Large numbers

The danger of dual trending

Forbes_peStatisticians have long advised against forcing two data series with different scales onto the same chart, using dual vertical axes.  The use of color to match data to axis reduces the confusion but in no way prevent the reader from coming to mischievous conclusions, such as this from Forbes magazine:  "If history is any guide, the recent run-up in assets [i.e. capital] ... bodes ill for future returns."

The "run-up" in assets evidently refers to the slight uptick in 2002.  The huge gap between returns and capital from around 1993 to 2001 gives the impression that high returns are correlated with low capital commitment. But this gap is completely an artifact of the chosen scales, as I have discussed before.

For two data series, the scatter plot provides the most illuminating insights.  In this format, one can hardly claim any strong association between the two variables!


Indeed, we notice that there have only been two observations in the last 20 years or so in which the capital commitment has exceeded 0.23% of the stock market.  While those two observations were both paired with low returns, they themselves do not indicate any trend.  Referring back to the trend chart, we further note that both those observations occurred about 20 years ago.  Besides, we have several instances of the same low returns when the capital commitment was low.

Moreover, at the most likely levels of capital commitment (i.e. between 0 and 0.2%), any level of returns have historically occurred ranging from 10% to over 50%.

Thus, the association between capital and return is weak, if it exists at all.  The line chart with dual axes presents the false impression of a strong association while the scatter plot shows a different story.

Reference: "Private Equities", Forbes, March 13 2006.


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