Suppose the six-month DAX futures contract trades at 4,000 when the current (spot) DAX index is 3, XXXXXXXXXXThe interest rate is 3% per year (about 1.5% over six months) and the dividend yield on the...

Suppose the six-month DAX futures contract trades at 4,000 when the current (spot) DAX index is 3,980.10. The interest rate is 3% per year (about 1.5% over six months) and the dividend yield on the index is 2% (about 1% over six months). These numbers fit the formula because Ft =3,980.10 x (1 +.015 -.01) =4,000 but why are the numbers consistent? Suppose you just buy the DAX index for 3,980.10 today. Then in six months you will own the index and also have dividends of .01 X 3,980.10 = 39.80. But you decide to buy a futures contract for 4,000 instead, and you put €3,980.10 in the bank. After six months, the bank account has earned interest at 1.5%, so you have 3,980.10 X 1.015 = €4,039.80, enough to buy the index for 4,000 with €39.80 left over, just enough to cover the dividend you missed by buying futures rather than spot. You get what you pay for.
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