# Hedging using futures and optimal hedge ratio

You wish to hedge 90 percent of the current portfolio value with futures. The value of the portfolio is $50 million and tracks the S&P 500 index. The index in 1,076.32 ($250 per point) and the portfolio has a beta of 1.2. Calculate the appropriate hedging using futures contracts.

Hint: Calculate using the optimal hedge ratio.

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You wish to hedge 90 percent of the current portfolio value with futures. The value of the portfolio is $50 million and tracks the S&P 500 index. The index in 1,076.32 ($250 per point) and the portfolio has a beta of 1.2. Calculate the appropriate hedging using futures contracts.

Hint: Calculate using the optimal hedge ratio.

Current index value= 1076.32

Current value of the portfolio= $50,000,000

Beta of the portfolio= 1.2

The value to be hedged=90% of the portfolio=90%*$50,000,000= $45,000,000

When the value of portfolio decreases by 10% the value of index will decrease by 10% / β=10%/1.2= 8.3333%

Therefore the value of index will be 1076.32X(1-8.3333%)= 986.63

Therefore short futures as we are long on ...

#### Solution Summary

The solution provides the step by step calculation for hedging a portfolio that is tracking S&P 500 index. It also provides illustrations for cases when S& P index rises and when S& P index falls