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

At the Time of Position :

PV of Income from the Stock I = Sum of Present Value of All Dividend from the Stock

Here

r = Risk free rate = 7% = 0.07

D1 = 0.70

T1 = 01 Months = 01/12

D2 = 0.70

T2 = 04 Months = 04/12

D3 = 0.70

T3 = 07 Months = 07/12

=0.6959 + 0.6838 + 0.67199

= 2.0517

Forward Price

Here S = Stock Price = 30

T = 08 Months Forward = 8 / 12

= 27.9483  * 1.0477

= 29.2814

Now after Six months later, the price of the stock has become $34  

After Six months PV of Income from the Stock I1

D = 0.70

r = Risk free rate = 7% = 0.07

T = Time till next dividend = (07 Months - 06 Months) = 01 Month

= 0.6959

Value of Short Position

S1 = Stock Price = 34 ( -Ve taken in formula due to short position)

= -2.9797

-Ve sign indicates Position value less than 0.

value position six months later = -2.9797 (Ans)