Financial Risk Manager Part 1
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A trader on the equity desk of a large banking institution is currently evaluating a 15-month futures contract on an equity index. This futures contract is quoted at a price of USD 3,750. At present, the underlying equity index has a value of USD 3,625 and it generates a continuously compounded dividend yield of 2% per annum. Additionally, the risk-free rate, which is also compounded continuously, stands at 5% per annum. Assuming there are no transaction costs to consider, determine the optimal strategy that the trader should employ to capitalize on an arbitrage opportunity, if one exists.
A trader on the equity desk of a large banking institution is currently evaluating a 15-month futures contract on an equity index. This futures contract is quoted at a price of USD 3,750. At present, the underlying equity index has a value of USD 3,625 and it generates a continuously compounded dividend yield of 2% per annum. Additionally, the risk-free rate, which is also compounded continuously, stands at 5% per annum. Assuming there are no transaction costs to consider, determine the optimal strategy that the trader should employ to capitalize on an arbitrage opportunity, if one exists.
Explanation:
B is correct. This is an example of index arbitrage. Arbitrage exists if the parity condition between the equity index price and the price of the futures contract underlying the index does not hold. The parity relationship is expressed by the theoretical value of the futures price: (Fo,t) = So * exp[(risk-free rate - dividend yield) * t) where So equals the current spot value of the index (USD 3,625) and t equals the time in years (= 15/12 = 1.25). Therefore, theoretical futures price = So * exp[(risk free rate - dividend yield) * 1.25] = USD 3,763.52 Since this theoretical (computed) futures price (value) is different from the current futures contract price, a potential arbitrage situation exists. Since the current futures price (USD 3,750) is lower than the theoretical futures price (USD 3,763.52) in this case, one can short the higher priced stocks underlying the equity index (or short the index) and buy the index futures contract at the current price. A, C, and D are incorrect per the explanation for B above.