You're Only Reading the Bad Advice

If there’s one thing investment managers love, it’s pretending to be philosophers; if there’s another, it’s pretending to be generals. While nobody should confuse receiving notice of an SEC investigation with sustaining a mortar barrage, and leading off your market take with a Sun Tzu quote will induce almost as many yawns as “be greedy when others…”, there are in fact some real nuggets of investing wisdom to be gained from the military world.

World War II marked the introduction of a wide variety of new technologies and techniques to the field of battle. Among those was the serious and widespread application of data analysis to battlefield decision-making, termed “Operations Research”. One early practitioner, statistician Abraham Wald, was tasked with analyzing locations of damage to allied aircraft returning from bombing missions, to determine if strategically-placed armor could improve the survival rate of bombers and their crew. The data he had to work with looked something like this:

*image from Wikipedia showing locations of damage to all returning planes as red dots; data is not actual

As is often the case in data analysis, a good visualization of the data makes the conclusion clear: the areas that appear most likely to be hit are the wings and fuselage, so any additional armor should be concentrated in those areas.

Except that in this case the obvious conclusion couldn’t be more wrong.

Wald theorized that there is no a priori reason to believe one area of the plane would be significantly more likely to sustain a hit from an anti-aircraft gun than another; the distribution of the actual hits ought to be relatively even across the whole body of the plane. Under that assumption, the above plot isn’t showing areas more likely to be hit; it’s simply showing the hits which a plane is able to survive. Damage to areas showing no red dots in Wald’s data is in fact the most dangerous; none of those planes made it back to base.

This phenomenon has a name: “survivorship bias”. The intuitive conclusion was so totally wrong because we were only looking at a particular slice of the data, one which was different in an important way from the whole dataset. The data from planes which were able to return to base tells a completely different story than that from planes which were destroyed. Survivorship bias is a well studied phenomenon present in many domains (Wikipedia overview); Wald’s research is just a particularly dramatic example.

Now, if you read 10 articles in widely available publications, and 9 of them express an opinion that a particular security (or sector, or the market as whole) is overvalued, what should you conclude? Abraham Wald would say it’s more likely just the opposite: undervalued.

Opinions in the stock market are like the hits from anti-aircraft guns: all over the place. It's pretty much guaranteed that there are roughly balanced sets of opinions about a particular stock: some market participants who think it's overvalued and others who think it's undervalued. The stock trades at a particular price because that's the price at which the market as a whole is equally willing to buy or sell the stock. So if everything you are reading says the stock is overvalued, it's not because everyone thinks the stock is overvalued. It's because the people who think it's undervalued aren't sharing their opinions with you. You are only seeing the hits that didn't bring the plane down.

So the key question is: Who do the hidden opinions belong to? Occasionally, they belong to retail traders or some other idiosyncratic group which doesn't do much publishing. See SPACs for most of 2021: the financial media consensus was that these securities were generally not good investments, and that consensus was spot on, because the hidden opinions belonged to retail speculators. More typically, though, the unpublished views belong to the smart money. See high-growth tech stocks during all the years numbered "201_". I saw a hell of a lot more “Tech is in a bubble” columns than bullish takes during that time, and yet tech and growth outperformed. Clearly somebody was buying Amazon and co. during that period, but staying much quieter than the other side. This is to be expected: the best investors are not writing articles for public consumption because that's not a good way to monetize their expertise. They are instead running hedge funds or family offices. You don’t get to read their advice because you can’t afford it.

This is one reason indexing is a great option for most individual investors. It guarantees you are buying equal parts good and bad opinions. It would be better to just buy the good opinions, but that option is not available. They are hidden. They are hidden because they are good. If you stray at all from buying the whole market, it will probably be towards the bad advice, because that's the advice which is available to you. You don't know which parts of the plane are most vulnerable, but you can always opt to just armor up the whole plane.

But if you must try to outsmart the market, you can try to create Wald’s plot for the market opinions which are visible to you, and tilt your portfolio towards the areas without much apparent positive sentiment; if everything you are seeing in the publicly available media says avoid tech stocks, buy more tech stocks. If you notice a surfeit of “Real estate likely to outperform equities” takes, sell your REITs. The broken-clock value investors who've held the mic for the last decade would have you believe that "contrarian style" means scooping up shares with low ratios and avoiding anything which has recently performed well. It simply means doing the opposite of what you are being advised to do, and if you're being advised by the, ah, "not as sharp" half of the market, it's the right way to go.

(oh and by the way, this blog is free to read and I don't even work in finance, so draw your own conclusions about which type of advice you'll find here)