A manager of $30 million in mid-cap equities would like to move half of the position to an exposure resembling small-cap equities. The beta of the mid-cap position is 1.0, and the average beta of small-cap stocks is 1.6. The betas of the corresponding mid and small-cap futures contracts are 1.05 and 1.5 respectively. The mid and small-cap futures prices are $260,000 and $222,222 respectively. What is the appropriate strategy?
A) Short 55 mid-cap futures and go long 72 small-cap futures.
B) Short 17 mid-cap futures and go long 17 small-cap futures.
C) Short 17 small-cap futures and go long 17 mid-cap futures.
That means will have to sell $15 million of mid-cap equities and use the cash (beta = 0) to buy $15 million of small-cap equities.
To replicate this synthetically using derivatives, we will synthetically sell by selling the mid-cap futures contracts on the $15 million of the mid-cap equities (to reduce the mid-cap beta from 1.0 to 0.0, i.e. synthetic cash/risk-free asset).
You’re not actually selling anything from the equity portfolio to do this. Your just reducing your exposure by selling futures. If the beta of the target portfolio is ever less than the current portfolio, you will be selling futures (as far as I know, no futures contracts trade with a negative beta).
If I have a portfolio worth $100 million SPX but sell $50million worth of SPX futures - I realistically only have a $50 million SPX portfolio with $50 million in cash on the side. Which is highly tax efficient if you don’t want to realize gains but prepare for a big downturn, or completely change exposure.
