Suppose the one$-$year futures price on a stock$-$index portfolio is $1218,$ the stock index currently is $1200,$ the one$-$year risk$-$free interest rate is $3\%,$ and the yfar$-$end dividend that will be paid on a $$1,200$ investment in the index portfolio is $$15.$

a$.$ By how much is the contract mispriced?

b$.$ Formulate a zero$-$net$-$investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing. Assume a zero bid$-$ask spread in security and futures transactions.

c$.$ Now assume that if you short sell the stocks in the index portfolio, the proceeds are kept with the broker, and you do not receive any interest income of the funds. Is there still an arbitrage opportunity $($assuming that you don't already own the shares in the index$)?$

d$.$ Given the short sale rules, what is the no$-$arbitrage band for the stock$-$futures price relationship? Specifically, how high and how low can the futures price be without giving rise to arbitrage opportunities.

MacBook Air