Suppose that the risk-free interest rate is 8% per annum with continuous compounding and that the dividend yield on a stock index is 3% per annum with continuous compounding. The index is standing at 350 and the futures price for a contract deliverable in 6months is 360.
#1) What should be the theoretical futures price for the stock index?
#2) What arbitrage opportunities does this create?
#1) theoretical futures price = $366.38 |
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#1) theoretical futures price = $358.86 |
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#1) theoretical futures price = $355.87 |
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#1) theoretical futures price = $368.35 |
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#2) long futures contracts, and short the shares underlying the index |
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#2) long futures contracts, and buy the shares underlying the index |
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#2) short futures contracts, and short the shares underlying the index |
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#2) short futures contracts, and buy the shares underlying the index |
Theoretical Futures Price
= Index x (risk free interest rate - dividend yield) x 6/12
= 350 x (8%-3%) x 6/12 = 358.75
Since the price is 360 after 6 months, the arbitrage should be short futures contracts and by the shares underlying the index
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