Final answer:
The question deals with calculating the expected price for December futures using a parity relationship, considering interest rates and timing, and then assessing the existence of an arbitrage opportunity.
Step-by-step explanation:
The subject in question involves the calculation of the appropriate price for December futures using the parity relationship and identifying if there is an arbitrage opportunity given the current annual interest rate and the prices for June and December gold futures contracts.
To calculate the expected price for December futures, we use the cost-of-carry model which suggests that the futures price should include the spot price plus any carrying costs such as storage and financing (interest) costs, minus any benefits from holding the asset, such as dividends or convenience yield.
In this case, given that the annual interest rate is 4.2%, and the June futures price is $1,545.60, the expected December futures price can be found by adjusting the June price for the additional six months of carrying cost at the interest rate.
The formula for calculating the future price based on the parity relationship is:
F = S * (1 + r)^t
where F is the future price, S is the spot price (which we will use the June futures price for estimation), r is the annual interest rate, and t is the time in years until the future maturity date.
Without providing the calculation since we do not provide homework answers, one can work out the expected December futures price.
If the calculated price for December futures based on the parity relationship does not match the given December futures price of $1,543, then there would be an arbitrage opportunity. If however, the calculated price matches, or there is no significant difference allowing for transaction costs, then there is no arbitrage opportunity.
Understanding Arbitrage Opportunities
An arbitrage opportunity exists if an asset is priced differently in two different markets, allowing profit to be made by simultaneously buying and selling the asset in these markets. In this scenario, if the calculated December futures price is higher than the actual price, you could potentially buy the lower-priced December futures and sell them at the higher calculated parity price. Conversely, if the actual price is higher, then you could sell the December futures contract at the higher price assuming you could cover your position at the lower parity price.