Question

The current spot price of gold is $1200 per ounce. The riskless interest rate is 1% per month. For simplicity, assume there are no storage/security costs of gold.

a) If you need to buy the gold in 8 months’ time, which position (long or short) will you take in the futures market to hedge the price risk of the gold?

b) What is the arbitrage-free futures price for the delivery of gold in 8 months’ time?

c) If you see an 8-month futures price of gold quoted at $1240 per ounce, explain how you would capture an arbitrage profit. Show your work in detail by clearly outlining the actions, initial cash flow and cash flow at maturity (T).

Answer 1

Spot Price $1,200 per Once

Risk less interest rate - 1% per month

There is no storage or security cost.

a) Long. If I know that I will be buying gold after 6 months I will go LONG to hedge myself against the risk of increase in price. Example - CMP is $1,200 per once what if price increases to $1,300 after 8 months so buying gold future at current rate will help me protecting myself from increase in price.

b) Arbitrage free future price is a price where spot price is equals to future price.

Futures Price = Spot price * (1+ rf*(8/12))

Where rf = Risk free rate

Futures Price = 1200 * (1+ .01*(8/12)) = $1,208

c) is 8 month future is trading at $1,240 this gives a good opportunity of arbitration trade. We will buy cheap and sale expensive to take perfect arbitration advantage. As future is trading at $1,240 this is way expensive than the price should be.

Points to remember - Future will be quoted either on premium or discount to spot based on the expectations from the commodity but on expiry both will be quoting very close as difference between future and spot will be almost nil on expie//ry.

So we will short future @ $1,240

Buy Spot @ $1,200

Price After 8 Months	Buy Spot	Short Futures	Profit
1200	0	40	40
1250	50	-10	40
1150	-50	90	40

We are in profit in any direction of the price movement.

Thanks, hope you like the answer. I would be great if you can share your feedback.