$3.$ Suppose that the standard deviation of quarterly changes in the prices of a foreign exchange is $$0\mathrm{.}65,$ the standard deviation of quarterly changes in a futures price on the foreign exchange is $$0\mathrm{.}81,$ and the coefficient of correlation between the two changes is $0\mathrm{.}8.$ What is the optimal hedge ratio for a three$-$month future contract? What does it mean?

$4.$ On July $1,$ an investor holds $50,000$ shares of a certain stock. The market price is $$30$ per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P $500$ futures contract. The index is currently $1,500$ and one contract is for delivery of $$50$ times the index. The beta of the stock is $1\mathrm{.}3.$ What strategy should the investor follow?

$6.$ A company wishes to hedge its exposure to a new fuel whose price changes have a $0\mathrm{.}6$ correlation with gasoline futures price changes. The company will lose $$1$ million for each $1$ cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is $50\%$ greater than price changes in gasoline futures prices.

a$.$ If gasoline futures are used to hedge the exposure, what should the hedge ratio be$?$

b$.$ What is the company's exposure measured in gallons of the new fuel? c$.$ What position measured in gallons should the company take in gasoline futures?

d$.$ How many gasoline futures contracts should be traded? Assume that each contract is on $42,000$ gallons.

$6.$ A bank executive has argued: $$There is no point in our using foreign currency futures. There is just as much chance that the price of foreign currency in the future will be less than the futures price as there is that it will be greater than this price.$$ Discuss the executive$$s viewpoint.

$7.$ Drago Inc. is planning to purchase plastic nuts and bolts from a Korean auto manufacturer. The purchase price was $7$ million Korean Won and is due in $3$ months. The exchange rate is $$1$ to $1120$ Korean Won. Discuss the utilization of money market hedge if the rates for borrowing and lending are as follow: $$ Deposit rates $(3$ months$)$: Korea $4\mathrm{.}5\%$ annual US $4\mathrm{.}2\%$ annual $$ Borrowing rates $(3$ months$)$: Korea $5\mathrm{.}75\%$ US $5\mathrm{.}1\%$ annual

$8.$ In another $6$ months, Drago Inc. will receive RM$10$ million from a Malaysian auto importer. The exchange rate is $$1$ to RM$4\mathrm{.}15.$ Discuss the utilization of money market hedge if the rates for borrowing and lending are as follow: $$ Deposit rates $(3$ months$)$: Malaysia $4\mathrm{.}4\%$ annual US $4\mathrm{.}1\%$ annual $$ Borrowing rates $(3$ months$)$: Malaysia $5\mathrm{.}65\%$ US $5\mathrm{.}2\%$ annual

$9.$ The following represents the exchange rate information for the Thai Baht and the Singapore Dollars $($SGD$)$:

Spot market: USD $1$: $30\mathrm{.}34$ Baht

USD $1$: SGD$1\mathrm{.}35$

$3-$month Forward market:

Baht: $3\mathrm{.}10$ discount

SGD: $0\mathrm{.}01$ premium

$$ Calculate the cross rate for the Thai Baht and the Singapore Dollars $($SGD$)$

$$ Calculate the percentage of Thai Baht expected to depreciate against the U$.$S$.$ Dollars in three months

$$ Calculate the percentage of Thai Baht expected to depreciate against the Singapore Dollars