Fuzzy Math!

Have you ever seen literature from a fund posting attractive gains and comparing its performance to that of the benchmark S&P 500?  Have you ever investigated how the figures listed were calculated?  If not, you will definitely want to read on!

Let’s take a fairly representative example.  Fund Manager Joe Bull, for example, is very good at generating profits in bull markets.  Let’s say Joe Bull made 20% in each of the years 2004, 2005, 2006 and 2007.  But Joe Bull does not have the toolset to survive bear markets and finds in 2008 that he is down 30%.  What has Joe Bull’s return been over 5 years?

It turns out, the answer to that questions depends greatly on what Joe Bull wants to report as his return!  Why? Because little regulation exists to prevent Joe Bull from choosing any number of mathematical approaches to calculate his return!

For example, fund manager Joe could simply take the average of his returns over 5 years.  This would be calculated as the sum of 20% + 20% + 20% + 20% -30%, all divided by 5.  So, this would be equal to 50% / 5 or 10%. 

Or Joe could choose to report the nominal annual rate with no compounding or the nominal annual rate with compounding or indeed the effective annual rate assuming continuous compounding!  Depending which of these approaches was chosen, the returns would be 9%, 7.7% or 7.4% respectively!

So, step into fund manager Joe’s shoes for a moment.  You need more investors because inevitably some existing investors will leave based on the most recent decline of 30%.  How should you market your return?  Which return should you choose?  Which will attract most new clients?

Obviously, the double digit average return stands out.  But that’s not where the marketing typically ends.  Joe now will want not only to show his return but his return relative to some benchmark, say the S&P 500.  So, if no regulation restricts Joe from choosing a methodology to denote the performance of the S&P 500, which do you think he will choose? 

That’s right, the lowest return; the effective annual rate assuming continuous compounding!

Most investors simply hand over their money in trust.  Few are sophisticated enough to know which method is used to calculate the overall return.  But now that you know the subtleties, make sure to look closely to determine which figures are being used and whether like-for-like comparisons are being made.

If you want to know what’s really scary about this.  Think about the fund manager who makes, 50%, 50%, 50%, 50% and -100%!  What’s left after 5 years?  Well zero obviously; all was lost in the final year!  But calculating the average return (50% + 50% + 50% + 50% - 100%) / 5 still results in a positive figure, 20%!  That’s right, the manger lost all the money but can still claim a 20% average return!  [For emphasis, make sure to read the fine print!].

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