Hello,It is a long time I dont enter the forum....old good times...Anyway....I have a question...you could gimme a hand...I am simulating a hedge fund...just to write a comercial brochure....which distribution do you think that would fit best? (I am not risk neutral or anything like that, just real world).I dont like the normal dist. since I guess the probs. of large losses are larger in this case.What do you think it is right: negatevely skewed? I have on my software: beta, chi, erlang, expon, gamma, logistic, lognormal, normal, triangular, uniform, weibull, pareto, pearson and rayleigh.....Any ideas?Thanks

QuoteOriginally posted by: MahofferHello,It is a long time I dont enter the forum....old good times...Anyway....I have a question...you could gimme a hand...I am simulating a hedge fund...just to write a comercial brochure....which distribution do you think that would fit best? (I am not risk neutral or anything like that, just real world).I dont like the normal dist. since I guess the probs. of large losses are larger in this case.What do you think it is right: negatevely skewed? I have on my software: beta, chi, erlang, expon, gamma, logistic, lognormal, normal, triangular, uniform, weibull, pareto, pearson and rayleigh.....Any ideas?Thankshow are you going to calibrate? most importantly, how are you going to account for the fact that many hedge funds exhibit strategy migration?

Nonius,I forgot to say it is a multistrategy fund....I guess, since it is an example for commerical use (just an example of a structured note linked to a hedge fund), I will use the result provided by the normal distribution, maybe with some bias towards negative results...But i still have the question on the best way to model a hedge fund...to keep it simple suposse it is a sinle strategy and it doesnt plan to movebyethanksMh

For most simulation purposes, I prefer to transform a normal rather than picking a more exotic distribution. x - ax^2 might be a good hedge fund model.

due to the central limit theorem, just feeding a simulation with a non-normal distribution won't help:http://www.statisticalengineering.com/c ... heorem.htm

Or, in other words, in the long run we are all dead. But the short run matters.

Thanks people!!! It seems we all agree and normal is our choice.Aaron: what do you mean by x-ax^2, the calibration for the normal?THANKS AGAIN......

Mahoffer, if you have historical data of the hedge fund that you will invest in or be exposed to, I would use a block bootstrap method instead of the monte carlo. At least you are not imposing a distribution which may not fit with the returns you expect to receive. There are alot of hedge fund investment styles and all multistrategy hedge funds are not the same. The fund's investment style allocation process will dictate the nature of its returns. Anyway, if you have the historical data, at least that is your starting point with the block bootstrap.Re: style drift in hedge fund returns, well that's another story .....I suppose most people on the forum will disagree, but I would rather use the empirical distribution from a block bootstrap than from a simulated monte carlo.

I mean simulate a normal r.v. x, then compute x - ax^2 for some a. That will give you the negative skewness and kurtosis typical of most hedge funds, while still allowing simple analytic methods.If you bootstrap, I recommend bootstrapping on all hedge fund returns normalized for the standard deviation of your fund. The trouble with bootstrapping on a specific surviving fund is survival means it hasn't blown up, so your results will ignore the possibility of blow up, which is the most significant risk for hedge funds as a group.

Thanks a loT!!!!! I am learning a lot reading yar forums

So what would be the vol, if we were to sim with normal??Thanks~

If you simulate a Normal with mean m and variance v, then x - a*x^2 has mean:m + a*vand variance:v - m^2 -2*a*m*(m^2 + 4*v) + a^2*(m^4 + 6*m^2*v + 2*v^2)If you know the mean and variance you want for the hedge funds, you can solve those equations in reverse.

Thanks!However, how do we get the mean (m + a*v) and variance (that whole eq) in the first place?Use statistical technique, like regression, etc??I don't like using historical data to say that this is our mean and more importantly our implied vol.. for obvious reason.. However, I can't find a good proxy for HF index in general.. I'm trying to price an option on HF.... How can I get the implied vol?? Thanks!