The Most Dangerous Math Mistakes Advisors Make

Numbers are affected by the real world. Tax rates change. Economies grow, or not. New management is brilliant, or criminal. Expansion continues until a market is saturated, or competition intervenes, or customers chase a new shinier object. Quarterly GDP figures and other official statistics are adjusted at least three or four times following the initial reports. When a number is projected into the future, the math may be accurate, but the answers are unlikely to be.

The two significant digit rule

A calculation can be no more accurate than the least precise input. Formulas and computers don’t distinguish between estimates and precision.

The statement that Americans will buy 17.5 million cars this year is not the same as saying that Americans will buy exactly 17,500,000.0 cars this year. If you want to calculate how many will be sold in four years if purchases grow by 2%, an answer of 19 million is more likely to be correct than an answer of 18,942,563. (What if actual sales this year turn out to be 17,299,456, or the average growth rate going forward is 0.5%? How do we project either of those numbers? Should we account for 2020 being a leap year?) Yet it seems unprofessional to announce a result of “about 19 million.”

(Fun fact: in 1855 the British determined that the height of Mt. Everest was exactly 29,000 feet, but they reported the height as 29,002 so the number would not look like an estimate. In 2010 China and Nepal agreed that the current surveyed height is 29,029 feet, or 8448 meters.)

Embrace a level of precision that is realistic. A 2018 flood in Paris generated damages estimated at 1 billion euros. Its projected impact in dollars would properly be “over $1 billion,” not $1.24 billion that was based on the exchange rate on a particular day. However, the exact number is what a newspaper chose to print. The likelihood of accuracy is worse when we calculate a forecast using multiple estimates and projections.

The short form of this rule is, generally, to disregard everything to the right of the decimal point. The numbers 12 and 14 may turn out to be the same number, while 10 and 25 probably are not. Projected numbers are directly or indirectly going to be used as the basis of a recommendation for future action in one form or another, and spurious precision is dangerous. For calculations of taxes owed or money to be collected, of course, be as precise as you can.

The client’s two-digit rule

Each line item in a report matters, and each needs its own explanation.

While working for the Senate Appropriations Committee in the 1970s, I saw that the Senators were generally more concerned about the percentage of change than in the amount of change. Cutting a line item from $400 million to $350 million felt the same as cutting another from $4 million to $3.5 million. The number of digits – the actual amount of money – didn’t matter as much as one would hope.

Later I realized that the same principle applied to clients evaluating their portfolio returns. I briefly used separately managed accounts (SMAs) for my clients instead of mutual funds, and saw that some clients looked at the change in each stock’s value, not the change for the entire account, much less how their overall portfolio had performed. Clients wanted me to explain why an account still held a particular stock that had gone down, something I never had to do when using mutual funds.

Even when looking at a mix of funds, each was often evaluated on its own merits, not as part of an overall strategy. A fund representing 1% of the portfolio got as much attention as one that represented 15%, because each had its own line in the report given the client. What I learned was that a simpler portfolio was easier to present than one with many narrowly-defined holdings. Clients can ask about any number we give them, so don’t include line items that have little impact on what should matter: reaching their goals.

If a formula can give a result of “NA,” it is a bad formula

One of the most-used measures of valuing a stock is its “price-earnings ratio.” The higher the number, the more fully- (or over-, or highly-) priced the stock is said to be. When a company is losing money, however, the PE ratio is “NA,” somewhere on the far side of infinity. The ratio of price-to-earnings is no longer relevant. Charts leave a blank space instead of a data point. If advisors invert the formula and use an “earnings/price” ratio, on the other hand, the numbers could move smoothly into negative territory when necessary. The NASDAQ 1999 PE ratio of almost 200 disguised the fact that many companies traded at a P/E of NA. In 2009, the S&P’s P/E ratio almost went to infinity after earnings dropped by 90%.

Michael Lewis’s The Big Short revealed that the formulas being used on Wall Street to evaluate mortgage-backed securities did not allow a projection of declining home values to be used as an input. House prices never decline, the story went, so the possibility did not even need to be considered. The result was false confidence in the values of the securities and the strength of the entire financial system – a mistake with catastrophic consequences.

Where are the “NA” results today? What if climate change or resource constraints reverse economic growth? What if the rate of return on pension funds turns negative? Can a variable insurance product be illustrated with declining equity valuations? What if there is a wide-spread debt default or another financial crisis? What if required rates of return, or required savings rates, move far beyond what is plausible? How do we calculate a net present value in a shrinking economy? We won’t know until a crisis comes and we realize we should have at least asked the questions.

