S&P 500 futures price is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
Multiplier is 50
What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
•What position is necessary to reduce the beta of the portfolio to 0.75?
•What position is necessary to increase the beta of the portfolio to 2.0?
Current Beta of portfolio = 1.50
Value of portfolio = $ 5 mn
Multiplier = 50 i.e. 50 S&P 500 positions in 1 future contract
To hedge the portfolio, we need to short S&P 500 since S&P 500 and portfolio both have positive beta
Beta of S&P 500 = 1 {beta of market portfolio is always 1}
Hedging the portfolio is same as bringing beta to zero
No of future contracts required to hedge the portfolio = value of portfolio x (target beta - portfolio beta) / (value of future contract x multipler)
No of future contracts required to hedge the portfolio = 5000,000 x (0 -1.5) / (1000 x 50)
No of future contracts required to hedge the portfolio = -150 contracts
-150 contracts suggest that we need to short the future contracts
Therefore, short 150 futures contracts on the S&P 500 to hedge the portfolio.
Similarly to reduce the beta to 0.75
No of future contracts to reduce portfolio beta = value of portfolio x (target beta - portfolio beta )/ (value of future contract x multipler)
No of future contracts to reduce portfolio beta = 5,000,000 x (0.75 - 1.5) / (1000 x 50)
No of future contracts to reduce portfolio beta = -75 contracts
Therefore, short 75 futures contracts on the S&P 500 to reduce the beta of the portfolio to 0.75
Similarly to reduce the beta to 2
No of future contracts to reduce portfolio beta = value of portfolio x (target beta - portfolio beta )/ (value of future contract x multipler)
No of future contracts to reduce portfolio beta = 5,000,000 x (2 - 1.5) / (1000 x 50)
No of future contracts to reduce portfolio beta = +50 contracts
Therefore, long 50 futures contracts on the S&P 500 to increase the beta of the portfolio to 2.0
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