The one year futures price on a particular stock index portfolio is 1,825, the stock index currently is 1,800, the one year risk free interest rate is 3 , and the year end dividend that will be paid on a $1,800 investment in the index portfolio is $25 a By how much is the contract mispriced b Formu...

a From parity F 0 S 0 1 r f d 1800 1 03 25 1829 Actual F 0 is 1825 so the futures price is 4 below i ...

The one-year futures price on a particular stock-index portfolio is 1,825, the stock index currently is 1,800,

Question:

The one-year futures price on a particular stock-index is 1,825, the stock index currently is 1,800, the one-year risk-free interest rate is 3%, and the year-end that will be paid on a $1,800 investment in the index is $25.
a. By how much is the contract mispriced?
b. Formulate a zero-net-investment arbitrage and show that you can lock in riskless profits equal to the futures mispricing.
c. Now assume (as is true for small investors) that if you short-sell the in the market index, the proceeds of the short sale are kept with the and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming you don't already own the shares in the index)? Explain.
d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relationship? That is, given a stock index of 1,800, how high and how low can the futures price be without giving rise to arbitrage opportunities?
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