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Hedging Portfolio Risk

As an example, recall from Chapter 7 that we estimated β = 2 against the S&P 500 for Citigroup. Suppose an investor wants to hedge downside risk on an investment in this stock. Suppose there is no futures contract available for Citigroup, but there is a liquid futures market for the S&P 500. This investor could short S&P futures contracts to hedge tail risk on a 2:1 basis. So, if she has a portfolio P = $100,000 in Citigroup stock and one-month S&P 500 futures are at F = $1,000, then she needs to short 200 futures contracts on the S&P 500. That is, the required short futures position N is equal to , where P is the value of the Citigroup portfolio and F is the futures price on the S&P 500.

It is worthwhile noting that short hedges like the one just described effectively change the portfolio's beta. In this case, the portfolio had a beta of 2, which was reduced to zero with the hedge. Thus, the hedge effectively eliminated the portfolio's exposure to broad market movements. In fact, investors can use short and long futures exposures to achieve any desired beta and, with it, the associated risk and return. In the previous example, shorting 100 futures contracts on the S&P 500, for example, would result in hedging out half the downside risk, effectively pulling beta back to 1 on the portfolio. On the other hand, a long futures position equal to 100 contracts will ...