AIM 4: Compute the forward price, given the underlying asset’s price, with or without considering the income or yield the underlying  asset generates.

1、The S& 500 index is trading at 1015. The S& 500 pays an expected dividend yield of 2 percent and the current risk-free rate is  4.1 percent. The value of a 3-month futures contract on the S& 500 is closest to:

A) 979.86.
 
B) 1,350.59.
 
C) 1,020.34.
 
D) 997.68.

[此贴子已经被作者于2009-6-24 16:05:18编辑过]

[此贴子已经被作者于2009-6-24 16:04:16编辑过]

2、Assume that the short-term interest rate in London is 4 percent and that the short-term interest rate in the US is 2 percent. If the current exchange rate between the euro and dollar is 1=US$1.2217, using the continuous time futures pricing model, what is the price of a three-month futures contract?

A) $1.2207.
 
B) $1.2156.
 
C) $1.2144.
 
D) $1.2235.

The  correct answer is B
The formula is: 1.2217e(0.02-0.04)(0.25) = $1.2156.

Foreign currencies are similar to index futures when it comes to computing the futures price. Since exchange rates are driven by interest-rate differentials, the exchange rate can be treated as an asset that pays a continuous rate, rf . More simply, interest-rate parity states that the forward exchange rate (measured in $/ unit of foreign currency), F, must be related to the spot exchange rate, S, and the interest-rate differential between the U.S. and the foreign country.

3、Which of the following is an important effect of dividends on the cost-of-carry model? Dividends:

A) reduce the value of the spot prices.
 
B) eliminate arbitrage opportunities. 
 
C) reduce the cost of carry. 
 
D) do not affect the cost-of-carry model.

The  correct answer is C

The cost of carry must be reduced by the dividends that are expected to be received while holding the underlying stock.

4、At the inception of a one-year forward contract on a stock index, the value of the index was $1,100, the interest rate was 2.6 percent, and the continuous dividend was 1.2 percent. Six months later, the value of the index is $1,125. Which of the following statements is TRUE? The value of the:

A) long position is -$17.17.
 
B) short position is -$17.17.
 
C) long position is $25.00.
 
D) short position is -$22.19.

The  correct answer is B
At the inception of the forward contract, the delivery price would have been:
1,100e(0.026 - 0.012) = $1,115.51.

The value to the long position after six months is: [1,125e(-0.012)(0.5)] - [1,115.51e(-0.026)(0.5)] = 1,118.27 – 1,101.10 = $17.17.

Therefore, the value of the short position is -$17.17.

5、At the inception of a six-month forward contract on a stock index, the value of the index was $1,150, the interest rate was 4.4 percent, and the continuous dividend was 1.8 percent. Three months later, the value of the index is $1,075. Which of the following statements is TRUE? The value of the:

A) long position is -$82.41.
 
B) long position is $82.41.
 
C) long position is $47.56.
 
D) short position is $47.56.

The  correct answer is A
At the inception of the forward contract, the delivery price would have been:
1,150e(0.044-0.018)(0.5) = $1,165.05.

The value to the long position after three months is: 1,075e(-0.018)(0.25) - 1,165.05e(-.044)(.25) = 1,070.17 - 1,152.31 = -$82.41. 

Therefore, the value of the short position is $82.41.

AIM 7: Define and provide an example of the cost-of-carry model for forward prices where the assets have no interim cash flows.

1、Using the continuous time forward pricing model, what is the no-arbitrage price of a 9-month forward contract if the interest rate is 2.4 percent and the spot price of the asset is $1,650?

A) $1,664.
 
B) $1,689.
 
C) $1,621.
 
D) $1,680.

2、Using the continuous time forward pricing model, what is the no-arbitrage price of a 3-month forward contract if the interest rate is 3.2 percent and the spot price of the asset is $750?

A) $780.
 
B) $756.
 
C) $744.
 
D) $729.