If the stock index is at 148,the three-month futures price is 151,the dividend yield is 5 percent and the interest rate is 8 percent,determine the profit from an index arbitrage if the stock ends up at 144 at expiration.(Ignore transaction costs. )
A)1.89
B)4.00
C)7.00
D)5.11
E)-7.00

Question

Quizplus · Accepted Answer

Using the formula for index arbitrage profit:
Profit= Futures Price - (Index Price - Present Value of Dividends)
Present Value of Dividends = Dividend Yield * Index Price * (Time to Expiration/12)
Time to Expiration = 3 months = 0.25 years
So, Present Value of Dividends = 0.05 * 148 * (0.25) = 1.85

Plugging in the values:
Profit= 151 - (144 - 1.85) = 1.85 + 7 = 8.85

However, since we are shorting the index (selling futures) and the index has decreased from 148 to 144, we need to subtract the profit of shorting the index:
Profit from shorting index = (Index Price at start - Index Price at end) = 148 - 144 = 4

Final Profit = 8.85 - 4 = 4.00

Therefore, the best choice is A) 4.00.

If the Stock Index Is at 148,the Three-Month Futures Price