Question

The one-year futures price of gold is $1210 per oz. (i.e., the futures price on a contract that expires in one year). The spot price is $1137 per oz. and the continuous risk-free rate is 2.56% per annum. The storage costs for gold are $2 per oz. payable in arrears and we assume gold provides no income. What is the arbitrage profit per 100 oz. of gold? Ignore transactions costs.

Answer 1

In the given case, the storage cost for Gold is given in absolute amount, i.e., $2 per oz. In a normal scenario, the storage costs are given in percentage terms.

Ignoring convenience yield (as we have assumed Gold provides no income), the expected futures price can be found using the formula below:

e stands for exponential and can be found using the scientific calculator.

In the give case,

Spot = $1137 per oz.

Storage Costs = $2 per oz.

Risk free rate = 2.56% p.a.

t = 1 year

Thus,

Expected Futures price = ($1137 + $2) * e^(0.0256*1)

Expected Futures price = $1168.53 per oz.

However, the available Futures price of gold is @1210 per oz.

Thus, an arbitrage opportunity is available.

We can earn an arbitrage profit by buying (going long) the Spot and selling (going short) the 1-year futures contract.

By going long the spot and including the storage costs, the cost after 1 year would be $1168.53 per oz. As we're going short the Futures contract after 1 year, we have fixed the selling price at $1210 per oz.

Thus, After 1 year, the Arbitrage profit per 100 oz. = 100 * ($1210 - $1168.53)

The Arbitrage profit per 100 oz. = $4147