[2008]Topic 23: Commodity Forwards and Futures相关习题 position, following, statements, long

Baran

 

AIM 2: Derive of the basic equilibrium formula for pricing commodity forwards and futures.

 

1、All of the following statements describing the formulation of synthetic forward commodity are correct EXCEPT:

      I. A synthetic commodity forward price can be derived by combining a long position on a commodity forward, F0,T, and a long zero-coupon bond that pays F0,T at time T.

     II. The total cost at time 0 is equivalent to the cost of the bond, or e-rTF0,T.

    III. The payoff at time T is ST – F0,T + F0,T = ST.

 

A) I only.

B) II only.

C) III only.

D) All of the statements are correct.

Baran

 

The correct answer is D

 

All of the statements are correct. A synthetic commodity forward price can be derived by combining a long position on a commodity forward, F0,T , and a long zero-coupon bond that pays F0,T at time T. The total cost at time 0 is equivalent to the cost of the bond, e-rTF0,T. The forward contract does not have any initial cash flows at time 0. The payoff at time T is ST – F0,T + F0,T = ST, where ST is the spot price of the commodity at time T. The present value of the expected spot price at time T is E(ST)e–αT. This amount is equivalent to the cost of the bond, e-rTF0,T, because both represent the amount you would pay today to receive the commodity at time T.

Baran

 

AIM 6: Define the lease rate and how it determines the no-arbitrage values for commodity forwards and futures, and explain the relationship between lease rates and contango and lease rates and backwardation, respectively.

 

1、Which of the following statements regarding the lease rate in commodity futures contracts is incorrect?

 

The lease rate is the return required by the lender in exchange for lending a commodity.

Assuming it is positive, as the lease rate increases, the futures price for a commodity increases.

In a cash-and-carry arbitrage, the lease rate is earned whether or not the underlying commodity is actually loaned.

Lease rates are similar to dividends paid to the lender of a share of common stock.

If the lease rate is less than the risk-free rate, the forward market is said to be in contango.

A) III and V.

 

B) I, III, and V.

 

C) II and IV.

 

D) II and III.

Baran

 

2、The expected spot rate in six months for a commodity is $24. The annual lease rate is 6 percent for the commodity. The appropriate continuously compounding annual risk-free rate for the commodity is equivalent to 7 percent. What is the 6-month commodity forward rate?

 

A) $24.12.

B) $23.91.

C) $24.00.

D) $24.22.

Baran

 

The correct answer is D

 

The lease rate is the amount that a lender requires as compensation for lending a commodity. In determining the price of a commodity futures contract, the lease rate, δl, is subtracted from the risk-free rate, r, as follows:

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Assuming a positive lease rate, the lease rate effectively reduces the futures price, all else constant. This also assumes that there is an active market for lending the commodity underlying the futures contract. The lease rate can only be earned by actually lending the underlying commodity.

[此贴子已经被作者于2009-6-26 14:09:57编辑过]

Baran

 

The correct answer is A

The 6-month forward rate is calculated as follows:

Baran

 

3、Which of the following is TRUE in normal backwardation? Futures prices tend to:

 

A) fall over the life of the contract because hedgers are net short and have to receive compensation for bearing risk.

 

B) fall over the life of the contract because speculators are net short and have to receive compensation for bearing risk.

 

C) rise over the life of the contract because hedgers are net long and have to receive compensation for bearing risk.

 

D) rise over the life of the contract because speculators are net long and have to receive compensation for bearing risk.

Baran

 

The correct answer is D

 

Normal backwardation means that expected futures spot prices are greater than futures prices. It suggests that when hedgers are net short futures contracts, they must sell them at a discount to the expected future spot prices to get speculators to assume the risk of holding a net long position. The futures price rises over the life of the contract, which compensates speculators for the exposure of their long positions.

Baran

 

AIM 8: Explain the impact storage costs and convenience yields have on commodity forward prices and no-arbitrage bounds.

 

1、If the October 2005 spot price for natural gas is 5.171, the annual risk-free rate of interest is 5 percent, and the November forward price is 5.253. What is the natural gas implied storage cost for the month of October?

 

A) 0.043.

 

B) 0.060.

 

C) 0.057.

 

D) 0.075.

Baran

 

The correct answer is B

 

The implied storage cost for October is calculated as follows: