Handbook of Hedge Funds

19

Return Statistics and Risk

Surprisingly, it seems impossible to meet with a hedge fund manager that is not top quartile

Despite the deep-seated belief of many people that human beings are the most intelligent and complex animals on earth, we have to temper this belief about our intellectual superiority with a measure of humility. The average human brain fails miserably when dealing with more than 10 to 15 numbers. By comparison, the simplest computer is many times more powerful and more capable because it can perform calculations thousands of times faster, work out logical computations without error and store memory at incredible speeds with flawless accuracy.

19.1 CALCULATING RETURN STATISTICS

When the number of returns increases significantly beyond the threshold of 10 to 15, the human brain needs statistics to summarize and understand the information. As we will see, dimension reduction is a leitmotif of statistics.

As an illustration, consider Table 19.1, which shows the series of simple monthly returns for a hedge fund since its inception. In total, there are 233 numbers, far too many for our brain to be able to identify any pattern or trend. To be interpretable, this collection of returns must be organized in some sort of logical way.

One of the easiest ways to reorganize a return series and make it more intelligible is to plot it in some sort of graphical form. The graph preferred by marketers is the historical evolution of $100 invested in the fund in question – ...