Problem $5\mathrm{.}1.$

Explain what happens when an investor shorts a certain share.

Problem $5\mathrm{.}2.$

What is the difference between the forward price and the value of a forward contract?

Problem $5\mathrm{.}3.$

Suppose that you enter into a six$-$month forward contract on a non$-$dividend$-$paying stock when the stock price is $$30$ and the risk$-$free interest rate $($with continuous compounding$)$ is $5\%$ per annum. What is the forward price?

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Problem $5\mathrm{.}4.$

A stock index currently stands at $350.$ The risk$-$free interest rate is $4\%$ per annum $($with continuous compounding$)$ and the dividend yield on the index is $3\%$ per annum. What should the futures price for a four$-$month contract be$?$

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Problem $5\mathrm{.}5.$

Explain carefully why the futures price of gold can be calculated from its spot price and other observable variables whereas the futures price of copper cannot.