Recently, one of our team members had lunch with a hot shot hedge fund manager in Hong Kong. This fund manager, a truly hot shot, multimillion dollar guy, who had finally acquiesced to the request of going out for a lunch after almost seven months, had simply come out to deride our company and all that we stand for. He found the concept of a few, supposedly well informed quants, running a noodle shop instead of working in an ibank or a hedge fund ridiculous. To him we were a bunch of jokers. But so be it, a lesser mortal was finally having an audience with the god.
He was surprised that we were still around and able to pay our bills after a year or so and updated us right away about he was panelist and a speaker in half a dozen investor and hedge fund conferences in AsiaPacific. After some time our mate found his voice and the first question he asked was how were his funds doing. ¡§Great¡¨ he replied. His star fund, a long short equity fund, had apparently returned 8%, 18% and 12% in the last three consecutive years and he was on top of the world. His fund had apparently grown to US$350 million in size. (Please note the use of word apparently, which is a must when we talk of specifics about any hedge fund).
Looking at the amazing returns and growth of the profits in the fund our mate couldn't help asking him a simple question: John, if you don't raise any more capital but use your current fund for trading, then what is the probability that your fund will grow to $700 million in five years time? I mean, assuming your past three years return are going to be consistently repeated what is the probability that $350 million will become double its size in five years?
The fund manager replied, "That's a stupid question, how the hell will I know what will be the return next year and the year after that and so on. I can only say that the returns will be great and our strategy is really fool proof and we will come out on the top". I can double my fund in a year or in ten years, who can tell. But we are confident of returning double digits returns consistently.
It wasn't a stupid question at all. It was actually a very fundamental question that our colleague had asked, a question that every investor should ask his fund manager before he hands over his money."What is the probability that $1 million will become $1.5 million in five years time?"
Let's say that you came to John, our fund manager, with a $1 million fund. And given the history of John's returns for the past three years you wanted to estimate what are the chances (read probability) that your $1 million will grown to $1.5 million in five years time.
Let us say past six years Investment Returns of John's long/short equity fund were: 11%, 6%, 2%, 8%, 18%, 12%. Then assuming that the natural logarithm of one plus the holding period returns are normally distributed (i.e. returns are lognormally distributed) we get a table like this:

Annual Return 
In (1 + Return) 
11% 
11.65% 
6% 
6.19% 
2% 
1.98% 
8.00% 
7.70% 
18.00% 
16.55% 
12.00% 
11.33% 
Arithmetic Average 
3.83% 
3.29% 
Standard Deviation 
11.00% 
10.72% 
The second column above is the natural logarithm of one plus the annual holding period return for the fund manager.
From the above we can compute the normal deviate Z as follows:
This shows that the value of the normal deviate is 1.005763. In other words the required five year continuous return (that will make $1 million grow to $1.5 million) is 1.005763 standard deviations away from the expected five year continuous return of the fund as given by the history of the fund.
If we look up the normal distribution table then we will find that the above corresponds to 15.73% chance that $1 million will grown to $1.5 million in five years time if history is any guide to John's performance.
But is history any guide to the future? And if we don't have history to guide us into the future then what do we have? Random events, uncertainty, and a whole lot of other unquantifiable numbers. So what do we do then?
Well, we can use Dynamic Financial Analysis (DFA) like the insurers do using Monte Carlo simulation and stress tests on John's portfolio to figure out Whither John!
But why spoil the lunch any further. John's apparently had lost his appetite and so he left our mate to finish the meal and left early. But he paid the bill. The upside about asking simple questions to hedge fund managers over an expensive meal is that they end up buying you lunch.
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