Question

A equity fund manager has a portfolio worth $100 million with a beta of 1.27. The current level of S&P 500 index is 2,650. The price of one- month S&P 500 futures contract is 2,680. One contract is on $250 times the index points.  What position should the fund manager take if she/he wants to change the portfolio to be a double- leveraged index ETF over the next month?

Answer 1

The current Beta of the fund is 1.27 which implies that if the excess returns on the S&P500 is 1%, the excess return on the fund would be 1.27%

The target is to make the Beta of the fund = 2 using S&P 500 futures. SInce the target is to increase the Beta of the portfolio, the direction of the position in the index futures should be long.

No. of lots to go long in S&P500 1m futures contract = (Target Beta-Intitial Beta)*(Portfolio size) / (futures price*multiplier) =

(2-1.27)* $100mn / (2680*250) = 109 contracts

The caveat here is that the portfolio is tracking the S&P500 index while the Beta has been increased through S&P 500 index futures. Change in basis i.e. the difference between the index and futures would require dynamic rebalancint to achive the stated objective.