Gary Smith pointed me to this post, “Don’t worship math: Numbers don’t equal insight,” subtitled, “The unwarranted assumption that investing in stocks is like rolling dice has led to some erroneous conclusions and extraordinarily conservative advice,” which reminded me of my discussion with Nate Silver a few years ago regarding his mistaken claim that, “the most robust assumption is usually that polling is essentially a random walk, i.e., that the polls are about equally likely to move toward one or another candidate, regardless of which way they have moved in the past.” My post was called, “Politics is not a random walk: Momentum and mean reversion in polling,” and David Park, Noah Kaplan, and I later expanded that into a paper, “Understanding persuasion and activation in presidential campaigns: The random walk and mean-reversion models.”
The random walk model for polls is a bit like the idea that the hot hand is a fallacy: it’s an appealing argument that has a lot of truth to it (as compared to the alternative model that poll movement or sports performance is easily predictable given past data) but is not quite correct, and the mistake comes when it is elevated from a heuristic to a principle.
This mistake happens a lot, no? It comes up in statistics all the time.
P.S. Some discussion in comments on stock market and investing. I know nothing about that topic; the above post is just about the general problem of people elevating a heuristic to a principle.
OK, I’m puzzled by Gary Smith’s column. He ran simulations that show an “unrealistically” large probability of long-term stock market gains or losses. What makes these unrealistic, however, appears to be that the reality over the past 100 years has not been nearly as extreme as the simulation suggests. Does that make the simulation wrong?
I get the point that a 37% stock market decline is unlikely to be repeated in the following year – that if you assume a distribution for annual returns that is independent over time, that probability will likely be overestimated. I think that points to the need to be more careful in modeling what the distribution of annual returns looks like and how it may be time dependent (e.g., exhibiting means reversion). But I don’t see how a failure for a 37% annual return to repeat in two successive years amounts to proof that the assumption of time independence is wrong. So, I guess I am saying I buy the argument, but find the proof unconvincing – evidence that it didn’t happen doesn’t convince me that the model was wrong. Similarly, does the Trump victory in 2016 prove that an 83% probability of a Clinton victory was wrong?
The human brain doesn’t seem designed to hold the insight that unlikely things happen all the time.
A frightening thing about investing is that the longest commonly used data set for stock markets is a series from the USA starting in the 1920s. Something that does not happen in 100 years is not all that rare! And for the 95% of us who are not Americans, its not clear if investing in a hyperpower during its rise is a good model for investing elsewhere in other circumstances. A comforting thing is that pretty much everyone in a rich country has access to diversified, low-cost investments and “save as much as you can” “diversify” and “minimize the cost of your investing” seem like strategies which will tend to be rewarded in most all circumstances. But decisions like how much to invest in stocks are hard!
They are, in fact, so hard that one should probably just take a reasonable guess then forget about it.
I agree. That part of the argument is hard to understand. The quote he critizices says “Prices dropped by 37% last year. While improbable, there’s nothing to say they couldn’t drop by that much again next year or the year before you retire.”
Improbable.
His counterargument: “A 37% price drop might be drawn over and over in a Samuelson simulation but won’t happen in the real world. At some point, stock prices will be so low relative to corporate earnings and dividends that investors will find stocks irresistible and stock prices will stop free falling.”
Maybe his point is that “improbable” is still too much and we should consider that “impossible”?
But in the 100 years of S&P 500 returns that he put into his computer he could have found a streak of four consecutive calendar years with negative returns that result in the same performance as four consecutive 25% drops. In fact the drop observed was of more than 80%, it took less than three years from peak to bottom and the annualized performance was around -50% p.a.
The post by Gary Smith is not a serious analysis of tail risks. And what is the title supposed to mean: “Don’t worship math”?? A model with stationary independent increments is probably the most simple model one can think of. So this is already too mathy for him, which is OK, but does he have a better alternative? Gut feeling? Faith? As in “Everything will be good in the end, if it is not good, it is not the end.”?
Oh, and anyone thinking that prices cannot possibly fall for a couple of years may have a look at the Nikkei Index starting from nineties. It lost 80% over this 20 year period. see here https://en.wikipedia.org/wiki/Nikkei_225
With regard to “Don’t worship math: Numbers don’t equal insight,” I offer this from today’s Washington Post article by David Kissinger, a celebration of his father’s 100th birthday tomorrow:
https://www.washingtonpost.com/opinions/2023/05/25/henry-kissinger-100th-birthday-appreciation/
As of this count, his article has generated about 1800 comments, typical of which are
“One of the biggest war criminals of all time,” “Kissinger bears significant responsibility for attacks in Cambodia that killed as many as 150,000 civilians” and “literally millions of people worldwide killed, maimed, and displaced as a result of policies propagated by Henry Kissinger.”
A few years ago, Tom Lehrer famously quipped, “Satire died when Kissinger received the Noble Peace Prize.” Lehrer also famously wrote that he never quite said that.
One the one hand, the reasoning here is sound – it’s dumb to move your assets to cash after a dramatic decline in the market. OTOH, Smith arguing against a boogeyman that doesn’t exist. Zvi Bodi may have given people such terrible advice, but almost no one else who’s a professional financial advisor would give such horrible advice. Almost universally professional financial advice is to hold through the dip.
I like this statement: “The validity of the assumptions is often more important than beauty of the math”
Although I suggest it be revised as such: The validity of the assumptions is as or more important than the math.
Regarding his one million simulations and the tendency of the simulations to more extreme outcomes than the actual market, I think I missed something? Isn’t it obvious that his one million simulations produce more extreme results because there are far more simulations than there are actual years of market returns? He’s doing 25 year periods with monthly prices. Over 225 years of stock market returns, that’s 2400 25yr periods compared to a million simulations, so it seems obvious that the simulations will produce a wider spread. But if I’m mistaken I’m sure Somebody will be here in a few seconds to explain just how mistaken I am! :)
I have always thought that the heuristic-to-principle transition is related to what philosophers call the “no true Scotsman” fallacy. You can start with a perfectly good heuristic (“Scotsmen don’t do phi”). Then, when you find an exception, a Scotsman S who does phi, you elevate your generalization to principle by denying that S is a “true” Scotsman.
So your perfectly good heuristic becomes true by definition, a criterion for the application of “true Scotsman.”
Their job was to prevent something like 2007 from happening. This idea that loaning out (“printing”) trillions of dollars is somehow genious or heroic is hilarious.
The unequal distribution of those trillions into healthcare, real estate, stocks, and education (whereever government and the well-connected put the money) is a huge source of wealth inequality. It took some time, but now those dollars are trickling out into the rest of the economy so we also get to enjoy the rising everday prices. Then to respond to that we now had to go from near-zero interest rates to 5%, and interest on the national debt is approaching $1 trillion per year.