**What are the chances that a new bear market is imminent?**

- I’ve seen a spike in the number of calls from clients asking this question.
- It’s a fair question, and one that deserves a thoughtful answer.
- There is no definitive answer, of course, but there are ways to make a reasonable estimate.
- I use a Bayesian approach to calculating the likelihood that a new bear market is imminent.

**Should you heed the warnings of bearish market pundits?**

Whenever the stock market is trading at all-time highs, pundits come out of the woodwork with predictions of an imminent correction, or a new bear market, or a market crash. Doom and gloom sells. Most of these dire predictions turn out to be just noise, but when I get a call from a client who is concerned about the prospect of losing a big chunk of her wealth, I feel an obligation to give a thoughtful and evidence-based answer.

But estimating the odds of a bear market (defined by convention to be a decline of 20% or more) is a very slippery endeavor. We can say with confidence that the odds of a fair coin landing on heads is precisely 50%. Likewise, we can say that a six-sided die has an equal 16.666% chance of landing on any given number. But calculating the odds of a bear market is a different matter entirely.

In the coin-toss and die roll examples, the range of possible outcomes is known. Not so in the stock market. That leaves us with only one option – looking at the historical record of all outcomes that were observed in the past, and assume that the same patterns will repeat in the future. It’s a big assumption, but it’s all we have.

Enter the Reverend Thomas Bayes, 18^{th} century mathematician. What Mr. Bayes did was look at the known observations to establish a baseline probability. Then he took things a step further by adjusting the baseline probability to take into account additional factors that might tilt the baseline probability one way or another.

**The Case of the Blue Taxi**

Take the case of the “Blue Taxi” for example. In this thought experiment, a pedestrian was struck by a taxi one night, and the driver fled the scene. The police want to find out who is responsible. They begin by looking into which taxi company was operating in the area at that time of night. The town has two taxi companies, the Blue Taxi Company and the Green Taxi Company.

As luck would have it, the police learn that there was an eyewitness to the hit-and-run. An elderly man says he saw the incident from his apartment window, which was 100 yards away from the street. He is certain that the taxi which hit the pedestrian was Blue.

They tested his vision and found that he could correctly tell a Blue taxi from a Green taxi 80% of the time. Now the police believe that there is an 80% chance that the taxi was in fact, Blue. But was it?

After further investigation the police find out that 85% of the taxis operating on the night in question were Green, and only 15% were Blue. Does this new information change the odds? According to Mr. Bayes, the answer is yes.

The only indisputable fact in this case is that there is an 85% chance that the taxi was Green. This is the baseline probability. The eyewitness testimony is important, but it’s only 80% reliable, and it’s based on a 15% baseline probability that the taxi was Blue. So the Bayesian solution is to start with an 85% probability that the taxi was Green, and then adjust that number by the eyewitness testimony. The end result is that the probability is 59% Green, and 41% Blue.

**The formula for Bayes’ theorem**

For you math wizards out there, here is the formula for calculating a Bayesian probability.

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* Source: Khan Academy*

**Now back to our stock market problem. **

My Bayesian baseline probability of a market decline of 20% or more from the most recent new all-time high is 1-in-3. This is based solely on the historical record of all trading days since 1950. Specifically, history shows that after each new high in the stock market, the market declined by 20% or more, 34% of the time.

This answer is similar to the police saying that there was an 85% chance that the taxi involved was Green, because 85% of all taxis operating that night were Green. But that’s not the end of the story. Just as the police made an adjustment to take into account the eyewitness, we have adjustments to make to our assertion that there is a 1-in-3 chance that a bear market is imminent.

I’ll have more to say about these adjustments in a subsequent article, but for now I’ll just talk about economic recessions. Recessions are bull market killers. The stock market tends to get wind of recessions about 4-6 months before they happen. The worst bear markets have been accompanied by recessions.

So I looked at just the periods of market history that involved a recession, and unsurprisingly the odds of a bear market went up. Instead of a 1-in-3 chance, it became a 1-in-2 chance, or 50-50. Conversely, when the onset of a new recession is more than 6 months away, as is the case today, the odds of a bear market drop to 1-in-4.

**Conclusion**

So there you have it. The answer to the question “What are the chances of a bear market starting now?” is 1-in-4. Here’s the important takeaway. If you are close to retirement, or very risk-averse, you need to ask yourself whether you can withstand a 25% chance of going through a new bear market. I can’t answer that for you. It’s a personal decision.

If you’re interested in the details, here is a table showing various levels of market declines in days and in percentages.