Why are we so bad at probabilities and worse at understanding consequences?
A client came to me recently with a net worth well over $10 million. He had enough money to support his family’s desired lifestyle for the rest of their lives, but not so much that he could withstand a large loss without cutting back substantially. Yet this client owned more than 130% in risky assets, meaning he had far more debt than fixed income. Much of the debt was in a variable rate margin loan against his brokerage account.
More on this client at the end of this piece, but first let’s look at the subjects of probabilities and consequences.
Forecasts and probabilities – the odds are you don’t know the odds
Have you ever turned on an investing show and heard the expert make predictions as ranges? That is to say, something like, “my forecast for U.S. stocks over the next year is a mid-point of 7% with a 95% probability that returns will be between a loss of 21% and a gain of 35%.”
I suspect not.
We all want to know precisely how markets will perform because we hate uncertainty. Precision gives us a sense of comfort. Unfortunately, that sense of comfort is completely false, dangerous, and makes us ignore consequences.
I’ve been teaching behavioral finance for about 15 years and go through some exercises with my students to demonstrate how bad we are at estimating probabilities. One such exercise involves asking the following question, which you may want to try to answer before reading on:
In college basketball, what percent of the time does the team behind at half-time come back to win the game?
If you are like most people to whom I’ve asked this question, you probably guessed somewhere between 30% and 50%, though I’ve had answers as high as 90%. I actually once counted a whole NCAA season and the answer was just a tad under 20%. It turns out that the team behind at halftime is typically the inferior team and that same team shows up in the second half.
Why then do we guess so much higher? Consider the following games. Which is more likely to make the news?
Game 1: Team A is behind by 15 points at halftime and loses the game by 25 points.
Game 2: Team B is behind by 15 points at halftime and comes back to win in triple overtime.
The obvious answer is the second game. A thrilling comeback is more memorable. Rarely has a movie been made where the horrible sports team in the beginning of the movie finishes in last place at the end of the movie. We want to hear about winners!
The same dynamic is present in investing. I bet you see advertisements for investment funds that have outperformed. These would be Morningstar four- and five-star funds. We think they are easy to find and the odds of picking one in advance are high. And you’ll see those managers on television touting about their own brilliance. Yet there are just as many one and two-star funds that you don’t see advertised. Admittedly, sometime you’ll see the managers of these funds bragging on television as well, but only because no one bothers to check their performance.
Much like the blowout game that didn’t make the TV highlights, here is a mutual fund advertisement you’ll never see in the financial media.
Wiley & Sons, How a Second Grader Beats Wall Street, 2009 by Allan S. Roth
In my class, I walk through other examples using our all-too-human failings such as heuristic biases that are mental short-cuts we take. My favorite is the Monte Hall Let’s Make a Deal problem, where one of the two booby prizes are shown once the contestant picks a door. Then the contestant is given the chance to change her pick to the other door and doesn’t realize this change will increase the probability of winning the shiny new car from one third to two thirds. Heuristics (mental short-cuts) lead us to believe there is now a 50-50 probability of being right. Don’t believe me? Try this simulator.
Recency bias is the most pernicious. After a 10-year bull market, we tend to think good things will continue. Though we know neither good nor bad times will last forever, we don’t internalize and act on that knowledge.
We advisors need to tell our clients to embrace uncertainty. Don’t blindly follow forecasts such as the top economists’ predictions of interest rates, which have been directionally correct about 30% of the time – less than a coin flip. When a client comes to me wanting to buy into a forecast, here are the three things I ask them:
- Have you checked the track record of the forecaster or of economic forecasts in general?
- Do you have any evidence that this forecast hasn’t already been priced into the market?
- Do you want to make changes to your portfolio based on this forecast, even though you likely know the herd is making these changes and following the herd typically ends badly?
