Forward Pricing Suppose that the current market price of a financial security is
ID: 2810342 • Letter: F
Question
Forward Pricing
Suppose that the current market price of a financial security is $225. An investor plans to purchase this asset in one year and is concerned that the price may have risen by then. To hedge the price risk, the investor enters into a forward contract on the asset in one year. Assume that the risk-free rate is 4.75 percent.
A. Calculate the appropriate forward price at which this investor can enter into the contract. Which position will the investor take, long or short?
B. Four months into the contract, the price of the asset is $250. Calculate the gain or loss that has accrued to the forward contract that the investor holds.
C. Assume that eight months into the contract, the price of the asset is $200. Calculate the gain or loss on the forward contract that the investor holds.
D. Suppose that at expiration, the price of the asset is $190. Calculate the value of the forward contract at expiration.
E. Now calculate the value of the forward contract at expiration assuming that at expiration, the price of the asset is $240.
Explanation / Answer
A
Let r = risk free rate , T = time in years
Forward price ( no arbitrage ) = 225 * erT = 225 * e0.0475*1 = 235.945
The investor needs to buy the stock in one year. She will take a long position (buy)
B)
Remaining period = 12 months - 4 months = 8 months = 8/12 years = 2/3 years
New forward price for the same expiry date ( after 8 months) = 250 * e0.0475*2/3 = 258.043
Gain = new price - original price of contract = 258.043- 235.945 = 22. 098
Present value of the gain = 22.098 * e-0.0475*2/3 = 21.409
C)
Remaining period = 12 -8 = 4 months = 4/12 years = 1/3 years
New forward price for the same expiry date ( after 4 months) = 200 * e0.0475*1/3 = 203.192
Loss = 203.192 - 235.945 = -32.753
Present value of the Loss = -32.753 * e-0.0475*1/3 = 32.238
D)
Value of contract = 190- 235.945 = - 45.945
E)
Value of contract = 240- 235.945 = 4.055