Question

A one-year long forward contract on Amazon is entered into when its stock price is $1,900 and the continuous compounded interest rate is 2.5%. (Note: Does Amazon pay dividends?) a) What are the fair forward price and the initial value of the forward contract? b) If the forward price is set at $1,950, how would you arbitrage it? c) Six months later, the stock price of Amazon rises to $2,000. What are the current fair forward price and the current value of the long forward contract?

Answer 1

a]

Fair forward price = spot price * e^(r-d)*t,

where r = continuous compounded interest rate

d = continuous compounded dividend yield

t = time to maturity

Amazon dividend yield is zero, as it does not pay dividends

Fair forward price = $1,900 * e^0.025*1 = $1,948.10

The initial value of the forward contract would be zero since it is priced fairly

b]

If the forward price is $1,950, the forward is overpriced. It can be arbitraged by selling the forward and buying the spot.

The stock would be borrowed in the spot market, and the forward contract sold at the same time. After 1 year, the stock is sold at the forward contract price of $1,950 and using these proceeds, the stock is bought at $1,948.10 in the spot market and returned to the lender. The arbitrage profit = $1950 - $1948.10 = $1.90

c]

Fair forward price = $2,000 * e^0.025*0.5 = $2,025.16

Value of long forward contract = $2,025.16 - $1,948.10 = $77.06