Question

Question: A stock is announced to pay $1.20 per share in one month and in also expected to pay $1.25 in 5 four months. The stock price is $90, and the risk-free rate of interest is 4% per annum with continuous compounding for this problem. Suppose you just took a short position in a six-month forward contract on the stock.

i.What are the “Forward Price” and the initial value of the forward contract?

ii. Three months later, the price of the stock is $98 and the risk-free interest rate is still 4%. What is the forward price at this point?

iii. What is the value of the short position in the forward contract you signed three months ago?

Answer 1

Solution:

Current price = $90

Present value of the dividend that will be paid after 1-month= $1.20 / Exp(4%*1/12) = 1.196

Present value of the dividend that will be paid after 5-months = $1.25 / Exp(4%*5/12) = 1.2293

Part I)

Forward price = (Spot price - Present Value of dividend) * Exp ( Interest * time)

Forward price = (90 - 1.196-1.93) * Exp ( 0.04 * 6/12) = 87.57465 * 1.02 = 89.34

The value of a forward contract at the time of initiation is zero.

Part II)

3-months later the stock price =98 and $1.25 dividend will be paid in 2 months

The present value of the dividend that will be paid after 2-months = $1.25 / Exp(4%*2/12) = 1.24

Forward price = (98 - 1.24) * Exp ( 0.04 * 3/12) = 96.76 * 1.01 = $97.73

Part III)

Forward price at the starting = 89.34 and 3-month later it is 97.73 hence value = 89.34 - 97.73 = -8.39