Consider a price-weighted index (I) and a synthetic index constructed from the constituent stocks (S). The current level of I is 10,000 and the price of S is $10,000. A forward contract on I mature after six months. The continuously compounded interest rate is 5% per year. Stocks constituting S are expected to pay $190 of dividends this year.

If a dealer quoted a forward price $10,231 for S, can you arbitrage this quote? If so, how would you do so and what would your arbitrage profits be? (Please read the hint first)

HINT:

Since we don't know the exact timing of the expected $190 in dividends and the underlying is a stock index. We assume that the dividends are paid continuously throughout the year and the dividend yield, "delta" can be calculated as 190/10,000.

A common feature of stock index products is that dividends paid on the constituent stocks are reinvested back into the product. So if the continuously compounded dividend yield, "delta" is automatically reinvested back into the index product, in order to generate a terminal payoff equal to one unit of the spot price of the underlying "asset", S_T , we only need to buy a fractional number of units of the spot index "S". Specifically, if we wanted to generate a payoff of S_T at delivery, we would only need to buy exp(-delta*T) units of the spot index "S", or pay exp(-delta*T)*10,000 dollars up front.

Every other aspect of the problem should be the same as the standard "forward overpricing" framework.