$27.$ The one$-$year futures price on a particular stock$-$index portfolio is $2,240,$ the stock index currently is $2,200,$ the one$-$year risk$-$free interest rate is $3\%,$ and the year$-$end dividend that will be paid on a $$2,200$ investment in the index portfolio is $$22.b.$ What interest rate will it pay on that synthetic

The one$-$year futures price on a particular stock$-$index portfolio is $2,240,$ the stock index

currently is $2,200,$ the one$-$year risk$-$free interest rate is $3\%,$ and the year$-$end dividend

that will be paid on a $$2,200$ investment in the index portfolio is $$22.($LO $17-4)$

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.

c$.$ Now assume $($as is true for small investors$)$ that if you short$-$sell the stocks in the

market index, the proceeds of the short sale are kept with the broker 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 $2,200,$ how high and how low can the

futures price be without giving rise to arbitrage opportunities?

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.

C$.$ Now assume $($as is true for small investors$)$ that if you short$-$sell the stocks in the

market index, the proceeds of the short sale are kept with the broker 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 $2,200,$ how high and how low can the

futures price be without giving rise to arbitrage opportunities?