Question

If the portfolio manager manages $100 million of equity with a beta of 1.2 and wishes to create a net short position with a beta of -2.0, and the equity futures contract size is (250 (multiplier) X 3,048 (current S & P 500 index)) = 762,000, the futures beta is 1.03, how many contracts must be transacted? Long or short?

Answer 1

Answer :

• number of futures contracts EQA = 408
• we should sell future

Explanation :

Summary of the information provided in the question :

• Asset size = $ 100 M
• Current beta = 1.2
• New beta = - 2.0
• future contract size = 250 (multiplier) X 3,048 = 762,000
• future beta = 1.03

The number of futures contracts EQA should use is

={(new beta - current beta) / future beta } x { (asset size) / (future contract size)}

={(-2.0 - 1.2) / 1.03} x { (100,000,000) / (762,000)}

={(-3.2) / 1.03} x { 131.23}

={-3.106796} x { 131.23}

= - 407.70

= - 408 (rounded to new $ 1.00)

Conclusion : as We have assessed the beta will be decreased to -2.0 from current beta of 1.2 (i.e. new beta will be less than current beta) sign of the number of futures contracts will be negative hence we should sell future. i.e. short contract)