Question

A one-year gold futures contract is selling for \(1,641. Spot gold prices are \)1,700 and the one-year risk-free rate is 2%. What arbitrage opportunity is available to investors? What strategy should they use, and what will be the profits on the strategy?

Short answer

Answer

Available for short sale; sell gold short $1,700 today. and lend money at the risk free rate and long gold future of $1,641 to earn profit $93

Step-by-step solution

Explanation on arbitrage opportunity

Future’s Price = $S_0{\left(1+r_f-d\right)}^T$

= $1700 x (1 + .02)1

= $1734

This implies that at the rate of $1,641, the gold future contract is underpriced.

Explanation on strategy

In order to benefit from mispricing, let’s sell gold short $1,700 today. and lend money at the risk free rate and long gold future of $1,641. One year down the line, there would be cash-flow from the loan and the proceeds from future position of (ST - $1,641) and outflow from short position of gold at spot price ($-S_T$).

The arbitrage profit therefore = $1734 + ($S_T$- $1641) + ($-S_T$). = $93