Question

The current continuously compounded risk free interest rate is 4% and we observe today, in May, that the November six months futures price for gold is £1,200. The one year May futures price for gold is £1,020.

Is there an arbitrage opportunity?

Demonstrate how we can exploit this arbitrage opportunity (No need to calculate the profits).

Answer 1

Yes, there is an arbitrage opportunity.

The spot price observe today for the November month, the futures contract is calculated as below:

Future = So * E^r*t

So = £1,200 * 2.7183^(4%*(6/12))

So = £1176.24

The Spot price observed today for the next year may month futures contract is calculated as below:-

Future = So * E^r*t

So = £1,020 * 2.7183^(4%*(12/12))

So = £ 980

Arbitrage Strategy is:-

Short, November Month Contract and Long, 1 Year May Month Contract.