Berkshire Hathaway Inc. (NYSE: BRK.A) would like to hedge its $5 million exotic

Question

Berkshire Hathaway Inc. (NYSE: BRK.A) would like to hedge its $5 million exotic insurance portfolio by using S&P 500 futures. Having heard about your excellent grades in the Derivatives class, Berkshire chairman Warren E. Buffett has hired you as a consultant to help construct this hedging trade. Mr. Buffett believes that the correlation between the returns of his insurance portfolio and that of index futures is -0.52. He also provides you that the standard deviation of the returns of the insurance portfolio and index futures is 5% and 2% respectively. Assuming that one contract of index futures has a value of $180,000 today, how many contracts should Mr. Buffett buy or sell for the best hedge?

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Explanation / Answer

Value of the Insurance Portfolio = $ 5,000,000

Standard Deviation of Insurance Portfolio SDp = 5%

Standard Deviation of S&P 500 Index Futures SDi = 2%

Correlation coefficient of Portfolio and Index Futures p = -0.52

Contract size of Index Futures = $ 180,000

Minimum variance hedge ratio can be calculated using the formula

h* = p * (SDp/SDi) = -0.52 * 0.05/0.02 = -1.30

Optimal Hedge Ratio can be calculated using the formula

N = h* * (Value of the Asset)/ (Size of the Futures contract)

N = -1.3 * 5,000,000/180,000 = - 36.11 or - 36 contracts

Since the value is negative the position taken will be opposite to that of the position held.

For example the asset held is in long position then the hedging position should taken in shorts.

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