Question

3. Suppose that the risk-free interest rate is 6% per annum dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitroge opportunities does this create? with continuous compounding and that the

Answer 1

4 Spot price Risk free rate Dividend yield Theoretical future price 696 496 402.68 10 Actual future price 405.00 Cash flow 12 13 Sell future today Borrow at risk free rate Buy index 0.00 400.00 -400.00 0.00 16 I 17 18 19 20 21 After four months Repay borrowings Receive future price Dividend on stock Deliver stock Arbitrage profit -408.08 405.00 5.37 23 25 27

4 Spot price Risk free rate Dividend yield Theoretical future price 0.06 0.04 -C5*EXP((C6-C7)*(4/12)) Actual future price 405 Cash flow 12 13 Sell future today Borrow at risk free rate Buy index -SUM(C13:C15) 17 18 19 After four months Repay borrowings Receive future price Dividend on stock Deliver stock Arbitrage profit -C5* EXP(6%"(4/12)) 405 -c5*EXP(4%"(4/12))-400 21 23 -SUM(C19:C22)