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A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9? A. Short 48 contracts B. Long 192 contracts C. Long 48 contracts D. Short 192 contracts

Question

A company has a 36millionportfoliowithabetaof1.2.Thefuturespriceforacontractonanindexis900.Futurescontractson36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on 250 times the index can be traded. What trade is necessary to reduce beta to 0.9?

A. Short 48 contracts

B. Long 192 contracts

C. Long 48 contracts

D. Short 192 contracts

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Solution

The correct answer is:

A. Short 48 contracts

Here's the reasoning behind this choice:

The company wants to reduce the beta of its portfolio from 1.2 to 0.9. The change in beta required is 1.2 - 0.9 = 0.3.

The value of the portfolio is 36million.Therefore,thechangeinvaluerequiredtoachievethechangeinbetais0.336 million. Therefore, the change in value required to achieve the change in beta is 0.3 * 36 million = $10.8 million.

Each futures contract is on 250timestheindex,sothevalueofeachcontractis900250 times the index, so the value of each contract is 900 * 250 = $225,000.

The number of contracts required to achieve the change in value is 10.8million/10.8 million / 225,000 = 48 contracts.

Since the company wants to reduce its beta, it needs to short the contracts. Therefore, the company needs to short 48 contracts.

This problem has been solved

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