The “long term” is an average over a period of years, not necessarily a trend line for the real world

When advisors say something is highly priced, it is often being compared to some long-term average or trend. However, those trend lines and averages can be very deceptive. For example, prior to 1995, the price-to-book ratio for the S&P 500 was rarely more than 2 or less than 1, apparently providing a channel for investment decisions. Since 1995, though, the P/B ratio has almost always been more than 2, reaching up to 5. Maybe “book value” means something different today, or other factors are more important, but merely following history would not have been helpful. Similarly, long-term interest rates rose steadily from 1945 to 1982, then fell steadily until very recently. It was said in 2001 that the last time interest rates had been that low (5%), they had never been that high. They have not reached 5% (more than briefly) since then. Is there any useful average value for, say, 10-year Treasury yields? What is the “mean” that values are supposed to “revert to”?

The future is often “outside the range of guesses” of forecasts

For many years the Wall Street Journal started each January and July asking more than 50 economists – in academia, banking, consulting, and elsewhere – for their forecasts, 6 and 12 months out, of the levels for a group of economic indicators including short- and long-term Treasury rates, inflation, economic growth, oil prices, and the dollar versus yen exchange rate. In a commendable exercise of transparency, the Journal also published what those same people had predicted six months earlier.

When I looked at the results from 1990 to 2003 (when I dropped the project), for each report there was at least one category where the actual number was outside the range of guesses (or of all but one extreme guess). Not that the average was wrong, but basically nobody got it right. Sometimes it was interest rates, or inflation, or the value of the dollar. The person closest on one prediction was often far off in other forecasts. (Just to confound the analysis, there was one exception in 1998 where the predictions were pretty accurate.) These experts were presumably being paid by somebody to make predictions, and the Journal would often run a headline along the lines of “experts see higher rates in the second half.” I always thought the story should be, “why do these people still have jobs?” Alternately, “why do we keep running this survey?”

Today’s experts have not improved. In January 2018, the Journal (which now does this monthly) asked its panel, among other things, to forecast oil prices. The guesses for June ranged from $45 to $70 a barrel – the actual price on June 30 was $74.15. At the start of July, they asked again for a year-end projection. The range was $57.60 to $81 – the actual price on December 31 was $45.41. (The July panel also all missed the rise in the Fed funds rate and the slowing in the growth of the CPI.)

We all want to know the future, so we can take advantage of it. There are large casinos across the country paid for by people who thought they could successfully bet on the future. Many political polls were wrong at the margin in 2016, giving us a president we didn’t expect; the polls seem to have been more accurate in 2018. The further into the future a prediction applies, the greater the chance that surprises and competing factors will make it wrong – in direction, amplitude, timing, or all three. I follow energy issues, and I am unaware of anyone who, 10 years ago, predicted that fracking of shale deposits would produce millions of barrels of oil per day in the U.S., but that’s happening. However, no one knows if those deposits will still be producing at those levels in another 10 years. The actual number could again be “outside the range of guesses.”

“The greatest shortcoming of the human race is our inability to understand the exponential function.”

The late Albert Bartlett, a physicist at the University of Colorado, would start his lecture on “Arithmetic, Population, and Energy” with that sentence. (It is worth your time to watch the whole lecture on You Tube.) Advisors (and politicians) often act as though real growth will continue indefinitely into the future, because that has been the case for the last few decades. We are often comfortable assuming an economic rate of growth of 3% net of inflation, without doing the math to see that the resulting economy would be 2.5 times the size of our current economy by the middle of the century, and 11 times larger by 2100. How would that work? What about resource use? Land use? Transportation? Climate impacts? Housing? Air conditioning? As Bartlett and others have pointed out, infinite growth on a finite planet is impossible.

If something cannot go on forever, it will stop

That is how Herb Stein, former chairman of the Council of Economic Advisors, put it in his “law.” It is not clear if Bartlett and Stein ever met, but they both shared a similar view that limits are inevitable, even if hard to discern in advance.

The Ditmas test – Does it make sense?

The final step in any calculation is asking whether the result makes sense. Should an investor really have 57% of their money in stocks rather than “about 60%”? Despite the software output, is it possible to save 43.4% of income to meet a retirement target, or accumulate 25 times one’s income by retirement day? Will a pension fund really average 5% real growth with a blended investment mix, for decades to come? Will carbon emissions really continue to grow by 3% per year through the end of the century? Should our client sharply reduce current consumption so they will have plenty of money at age 98?

In all these cases, think through the meaning of the results of your calculations in terms of the real world, and be prepared to explain them in those terms. Talk about uncertainty, false precision, variability, and how you can make adjustments when the future turns out to hold the surprises you know will be there, even if they cannot yet be identified.

Don’t be afraid to mention the 5-100 rule.

Richard Vodra, J.D., is the president of Worldview Two Planning of McLean, VA. He is retired from a 27-year career as a personal financial planner, and received the 2019 Lifetime Achievement Award from the National Capital Area chapter of the Financial Planning Association. He is an original member of the Nazrudin Project. He currently focuses on the linkages between financial planning, climate change, and resource constraints. He can be reached at [email protected].

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