Question

A stock is expected to pay a dividend of $0.60 per share in one month, in four months and in seven months. The stock price is $25, and the risk-free rate of interest is 6% per annum with continuous compounding for all maturities. You have just taken a long position in an eight-month forward contract on the stock. Six months later, the price of the stock has become $29 and the risk-free rate of interest is still 6% per annum. What is the value your position six months later?

Answer 1

Forward Price as per the Cost of Carry Model ,

= Future value of Stock price - Future value of dividends

= 25 * e^0.06/12*8 - ( 0.6*e^0.06/12*7 + 0.60*e^0.06/12*4 + 0.60*e^0.06/12*1)

=25*e^0.04 - ( 0.60 *e^0.035 + 0.60*e^0.02 + 0.60*e^0.005)

= 25 * 1.04081 - ( 0.60*1.0356 +0.60 * 1.0202 + 0.60*1.0051)

=26.02 - ( 0.62136 + 0.61212 + 0.60306)

=26.02 - 1.84

=$24.18

Value of prosition after 6 months = Present value of forward price after 6 months - stock price after 6 months

= 24.18 / e^0.06/12*2 - 29

= 24.18 / 1.0101 - 29

= -5.06