Question

A stock is expected to pay a dividend of $0.70 per share in one month, in four months and in seven months. The stock price is $30, and the risk-free rate of interest is 7% per annum with continuous compounding for all maturities. You have just taken a short position in an eight-month forward contract on the stock. Six months later, the price of the stock has become $34 and the risk-free rate of interest is still 7% 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 recieved

= Stock price * e^n - Dividends*e^n

= 30 * e^7/12*8 - ( 0.7 *e^7/12*7 + 0.7 * e^7/12*4 + 0.7*e^7/12*1)

= 30 * e^0.0467 - ( 0.7 *e^0.0408 + 0.7 * 0.0233 + 0.7*e^0.0058)

= 30*1.0478 - ( 0.7* 1.0416 + 0.7*1.02358 + 0.7*1.0058)

= 31.434 - ( 0.7291 + 0.7165 + 0.7041)

= 31.434 - 2.1497 = $29.28

Value of Position six month later = Present value of Forward price - Stock price after 6 months -

=29.28 / e^7/12*2 - 34

= 29.28 * e^0.0117 -34

= 29.28*1.0118 -34

= 29.54 -34

= -4.46