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Sunday, April 3, 2016

Trump v. S&P, & @salilstatistics

Side note: happy to be the first to let you know that Statistical Ideas is finally on twitter at @salilstatistics!  Please check us out there, and share this with any friends you have on twitter who would like this material.  Thanks much to the many fans who have encouraged me over the years to join the larger social media platform.

With Donald Trump's sustained rise in the primaries, opponents on both sides of the aisle have recently been vigorously questioning his business savvy.  Amusingly stating that his family wealth could have yielded better results if it were instead in the S&P 500 index.  But unlike Warren Buffett, Mr. Trump isn't in the financial markets but rather mostly in real estate development (having had a home office in his Central Park building it's recognizable how terrific a job he does).  It's further unclear if anyone with robust careers should ex-post spontaneously be contrasted against the winning market benchmark over the past several decades.  If that were not true, then where are Senators Warren's and Rubio's historical net worths, audited and contrasted to the S&P 500?  Having said that, we can look anyway at Mr. Trump's historical net worth and contrast it to the S&P to assess these comments.  For much of the past 1/3 of a century, Mr. Trump's net worth has been disputed (by himself) in the illustrious Forbes magazine.  The data collected here reveals massive volatility in Mr. Trump's net worth versus a broad index, and as a result likely decent underperformance on both a risk-adjusted and a risk-unadjusted bases.  A pro-Trump analysis is fully dependent on some major assumptions, mostly how we deal with or discount the lack of all Forbes' data prior to 1982.  This is not trivial to any conclusion since Mr. Trump was already a reputable 13-year veteran by then and had a net worth of nearly $200 million!

The only difference between the two charts on the left is that the top chart has the vertical axis shown on a normal scale, while the bottom chart has the vertical axis shown on a log scale to allow one to better see the smaller historical values.  The S&P total return index (blending in my colleague's Robert Shiller's data) is scaled to match today's Forbes valuation of Mr. Trump (~$4.3 billion).  So the question is, would we have needed more or less than Mr. Trump's family money invested in the index (starting at some historical date) in order to to equal his net worth today?  He claimed at age 23 that he had a net worth of $200,000 (or $0.0002 billion).  That implies a 34% continuous annual return to today's $4.3 billion.  Since the S&P 500 earned a lower 15% continuous annual return instead (since 1968), one would have needed to invest a lot more (~$54 million) in the S&P to match Mr. Trump's current net worth.  The risks related to this outperformance would have been monstrous, with annualized volatility of 28% for the market and 131% for Mr. Trump.  If this single data point for for all years prior to the Forbes' 1982 statistic (a data point for when Mr. Trump was 23) is to be believed as comparable to the rest of the time series in illustrations above, then Mr. Trump has outperformed and perhaps by a statistically significant amount of skill!

Other than this single data point, much of the rest of the time series comparison between Mr. Trump and the S&P look far less favorable.  For example from 1982, to many years after, Mr. Trump earned a lower rate of return versus the market.  From 1982 specifically, through today, the annual return for Mr. Trump was 11% (just shy of the S&P's annual return of 12%).  Of course this mild underperformance (which also implies a lack of alpha) comes with much higher annual volatility still for Mr. Trump (36% versus the market's 24%).  While the correlation of the net worths appear high (~0.9) throughout the time series charts above, the correlation of the annual changes in both the returns series is far weaker (~.35).  Between the latter, and the underperformance since 1982 (where continuous Forbes' data is known) with 50% higher volatility, it is much more likely that Mr. Trump underperformed by a statistically significant amount (reflecting terrible skill and not bad luck).

So the conclusion of this analysis is that Mr. Trump's net worth was been exceptionally volatile!  And while it is possible that he performed quite well during the first 1/4 of his career, since the Forbes publication tracked his net worth 34 years ago, his net worth has performed poorly on a risk-adjusted basis.  We glean similar lessons for Mr. Trump as we do for Mr. Buffett (who also has underperformed by a large amount in recent years and yet he is still widely idolized!)  That strategies and performance tends to come and go, and that even if one uses a correct benchmark, by it's very definition it becomes hard for anyone to significantly outperform that benchmark with skill (here, here, here) over the long-run.  Mr. Trump's success as a business person should likely rest on a richer set of life metrics besides simply the S&P 500.

3 comments:

  1. Maybe he spent money on basics like food, hairdresser and a 757 and wasn't fully invested all the time ?

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    1. Agreed, and as noted part of the article is to first debase the notion that contrasting anyone's lifetime wealth growth to the S&P rarely makes sense! Heaven knows no other political candidate or pundit is subject to this argument.

      Incidentally my friend -and Fox Business host- Mr. Scaramucci was on such 757 this week, citing the fascinating experience: https://twitter.com/Scaramucci/status/735260772423454721

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    2. Additionally, concerning your question on the previous blog post "From the probabilities, if the events are not correlated, there was 58% chance (99%^19 x 97% x 96% x 94%^3 x 92%^2 ) that all predictions were correct, not a 98% accuracy claim. Similarly, 32% chances that 1 was wrong. So that left us with 10% that 2 or more went wrong. That's a 1 in 10 event, not so surprising ? "

      The accuracy here is on a per forecast prediction basis, not an all or nothing on all forecasts, per your question. Incidentally Professor Gelman and others thought my analysis was cogent, and Nate Silver has conceded he badly flubbed the predictions. Thanks. https://twitter.com/salilstatistics/status/733446598055895041

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