Question

A stock is expected to pay a dividend of $2 per share in three months. The share price is $75, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a long position in a six-month forward contract on a share of stock.

1. a) What are the forward price and the initial value of the forward contract?

2. b) Three months later, immediately after the payment of the dividend, the price of the stock is $90 and the risk-free rate of interest is still 8% per annum with continuous compounding. What are the forward price and the value of the long position in the forward contract taken three months before?

Answer 1

a) The forward price  is the agreed upon price of an asset in a forward contract. Forward price of tradable dividend paying share is as follows: Forward Price = Future Value of Share - Future Value of dividend

We know, Future Value = PV * e^ (R*N)

Share will be continuously compounded by 6 months, and dividend will be compounded by 3 months. Value of dividend is reduced from the future value as one will not receive a dividend if he enters in a forward contract unlike holding a share.

Hence, Forward Price = 75 * e ^ (8%*6/12) - 2 * e ^ (8% * 3/12)

= 78.06 - 2.04 = 76.02

b) , the value of the forward contract is the difference between the price of the underlying asset today and the forward price discounted at the risk-free rate

i.e Value = Present Value of Underlying - Pesent Value of Forward Contract

= 90 - 76.02/( e ^ (8%*3/12))

= 90 - 74.51 = 15.49

Forward Price for 3 months to maturity = 90 * e ^ (8%*3/12) = 91.82