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

As per the Cost of Carry Model,

Forward Price = Future value of Stock Price - Future value of Dividends.

= 25 * e^0.06/12*8 - ( 0.60*e^0.06/12*7 + 0.6 *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*1.0408 - (0.60*1.0356 + 0.60*1.0202+0.60*1.0050)

= 26.02 - ( 0.62136 + 0.61212 + 0.603) = 26.02 - 1.8365

= $24.18

Value of Position Six months later = Present value of Forward Price - stock price after 6 months

= 24.18 / e^0.06/12*2 - 29 = 24.18/ e^0.01 - 29 = 24.18/1.01001 - 29

= 23.94 -29 = - 5.06