a) The current price of gold is $300 per ounce. Carrying costs in total are 0.5

Question

a) The current price of gold is $300 per ounce. Carrying costs in total are 0.5 % (not including interest) of the gold value payable in 6 months time. If the interest rate is 8%, is there an arbitrage opportunity if the gold futures price for delivery in six months is $310 per ounce?

[3 marks]

Compare futures price and theoretical price.

b) If an arbitrage opportunity exists, explain how you would conduct it and calculate the arbitrage profit.

[2 marks]

Illustrate arbitrage transaction and compute profit therefrom.

c) Why is it not possible in reality to perfectly hedge a portfolio using options and/or futures Instruments?

[2 marks]

Review hedging concepts.

Explanation / Answer

As per cost of carry model the theoritical price of Future is as follows:

Future Price = Spot price + Interst Cost + Storage Cost

Future Price = $300 +$300 * 8% * 6/12 + $300 * 0.5% * 6/12 (6/12 indicates for 6 month calculation)

Future Price = $300 + $12 + $0.75

Future Price = $312.75

So the Theoritical price would have been $312.75 but given future price is $310 and hence arbitrage opprutunity Exist.

B) Since the future is at lower price hence we will buy the future and sell spot which will give the net profit of the difference in price of future and theoratical price i.e. Profit = ($312.75 -$310) i.e. $2.75 per ounce.

C) In reality it is not possible to perfectly hedge a portfolio using optons or futures because in reality there are unsystematic risk that cannot be deviated. Say for example Taxes, Government policies, Change in Market due to new players, Innovations. These can change the market force and it cannot be assumed precisely about this changes. So in reality we cannot do a perfect hedge.

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