Dilemmas in Hedging

When constructing a long/short, market neutral portfolio, the goal is to have the short portfolio "perfectly" hedge the long portfolio, neutralizing the market's influences, leaving the relative performance between the two from just stock selection. This construction is easier said than done.

A common technique is to construct a well-diversified long portfolio, then use a "mirror image" short portfolio that has similar industry, sector and other exposures to match the long portfolio?s market sensitivities. This could be a "dollar-neutral" construction, or the same amount invested long and short, but this might not form a perfect hedge. Despite similar sector and industry exposures, parallel long and short portfolios can have quite different market sensitivities.

The overall market sensitivity is measured by beta, or the portfolio's ratio of covariance with the market to the market's volatility. The market beta is defined as 1.0, so a portfolio with a lower beta, say 0.8, will move roughly 80% of the market's movement, up or down. Conversely, a portfolio with a higher beta, say 1.2, will move 20% more, up or down, than the market.

To hedge a long portfolio with a short portfolio that has a different beta, perhaps due to mirror image holdings that are perceived as overvalued but riskier, the key is to match the dollars invested times the beta. Thus, a $100,000 long portfolio with a beta of 0.8 has $80,000 of market "exposure", and to hedge it with a 1.2 beta short portfolio would require that it be worth ($80,000 / 1.2) $66,666.

So the "market neutral" portfolio would have $100,000 of longs and just $66,666 of shorts, with the expectation that the dampened response of the long portfolio relative to the market would be hedged by the much lower value but more volatile short portfolio. Only under the special circumstance where the long and short portfolios have the same betas will the dollars invested be the same, otherwise there will be a dollar mismatch, but the overall portfolio will be beta-dollar neutral.

A further wrinkle to dollar-beta neutral hedging is the phenomena of up and down market betas. These are the subset sensitivities that stocks or portfolios have depending on the market's direction. An up market beta is how a stock or portfolio behaves when the market is up and vice versa and these values do not have to be the same. Thus, in theory a long portfolio with an overall beta of 1.0, might have an up market beta of 0.9 and a down market beta of 1.1, whereas a short portfolio could be just the reverse, 1.0 overall, 1.1 up, 0.9 down.

In that case, during up markets, the short portfolio "over-hedges" the long portfolio, potentially causing a loss, and during down markets, the short portfolio "under-hedges". So, despite appearing perfectly hedged using the overall betas, market direction can undo the presumed "market neutrality".

Lastly, betas aren't stable, they can change over time, although less so at the portfolio level. And the calculation method can lead to quite different results. Typically, betas are measured from monthly returns over the last five years, but shorter, more frequent measurements might be more appropriate and predictive. Overall, hedging the market with anything other than an exact duplicate investment (which leaves no room for return other than potentially a little arbitrage) is a challenging endeavor. And this doesn't even touch the stock selection methodologies, which are the primary sources or returns. Hedging market risk is risky!

Comments

[Z PM]

Very good article Dan, allows people to really understand the quantitative analysis that goes into investing. I've never actually used the up or down beta, but that was very interesting. Sort of the same situation as Sharpe vs. Sortino. Although overall, I tend to treat the beta's with a 'grain of salt' as there are so many different ways of calculating them, and there are plenty of problems with the simple regression model. You really need a high R-squared for the beta to have real meaning.

[DaveW]

Easier answer: move porfolio to cash = market neutral, step out of the think tank and breathe the fresh air. :)

[icandoitdon]

yes. move to cash if you want neutrality. i'll change my mind if you can recommend a hedge fund that will guarantee no less than a t-bill rate of return. good luck. they don't exist.