Question

Assume that forward contracts to purchase one share of Sony and Disney for $100 and $40, respectively, in one year are currently selling for $3.00 and $2.20. Assume that neither stock pays a dividend over the coming year and that one-year zero-coupon bonds are selling for $93 per $100 of face value. The current prices of Sony and Disney are $90 and $35, respectively.

1. Are there any arbitrage opportunities? If so, describe how to take advantage of them.
2. What is the fair market price of a forward contract on a portfolio composed of one-half share of Sony and one-half share of Disney, requiring that $70 be paid for the portfolio in one year?
3. Is this the same as buying one-half of a forward contract on each of Sony and Disney? Why or why not? (Show payoff tables.)

Is it generally true that a forward on a portfolio is the same as a portfolio of forwards? Explain.

Answer 1

a) One year zero coupon bond are selling at $93 per $100.

So to calculate the interest rate we will follow

$93=100/(1+r)$

on solving r, we will get r=0.0752688

Now, Price of a $90 Sony share after one year = 90*(1+r) = 90(1+0.0752688) = 96.77419

Similarly price of $35 Disney share after one year = 35*(1+r) = 37.63441

Forward price of the $3.00 option = 3*exp(r*1)=3exp(0.0752688) = 3.234522

Similarly forward price of $2.20 option = 2*exp(r*1) = 2.371983

Price of sony share + price of forward option after 1 year = 96.77419+3.234522 = $100

Similarly price of Disney share + price of forward option after 1 year = 37.63441+2.371983=$40

So there is no difference in the prices before one year and after 1 year. So there is no arbitrage opportunities.

b) Price = (3+2.20)/2= $2.60

c) yes