Consider a price-weighted index (I) and a synthetic index constructed from the c

Question

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 matures after six months. The continuously compounded interest rate is 5% per year. Stocks constituting S are expected to pay $190 of dividends this year. a) If a dealer quoted a forward price $10,231 for S, how would you arbitrage this quote? O Short the forward, short sell exp(-delta T) units of the underlying, and lend the cash proceeds O Long the forward, short sell exp(-delta T) units of the underlying, and lend the O Long the forward, buy expl-delta T) units of the underlying, and lend the cash O Short the forward, buy exp(-delta T) units of the underlying, borrowing cash cash proceeds proceeds to do so.

Explanation / Answer

Part (a):

Ans:- Long Forward, Sell stock and lend the cash proceeds.
Reason: Since synthetic price of stock after 6 months is $10250 (i.e. $10000*(1+5*6/(12*100)) and forward price is $10231. Therefore, a profit of $19 could be earned. Also the cash proceeds lent will generate an interest income over it.

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