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Consider first the simple convergent strategy to invest some amount $X$ in a game, if you win you simply take the winnings and keep playing a subsequent game. In the case of a loss, you believe in your belief and doubles up in the same game until finally you win. This strategy would mostly experience small winnings up until some point when the losses are huge, in other words the distribution is heavily left skewed with a fat tail.

Now consider the divergent strategy to double winnings in case the game is won, i.e. holding on winners, and turn to the subsequent game in case of a loss. This strategy does instead experience small losses up until some rare occasions when there are huge winnings. The distribution of the divergent strategies is instead heavily right skewed, also with fat tails.

Going long in options, anticipating these rare events when the stock price plummets/sky rockets, etc.

Reality is rarely black and white, and more often than not you'll probably not able to classify more complex strategies as either divergent or convergent. But in general, is there any tendency in the hedge fund industry to prefer one over the other. It feels like there are a lot of greedy managers who would prefer earning lots of money fast, then there is this rare event which causes the fund to experience great losses and possibly even go bankrupt. However, it feels like the divergent strategy is a more sensible choice to stay competitive in the long run.

By looking at the larger and more successful managers/fund, what type of strategies do they use.

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Well, well ... First of all, i doubt people would think of hedge fund strategies in the way you are thinking. If I were to classify, the first order of a super high-level classification would be, for example, equity stock selection (e.g. say Apple vs Google, etc.), macro selection (e.g. currencies, commodities, country bets via stock indices, etc.), or bond/fixed income selection (e.g. NY muni vs. NJ muni, etc.). A second level of classification would be, frequency, i.e. short term, long term, etc.

Coming back to what you wrote, the largest managers are usually all very highly diversified and NO they won't be taking absurd bets any one thing (and kill any golden goose).

In terms of what you asked, the best hedge fund managers typically have (or aim to have) multiple strategies that would usually end up in a distribution (of daily returns) as close as possible to normal (due to central limit theorem), but with the mean of the returns as positive as possible (or rather the mean/std as high as possible). so, using your lingo, they are neither divergent nor convergent. Managers with daily returns that are either divergent or convergent wouldn't survive for long.

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I know, after googling the terms I can see that the notions are not widely applied in finance. Nonetheless, I think it is a useful way of thinking. Of course you can classify in terms equity, FX, commodities and what not. It doesn't tell you much more than what you're actually investing in. With regards to your last paragraph, that is not the CLT. Frankly, I think it's both naive and ludicrous to think that the aggregated returns of a hedge fund would be normally distributed just because they have multiple strategies (or in any case). –  Good Guy Mike Apr 9 at 15:02
    
@GoodGuyMike, not in my experience (14 years as a hedge fund/fund of hedge fund quant). top hedge funds (wherever I had access to managed accounts, i.e. daily positions) indeed had normally distributed returns. there have been weaker funds that solely do niche strategies like carry, levered bond (coupon collecting) that have non-normal distributions, but such firms either lose a lot of money once every bear-bull cycle (e.g. in 2008) and go out of business OR don't make much money most of the years (e.g. short sellers) except a few years and investors lose interest in them. –  uday Apr 9 at 17:14
    
Well Ok, obviously I can't really argue against it since I haven't seen the figures. What you mention last is more to my point though. So the weaker funds do niche strategies that for some period of time makes a lot of money. But then, as a result of some rare event, they lose a lot of money. In other words they have a very fat left tail. This is typical characteristic of the convergent strategy. My point is now that even though it is a niche strategy, it must not be convergent. If they instead deployed a divergent strategy they could survive these rare events. –  Good Guy Mike Apr 9 at 19:19
    
@GoodGuyMike, Well, the thing is that most established managers combine a lot of strategies, some of which individually could be convergent or divergent in your terms, and most neither. The net result is often a normally distributed daily returns. Niche strategy managers like the ones I described are usually quite rare. More over, most hedge fund investors (institutions, pensions, etc) implicitly or explicitly prefer managers that don't have weird distributional performance behavior. –  uday Apr 10 at 13:03
    
Of course, having multiple strategies is certainly better. That requires a lot of recourses thought, in particular human capital. –  Good Guy Mike Apr 10 at 17:55
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