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Chapter 19 - Return Statistics and Risk > 19.1 CALCULATING RETURN STATISTICS

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 – see Figure 19.1. While informative about the final value of the investment, this type of graph does not throw much light on progress since the inception. The reason is that the whole graph is conditioned on the terminal value, so that a large percentage loss at the beginning (e.g. -17.46% in November 1987, when the amount invested is small) will appear smaller than a small percentage loss towards the end (e.g. -6.53% in April 2000, when the amount invested is large).

  

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