated over the horizon of a hedge,then

A)The minimum variance hedge ratio is $+ 1$
)
B)The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero.
C)The net cash flow at maturity of the hedge is zero.
D)The standard deviation of spot price changes must equal the standard deviation of futures price changes.

Question 15

The correlation between changes in price of a spot asset and futures asset is 99%.The standard deviation of changes in spot prices is $2,and that of futures prices is $3.What is the standard deviation of a position that is long 5 units of the spot asset and is optimally (i.e. ,minimum-variance)hedged by using futures?

A)1.41
B)1.99
C)2.52
D)3.11

Question 16

If changes in spot and futures prices are uncorrelated,then

A)The minimum variance hedge ratio is zero.
B)Basis risk is zero.
C)Hedging the spot position with futures is effective because the portfolio is well-diversified.
D)The minimum variance hedge requires holding equal amounts of spot and futures.

Question 17

The tailed minimum-variance hedge ratio becomes lower in comparison to the untailed one when

A)Nominal interest rates rise and hedge maturity increases.
B)Real interest rates rise and hedge maturity decreases.
C)Nominal Interest rates fall and hedge maturity increases.
D)Real interest rates fall and hedge maturity decreases.

Question 18

Using a linear regression of changes in spot asset prices on changes in futures asset prices,the minimum-variance hedge ratio may be obtained

A)As the intercept coefficient in the regression.
B)As the slope coefficient in the regression.
C)As the $R ^ { 2 }$
Of the regression.
D)As the square-root of the variance of the residuals from the regression.

Question 19

If changes in spot and futures prices have a correlation of $- 1$ ,then

A)The hedge ratio is $- 1$
B)The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero.
C)The net cash flow at maturity of the hedge is zero.
D)The standard deviation of spot price changes must equal the negative of the standard deviation of futures price changes.

Question 20

"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.

Question 21

Refer again to the data in Question 23.The minimum-variance hedge is a

A)Long USD/EUR forward.
B)Short USD/EUR forward.
C)Long USD/CHF forward.
D)Short USD/CHF forward.

Question 22

Refer again to the data in Question 23.The minimum-variance hedge,if CHF were to be used for the hedge,is a forward contract calling for the delivery of

A)CHF 500 million.
B)CHF 100 million.
C)CHF 104 million.
D)CHF 96.2 million.

Question 23

Refer again to the data in Question 23.The minimum-variance hedge,if EUR were to be used for the hedge,is a forward contract calling for the delivery of

A)EUR 500 million.
B)EUR 90 million.
C)EUR 122.4 million.
D)EUR 367.65 million.