Question

Assume that you own a dividend-paying stock currently worth $150. You plan to sell the stock in 250 days. In order to hedge against a possible price decline, you wish to take a short position in a forward contract that expires in 250 days. The risk-free rate is 5.25% per annum (discretely compounding). Over the next 250 days, the stock will pay dividends according to the following schedule:

Days to Next Dividend	Dividends per Share ($)
30	1.25
120	1.25
210	1.25

(a) Calculate the forward price of a contract established today and expiring in 250 days.

(b) It is now 100 days since you entered the forward contract. The stock price is $115. Calculate the value of the forward contract at this point.

Answer 1

(a) Forward Contract Value (F) =Stock Price + [ Stock Price (S) - Dividend (D)]*Risk free rate*No. Of Days/365

= 150 + [(150 - 1.25 - 1.25 - 1.25)*0.0525*250/365]

= 155.26

(b) Forward Contract Value = 115 + [(115-1.25-1.25)*0.0525*100/365]

= 115 + 1.62

= 116.62

Note: Since only two dividends remain after 100 days, that is why 2.5 has been deducted in (b)

Since the period of discrete compounding is not given, it is assumed that interest is compounded annually.