Question

1. You are expecting to receive an inheritance in 6 months and wish to use a long position in a forward contract to pre-invest the proceeds. A dealer offers a forward contract for 1,000 shares of Gargantuan Industries. The current price of Gargantuan is $89 per share and Gargantuan is expected to pay dividends per share over the next 6 months with a present value of $4.56 per share.
   1. If the risk-free rate is 3.80% compounded annually, what is the no-arbitrage forward price per share for the 6-month forward contract?

b. Two months later the price of Gargantuan Industries is $92.25 per share and the risk-free rate is still 3.80%. What is the value of your 1,000 share forward position?

Answer 1

a) The no-arbitrage forward price per share for the 6-month forward contract (F) is given by

F= (S-I)*(1+r)^t

where S is the spot price of the asset/stock

I is the present value of dividends from the asset/stock during the period

r is the annually compounded risk free rate and

t is the time till maturity in years

So, F = (89-4.56) * (1+0.038)^(6/12) = $86.029/share or $86.03/share

b) Assuming that the dividends were distributed evenly throughout the six months

The present value of dividends at the end of two months

= Present Value of dividends at the time of Forward contract * 1.038^(2/12)

= 4.56*1.038^(2/12) =$4.588

So, the No arbitrage Forward price after two months

= (92.25-4.588)*1.038^(4/12) = $88.758 or $88.76/share

So, the value of Forward per share

= (Forward price today - Forward price contracted)/1.038^(4/12)

=(88.76-86.03)/1.038^(4/12)

= $2.69506/share

or $2695.06 for 1000 shares