Saturday, February 06, 2016

Investing (optical) illusion: Why a logarithmic graph is better than linear.

Warren Buffett in 1984 said that the Sequoia Fund which invest in stocks (public equity) were Superinvestors having outperformed the S&P 500 index uptil 1984. After that date they have also outperformed the S&P 500 index in the long-term, but the difference has gotten smaller not larger. During the past 5 years (Dec 31st 2010- Dec 31st 2015) relative results have been bad: Sequoia earned 11,9% while the S&P 500 gained 12,6% per year. (Style drift might be a factor?)

If you invested money with Sequoia on January 1st 2011 you might get the impression you beat the S&P if you based your evaluation on the linear chart Sequoia updates every year. The day you invested. December 31st 2010:

Change after 5 years: Graph on December 31st 2015

You could be forgiven for finding it "obvious" that Sequoia has done much better than the S&P 500 in the 5 years after 2010. This is an illusion, that is why professional fund managers prefer logarithmic charts over linear charts.

This one of the reasons early success for some years is so valuable for fund managers when marketing their fund to investors. A friend of mine has a great track-record, having increased $100 into more than $1200 since 2008. If he decided to open his fund to outside investors, he could underperform the index by 3% a year for 20 years and in a linear graph his fund would still look like a success.

Consider the >optical< difference between the same set of results presented in a linear and logarithmic scale. The results are exactly same, in both cases investors who invest money after year 10 earn more in the red fund than the blue fund!

Comments, questions or E-mails welcome:

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