Question

The current value of the index is 585. Three-month futures on the index are trading at 600. The continuous dividend yield on the index is d= 3% and the continuously compounded riskless rate is also 3%.

1. What is the fair futures price?
2. Construct an arbitrage free strategy that exploits the situation.

Answer 1

a)

Futures Price = Spot * e^{(risk free rate - dividend yield) * Time to expiry}

Futures Price = 585 * e^{(3% -3%) * (3/12)}

Futures Price = 585

b)

To advantage of this arbitrage opportunity

At time t = 0

Take a short position (Sell) the Futures contract at 600

Borrow 585 at the risk free rate =3%

Take a long position on the Index

At time t = 3 months

The borrowed amount at maturity = 585 * e^{3% * (3/12)} = 589.40

Deliver the index in the Futures contract and receive 600 to close the contract

Arbitrage profit = Futures price - Borrowed Amount

Arbitrage profit = 600 - 589.40

Arbitrage profit = 10.60