Question

QUESTION 9 The current value of the P&S 347 index is 2300 points while the price of a P&S futures contract for delivery in six months is $60,000. The risk-free interest rate is 10% per year and the future value of the dividends paid out to one share of the P&S index is $2500. The contract multiplier is $25, which means that for the purposes of this futures contract each index point is worth that much. No need to compound interest. What is the value of the arbitrage profit per contract that can be made here? Provide your answer in whole dollars and omit units (i.e. enter only the number of dollars of profit). QUESTION 10 If the cost of short-selling stock shares corresponding to one P&S index future is $3000, how does this affect the value of the arbitrage profit? The arbitrage profit would be eliminated. The arbitrage profit would be reduced. The arbitrage profit would be unaffected. QUESTION 11

please shown in STEPS

Answer 1

(9) Initial Index Value = 2300 and Index Multiplier = $ 25

Current Index Portfolio Value = 2300 x 25 = $ 57500

Expected Dividend = $ 2500, Risk-Free Rate = 10% and Tenure = 6 months

Future Contract price = $ 60000

Expected Future Price of Index Portfolio = 57500 x e^(0.1 x 0.5) - 2500 / e^(0.1 x 0.5) = $ 58070.01448

An Arbitrage can be executed as per the following process:

- Borrow stocks under the index portfolio and sell a futures contract at $ 60000

- Borrowing stocks creates a repayment liability worth the original stock's value after 6 months plus the value of any benefits accruing to the stock's holder.

- Repayment Liability = 57500 x e^(0.5 x 0.1) - 2500 / e^(0.5 x 0.1) = $ 58070.01448

- Upon completion of 6-Months one can sell the borrowed stocks under the futures contract price of $ 60000 and purchase stocks for meeting borrowing liability at $ 58070.01448

- Arbitrage Profit = 60000 - 58070.01448 = $ 1929.98

NOTE: Please raise a separate query for the solution to the second unrelated question as one query is restricted to the solution of only one complete question with up to four sub-parts.