Friday, August 29, 2008

Which Type of Hedge Funds Give the Most Diversification Benefits?

I recently read a very interesting article about using hedge funds to diversify that was discussed by AllAboutAlpha. Adding hedge funds to a portfolio can both increase returns and reduce variability. Even if a hedge fund's returns were perfectly correlated with your existing portfolio's, if it had a positive alpha, allocating some money to the hedge fund might increase return and reduce drawdown relative to your existing portfolio. See my discussion of alpha-beta separation. But usually what is meant by diversification is adding assets whose returns are imperfectly correlated to the returns of the original portfolio. But you can go beyond that to also take into account "the higher moments" of the return distribution.

So what are "higher moments"?

The first moment of a distribution is the mean or in ordinary English the average. The second moment is the variance or its square root the standard deviation, which captures how tightly packed values of the variable are around the average. The "normal distribution" - the classic bell curve - can be entirely captured by these first two moments:

The mean is at zero and the numbers on the x-axis are standard deviations from the mean. The normal distribution always looks exactly like this, though the actual numerical value of a standard deviation could be larger or smaller and the mean might be different to zero.

The third moment of a distribution is skewness. A distribution is skewed if one side of the distribution is much more stretched out than the other:

A positively skewed distribution has a long-tail to the upside. The fourth moment is kurtosis which measures how sharply the distribution peaks and how fat the tails are:

The distribution marked in red is the most kurtotic. No longer is there a plateau of many values clustered around the mean, but values are dispersed towards the extremes.

An investment with negatively skewed and positively kurtotic returns is prone to "crashes". The MSCI world index has negative skewness and positive kurtosis.

The standard "beta" in the finance literature measures how much an investment's returns change when the returns on another investment change. Usually we are measuring how much a security's or an asset class' returns change in relation to the returns of the "market portfolio" or a stock index like the S&P 500. But we could also measure the relationship between the variances of two investments and the relations between the higher (3rd and 4th) moments of the distributions.

An investment with a low (less than one) or negative conventional beta to an existing portfolio will reduce the volatilty of that portfolio. A low variance beta means that when the volatility of the portfolio rises due to market conditions the additional investment will mitigate that increase in volatility by contributing less or even a negative amount to the increase in volatility. As is well known, the correlation between most investments seems to rise when market volatility rises. It would be really nice if we could find investments that reduced the tendency of our portfolio to experience extreme negative events. Investments with low and negative skewness and kurtosis betas will be best at achieving this.

Finally getting to the point :), the paper computes these higher order betas for a variety of hedge fund indices with respect to the MSCI index (the estimates are for monthly data from January 1994 to February 2006):

Any betas below one have diversification benefits. By far the best diversifier is managed futures. Fixed Income Arbitrage, Equity Market Neutral, and Convertible Arbitrage are also good diversifiers. The least good diversifier is long-short equity, which includes the likes of 130/30 strategies. Only managed futures and equity market neutral have normal returns, though Global Macro and Long-Short Equity also both have zero or positive skewness:

The author adds a mixture of the best diversifying hedge fund indices to a 60% equities and 40% bonds portfolio and finds increased returns and reduce variance for all mixes up to a 35% allocation to diversifiers. I have a feeling that if he tried pure managed futures the gains would be even better.

Given these results, and the high returns to some managed futures funds a large allocation to managed futures could be very advantageous (subject to tax considerations). For more on the advantages of commodities and managed futures see the Ibbotson-Pimco study.

BTW, another new category today: "Hedge Funds".

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