Math manipulation makes the unremarkable look impressive. Caveat emptor.

It’s fairly easy to manipulate statistics and mathematical figures in order to present a conclusion that looks significant and impressive at face value.  These two factors (that it is easy and that it produces impressive-looking results) are probably the reason that the media uses such manipulation.  Take for example, the article in Saturday’s New York Times, The Long-Term Argument for Dow 20,000 by Jeff Sommer.  This article references a position paper by Seth Masters of Bernstein Global Wealth Management called “The Case for the 20,000 Dow.”  Looking solely at The New York Times article and not having read the entire paper, I’ll briefly mention what looks striking to me.  The article discusses an expected, or at least a plausible case for a 50% increase in the Dow Jones Industrial Index.  50%!  That seems impressive.  However, if you step back and consider the underlying math, I would suggest that this is not as impressive as it seems at face value.  The article suggests, “the odds of that [the 20,000 Dow level] happening by the end of this decade are excellent.”  The article later qualifies that the time frame that Mr. Masters is considering is between 5 and 10 years.  Let’s consider these three time frames.  First, there is the period from now until the end of the decade which is 8.5 years.  The second time period would be the early length of time that Mr. Masters mentions which is 5 years.  The third time frame is the end of the time period window which is 10 years.

Yearly returns (CAGR) implied for a 50% rise in the Dow Jones Index
Assumes principal grows tax free until period end, at which time there is a 1x tax charge

ZERO tax rate

20% tax rate

35% tax rate

Investment horizon – years

CAGR (%)

CAGR (%)

CAGR (%)

5.0

8.4%

6.9%

5.7%

8.5

4.9%

4.0%

3.4%

10.0

4.1%

3.4%

2.9%

Note in addition that the return that Mr. Masters discusses are pre-tax returns.  To the extent that the investor withdraws his money, which at some point one would presume that this would be done, there would be a definite tax penalty that would reduce the returns beyond the simple appreciation seen in the increasing level of the stock market and returns could be reduced even further if the principle does not grow purely on a pre-tax basis annually, but instead grows at a rate that is taxed on an annual basis.  So let’s take a look at what the actual implied returns are assuming that the amount invested grows tax free until it is withdrawn at the end of a given period.  We will look at the periods that Mr. Masters potentially mentions (5 years, 8.5 years, 10 years).

It’s clearly evident that the returns on an annual basis are much less striking than what the headline rate of a 50% increase suggests.  If the Dow reaches a level that is 50% higher, in a period of 5 years and an investor is able to collect this return with no tax, that still only suggests a compound annual growth rate of 8.4%.  That’s an excellent growth rate and one that I think most investors would be happy with knowing that a priori that they could get this with certainty.  Having said that, 8.4% is still not necessarily headline grabbing from a sensationalist standpoint.  There are many other caveats that could be mentioned, such as the potential risk associated with investing.  If an investor is hoping to earn a 3% to 5% return in an environment where there is volatility and there is potential to not generate this return or to even lose money, then that might mean that the risk-adjusted return is even less than the headline expectations would suggest.  However, the main point and assertion that I think is worth noting is that the media is not only tasked with disseminating information, they are tasked with selling their own media stories.  This represents a clear cut example of why it is important to read media stories with a skeptical eye, especially when mathematical and statistical information is being presented.

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