Convergent and Divergent Strategies: Return Skew and Diversification
Summary
The document contrasts two stylized betting approaches. A convergent strategy increases exposure after losses and takes gains after wins, producing frequent small gains alongside the possibility of a very large loss. A divergent strategy increases exposure after wins and stops or moves on after losses, tending toward frequent small losses with occasional large gains. Long option positions are offered as an example of seeking rare, outsized market moves.
The response argues that hedge fund strategies are usually classified by markets and investment horizon rather than this simple distinction. It describes larger managers as diversified across strategies and says they seek positive average returns with comparatively stable daily outcomes and an attractive mean relative to volatility. These are broad claims, not supported with performance data or a detailed risk model. The answer also treats the normality of diversified returns as an aim or intuition, not a guarantee; the document does not explain how diversification handles dependence, tail events, leverage, or funding risk.
Key ideas
- Increasing exposure after losses can create frequent small gains and large downside losses.
- Increasing exposure after wins can create frequent small losses and occasional large gains.
- Long options are presented as one way to seek gains from rare, substantial price moves.
- The response says managers commonly classify strategies by asset area and time horizon.
- Diversifying across strategies is described as a way to pursue positive average returns relative to volatility, though no evidence or implementation method is provided.
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Full text
# Divergent or Convergent Strategies? Which is the way to go? # Divergent or Convergent Strategies? Which is the way to go? 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. ## Answer by uday (score 2) https://quant.stackexchange.com/a/10867 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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