# Example three a portfolio manager decides to hedge

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Example three
A portfolio manager decides to hedge his equity portfolio with an index futures contract. Thecorrelation between the portfolio value and futures price is 0.8. The standard deviation of theportfolio value is 40% and that of the futures price is 38% per annum. Calculate the hedge ratioand comment.
Example fourConsider a long forward contract to purchase a non dividend paying stock in three months.Assume the current stock price is sh 40 and the three months risk free interest rate is 5% perannum. We consider strategies open to an arbitrageur in two extreme situations.
Suppose first that the forward price is relatively high at sh 43. An arbitrageur can borrow sh 40 atthe risk free interest rate of 5% per annum, buy one share and short a forward contract to sell oneshare in three months. At the end of the three months, the arbitrageur delivers the share andreceives sh 43. The sum of money required to pay of the loan is;40e0.05x123sh40.50By following this strategy the arbitrageur locks in a profit of sh 43.00 - 40.50 = sh 2.50 at the endof the three months period.Suppose next that the forward price is relatively low at sh 39. An arbitrageur can short one share,invest the proceeds of the short sale at 5% per annum for three months and take a long position3in a three month forward contract. The proceeds of the short sale grow to;40e0.05x12Or sh 40.50 in three months. At the end of the three months, the arbitrageur pays sh 39, takesdelivery of the share under the terms of the forward contact and uses it to close out the shortposition. A net gain of sh 40.50 – 39.00 = sh 1.50 is therefore made at the end of the three months.Example fiveConsider a nine month futures contract on a non dividend paying stock with a share price of Sh.60 and a risk free rate of 10% per annum. The theoretical futures price is Sh. 64.67.Determine the cash and carry arbitrage opportunity if the actual future price available in themarket is:(i)Sh 65(ii)Sh. 64
Buy the underlying asset (share) immediately for Sh. 60It will be assumed this sum will be borrowed at 10% pa for 9 months.

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Term
Fall
Professor
Professor George Musumba
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