Base Rate

Base Rate

Published On: August 7, 2020

Written by: Ben Atwater and Matt Malick

Behavioral finance is the crossroads of psychology and economics.  It recognizes that investors are not always rational, have limits to their self-control and have biases that influence their decision-making. 

Readers have been particularly interested in this series.  For your easy reference, we created a landing page for Behavioral Finance on our website.  On this page you will find all the essays in this series.  Please feel free to share with your friends, family, and business associates. 

As we continue our series today, we turn to representative heuristics.  Heuristics involve cognitive shortcuts or rules of thumb we use to simplify decision-making under conditions of uncertainty.  Heuristics are not necessarily bad, as we often need a framework with which to make important decisions quickly, but we must be cognizant of how this framework might impact our decision-making.

Representativeness is a form of heuristic bias occurring when we make the mistake of believing two similar things are more closely correlated than they are.  Simply because an event is representative does not mean its occurrence is more probable. 

To best understand representativeness, we need to define the base rate fallacy (stick with us, this gets more interesting).  The representative fallacy is our tendency to overemphasize a certain case (prototype) and forget the larger context of data (base rate).  In other words, we get caught-up in the moment and forget the context – we look at the prototype and ignore the base rate. 

The proverbial coinflip exercise is an excellent illustration of this.  Say you observe someone flipping a coin and four times in a row it comes up heads.  The coin flipper asks you to wager on the fifth flip – heads or tails.  Most of us would choose tails because it seems a low probability that the flipper would flip heads five times in a row.  This is the prototype.  However, the fifth flip’s probability of heads is still 50% and of tails is still 50%.  The prior flips, no matter their result, do not impact the probability of the next flip.  This is our base rate. 

Imagine researchers would have presented the following scenario to a group of subjects: 

A pandemic will strike the world.  It will be particularly damaging in America where over a five-month period the U.S. will have 4.85 million people test positive and will experience 159,000 deaths.  On some days, the death toll in the U.S. will exceed 1,000 people.  At one height of the pandemic, the U.S. economy will suffer its biggest annualized GDP (gross domestic product) drop in its recorded history.  With the pandemic raging during a quarter where U.S. GDP falls an annualized 34.3%, is the U.S. stock market more likely to gain or lose value?

Of course, the overwhelming response, if such a study were to have taken place, would have been for people to say the stock market would lose value.  The story of the pandemic, the prototype, is shockingly compelling.  However, the data, the base rate, tells us that the stock market historically goes up in more quarters than it goes down, often during calendar quarters that coincide with economic weakness.  Therefore, from a pure probability standpoint, the answer to the question is that the stock market would be more likely to gain value

To look at another scenario, suppose researchers ask subjects the following: 

William “Bill” Fitzgerald is a great mutual fund manager.  Not only does he have an inherent business genius, but his MIT mathematics PhD gives him a quantitative edge as well. His fund has a 10% average annual return going back 20 years, a period that includes some tough times for the market like the dot com bear market, the financial crisis and the COVID-19 drop.  However, despite these market losses, his fund has prevailed over time.  Working for the largest asset manager in the world, Bill has a tremendous information advantage as he sees trading data not available to other fund managers.  Crucially, Bill’s fund has now reached a large enough size where he will now have access to investment opportunities others will not.  Given these advantages, Bill is supremely confident his next ten years will surpass his first twenty years.  Will an investor who buys Bill’s fund now likely experience 10% or greater average annual returns over the next 10 years? 

Most subjects would likely say the investor would receive average annual returns greater than 10% given Bill’s superior advantages as a fund manager.

However, based on two separate base rates, the average investor is actually more likely to realize lower than 10% average annual returns. 

The first base rate problem is that most investors don’t hold mutual fund positions for 10 years.  At some point during the next decade, Bill will undoubtedly suffer through periods of short-term underperformance, during which impatient investors tend to sell their holdings.  According to DALBAR QAIB, the average mutual fund holding period is less than 3 years.

The second base rate problem is that due to poor timing getting in and out of mutual funds (including index funds), investors lose more than 1.5% per year from a mutual fund’s average annual return, according to a study from the University of Nebraska.  Hence the second base rate problem, it is unlikely the investor would buy and sell the fund at appropriate enough times to realize their full return regardless of Bill’s performance. 

Therefore, for two different base rate reasons, it is probable that an investor would earn substantially less than the scenario implies. 

Although we are criticizing them for illustrative purposes, representative heuristics are often correct.  They can be a great basis for quick decision making.  However, often they are wrong.  Markets are complicated and there are a lot of false set-ups out there.  Evaluate with discipline and skepticism. 

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