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I know that a lot of work has been done characterizing the first four moments of monthly hedge fund returns across a variety of fund types and strategies, and that work indicates that the higher moments are likely important. See for example Malkiel and Saha 2005.

However that information alone does not suggest any particular model.

Has anyone seen an expansion of the normal density or any other type of distribution used to model hedge fund returns, either for Monte Carlo simulation or some other application?

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References of the research mentioned in your question would enhance the overall quality. –  SRKX May 16 at 15:19
    
Is there anything else we could do for you? Otherwise it would be helpful if you accepted one of the answers - Thank you :-) –  vonjd May 23 at 14:14
    
There is a special issue of bankers, markets and investors about hedge funds: revue-banque.fr/medias/revues/bankers-markets-investors/… a very good reference indeed. –  lehalle Jun 5 at 5:21

4 Answers 4

I think modelling hedge fund returns is a very interesting yet demanding task. Your model will have to strike a balance between the tangibility of the model on the one hand and the possibility of parameter estimation on the other. Plus I think you will encounter hedge funds that resist all modelling attempts because there strategies are just too elusive.

The following very recent paper does a decent job in my opinion. They model hedge fund returns as a combination of factors (they use even investable ETFs to replicate the hedge fund returns) and estimate the parameters through a three step process.

In Search of Missing Risk Factors: Hedge Fund Return Replication with ETFs by J. Duanmu, Y. Li and A. Malakhov (March 2014)

From the abstract:

Properly considering all potential risk factors through tradable liquid portfolios in the context of a risk based factor model is paramount to quantifying the benefits of investing in hedge funds. We attempt to span the space of potential risk factors with exchange traded funds (ETFs). We develop a methodology of hedge fund return replication with ETFs based on cluster analysis and LASSO factor selection that overcomes multicollinearity among ETFs and the data mining bias. We find that the overall out-of-sample accuracy of hedge fund replication with ETFs increases with the number of ETFs available. This is consistent with our interpretation of ETF returns as proxies to a multitude of alternative risk factors that could be driving hedge fund returns.

We further consider portfolios of “cloneable” and “non-cloneable” hedge funds, defined as top and bottom in-sample R2 matches. We find superior risk-adjusted performance for “non-cloneable” funds, while “cloneable” funds fail to deliver significantly positive risk-adjusted performance. We conclude that our methodology provides value in both identifying skilled managers of “non-cloneable” hedge funds, and also successfully replicating out-of-sample returns that are due to alternative risk exposures of “cloneable” hedge funds, thus providing a transparent and liquid alternative to investors who may find these return patterns attractive.

You can then also use the resultant model to feed it into a monte carlo simulation because it is then only a combination of (tradable) ETFs which can be modeled and estimated with greater ease. So you effectively broke the whole task down into simpler subtasks which is always a good strategy.

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The higher "moments" are skewness and kurtosis. My former boss at Value Line wrote a paper that suggests that stocks that are "rich" in these higher "moments" tend to outperform. The reason would be the greater "optionality" (option potential) of stocks with these characteristics.

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I think the return distribution of a given hedge funds depends very much on its strategy. It can be well diversified (index-like return distribution, like gaussian with bigger tails) or it can basically have a strategy like some vanilla derivative (long/short call, put, straddle, butterfly). Depending on this the returns are convoluted with the payoff-function of the derivative the hedge funds strategy mimics.

I guess I'd try to classify hedge fund returns according to this.

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I'm sorry but you're not really answering the question; I think he wants the distributions you've seen used for HF (which will be different depending on their strategy, I agree on that). –  SRKX May 16 at 15:22
    
I said convolution of the measure with the pay-off function gives you the desired measure. So this is an answer on how to calculate a hedge funds return distribution. I proposed a toy model on how to classify and actually calculate the distribution. I think that should qualify as an answer. It is quite literally an expansion of the normal returns to other returns depended on specific investment strategies. What do you think how should an answer look? –  Marco Breitig May 17 at 10:28
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Well in my opinion it's still too vague for what was being asked. Could have been a simple comment. –  SRKX May 17 at 14:51

This is what I use see Why Distributions Matter

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This only links to a log-in screen :-( But anyway: What is your point? You should extend your answer considerably! It is no good fit as it stands. –  vonjd May 23 at 14:10

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