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.

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

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 of a dividend paying stock is given by

F = (S-I)*e^(rt)

where S is the spot price =$75

I is the present value of dividends = $2*e^(-0.08*3/12) =$1.9604

r is the riskfree continuously compounded rate of interest =0.08

and t is the time till maturity in years = 6/12 = 0.5

So,

F = (75-1.9604)*e^(0.08*0.5) =$76.02

The initial value of a forward contract is 0

b) After three months the forward price is given by

F= S*e^(rt) as there are no expected dividends in the remaining three months

=90* e^(0.08*3/12) only 3 months left to maturity

= $91.82

The long position is in profit as the stock price has increased

So, the value of the long position = present value of expected profit

= (91.82-76.02) *e^(-0.08*3/12)

= $15.48