Consequences are more important than probabilities
I’ve never developed a financial plan that will withstand the U.S. government going out of business. I can’t tell you the probability is zero, but I know it’s very remote. Still, probabilities of other bad outcomes can be far higher. For example, stocks fell by about 88% during the Great Depression. In Japan, the Nikkei average is still well below its 1989 high. Think that can’t happen here in the U.S.? Some of the largest companies on the planet have gone belly-up. Once many people believed in the statement “so goes GM goes America.” I’m awfully glad that wasn’t true.
The world is risky – always has been and always will be. I tell clients that any of these things can easily happen again, though it will likely have different causes and outcomes. There is at least a 10-20% chance of a 60-90% market decline over the next three decades. Once I get a client to understand that we do indeed live in a risky world, I shift to what the consequences to them would be.
One of my favorite quotes comes from financial theorist William Bernstein, “When you’ve won the game, stop playing.” Sure, passing money on to heirs is an important secondary goal, but the key word here is “secondary.”
Bernstein’s quote does not mean he thinks all risk should be taken off the table when the client has won the game. That’s because the possibility of hyperinflation requires some assets that may keep up, meaning shifting allocations holding less equities and more high-quality fixed income. During our current bull market, there is quite a bit of resistance to this advice.
I do my best to have clients imagine their lives after a 60% - 90% stock plunge where a recovery could take a decade or three. Though imagining a bad outcome is a poor approximation of the actual pain they would experience should it occur, it is the most pain I can legally inflict.
I’m not a sadist trying to inflict pain, I argue. I’m doing it for a good cause: to get the client to reduce unnecessary risk.
Combining probabilities and consequences
I’m going to use two of the most extreme examples to illustrate the point of combining both – one lottery ticket and a bet on one’s life.
It’s not exactly a secret the odds of buying one Mega-millions ticket and winning the jackpot are virtually zero. But buying one or two tickets a year is a guilty pleasure. I enjoy imagining being the winner and the consequences of losing a couple of dollars are ultra-low.
On the other hand, if I were offered the ultimate wager where I had a 90% chance of winning $300 million and a 10% chance of dying, I would turn it down (or at least I hope I would).
The lottery ticket had horrible odds, but low negative consequences; the ultimate wager had great odds with horrible negative consequences.
Thankfully, most investment decisions are far less extreme than these two examples. When it comes to risk in a portfolio, decisions are tougher. We typically underestimate both negative probabilities (especially after a long bull market) and the consequences it would have on our lives. Those consequences could be anything from having to work for the rest of our lives, to a meager subsistence on Social Security, or merely cutting out expenditures that bring us happiness.
Back to the client
Remember the client I mentioned earlier who had over a $10 million net worth with 130% in risky assets? It might surprise you to know that he is a statistician with a Ph.D. and arguably the most mathematically sophisticated client with whom I have ever worked. Though I used all of the arguments in this piece, I was only able to get him to marginally reduce risk. There were some circumstances to decrease risk, which would have meant selling some investment real-estate at either taxable losses or gains, but neither was acceptable to him. I argued recognizing the losses was mathematically superior due to the tax benefit.
While I got through to him to some extent and he did lower risk, he was still taking unnecessary risk. Despite clearly understanding the logic of my argument, emotions prevented this most logical and mathematical person to lower risk further.
Conclusion
All of us are bad at thinking in probabilities and understanding consequences. We are emotional beings with many biases explained in the new science of behavioral finance. I’m no different in that I have a long and growing list of behavioral mistakes.
Risk-profile questionnaires do a poor job of assessing one’s willingness to take risk and ignore one’s needs. It’s our obligation as advisors to point out probabilities and consequences to the best of our abilities. In most cases I succeed. Even for this client, I was at least modestly successful.
Allan Roth is the founder of Wealth Logic, LLC, a Colorado-based fee-only registered investment advisor. He has been working in the investment world with 25 years of corporate finance. Allan has served as corporate finance officer of two multi-billion dollar companies, and consulted with many others while at McKinsey & Company.
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