Bear Markets and Their Likelihood

Background

The fear of losing a big chunk of your life savings when the next bear market hits is something all of us experience as investors. I often hear people say, “I’m not worried about bear markets because I’m a long-term, buy & hold investor. Nobody can time the market, so the best strategy is to just stay fully invested and ride the ups and downs.” My reaction is usually “Seriously? You really don’t care if your $500,000 retirement account turns into a $250,000 retirement account?

The point I’m making is this. It’s one thing to have a strategy based on a belief, but that doesn’t keep you from suffering the emotional pain that bear markets can cause. The 1973-74 bear market caused so much damage and pain that nearly 30% of the baby boom generation abandoned the stock market and never returned.

After the tech bubble burst in 2000-02, the mindset of gen-x investors changed from “this is a new era of unlimited stock market gains,” to “buy & hold is dead. About 30% of them have still not returned to the stock market. The same story was repeated in the 2007-09 market crash.

There is an old Army saying that “there are no atheists in foxholes.” When you’re surrounded by enemy troops, and mortars are landing all around you, even atheists will pray for salvation. This is the argument I’m making about buy & hold and bear markets. Isn’t it just common sense to pay attention to what’s going on in the market, and take some kind of steps to at least limit your downside risk?

To help my clients deal with this question, I undertook a study to find out if it was possible to assign probabilities to the risk of a new bear market. If I could do that, my clients would be able to adjust their exposure to stocks and other risky assets, in gradual and measured steps, based on how much risk they were willing to take.

The answer is yes – it is possible to “rate” the risk of future bear markets using simple math and Bayesian Inference.

The Study

This study covers the period from 1941 – 2017; 79 years or 19,800 trading days. The goal is to calculate the probability (the odds) of various degrees of market declines occurring in the future.

The study looks at three different time frames:

1. the full 79 years
2. rolling 12-month periods
3. rolling 24-month periods

Definition of Terms

• A Drawdown (DD) is a percent price decline over a given period.
• A Dip is a DD of 5-10%.
• A Correction is a DD of 10-20%.
• A Bear is a DD of 20% or more.
• A Super-Bear is a DD of 40% or more.
• A New High is a fresh high-water mark for the market.

Base Rate Probabilities

Table 1.  Current DD from most recent new high

Table 2.  Maximum DD from today forward

Table 3.  Maximum DD next 12 months

Table 4.  Maximum DD next 24 months

Table 5.  Maximum DD next 12 from new high

Table 6.  Maximum DD next 24 from new high

Table 7.  Maximum DD from any new high (1,066 observations)

Interpreting the Data

The data in the tables above enable us to answer several questions about market risk:

1. What are the odds that a new bear market will arrive sometime in the next 12 months?
2. What are the odds of a bear coming sometime in the next 24 months?
3. Do the odds of a new bear market change when the market makes a new high?
4. Do the odds change after the market dips by 5%?
5. Are there other factors that change the odds of a new bear market significantly?

If a client were to ask me question #1 – what are the odds that a bear market will hit sometime in the next 12 months – I would first need to ask for clarification. Since we define a bear market as a decline of 20% or more, what is the starting point for the calculation? Convention says that the starting point for a bear market is the most recent new high. This may have occurred weeks or months ago.

The client may be more concerned with what might happen beginning today, and looking ahead 12 months. This must be clarified before going to the next step. For now, we’ll use the conventional method and use the most recent new high as our starting point.

To answer this question, we start with Table 1. This table looks at all 19,800 days in the dataset and counts the number of days the market was in “bear condition” of at least 20% below the most recent new high.

Table 1.  Current DD from most recent new high

We see that the market has been in bear mode 33.6% of all days for the past 79 years. Therefore, the odds of being in a bear market on any given day are 1-in-3. But this is only part of the answer. The next step is to look at Table 2. This table differs from Table 1 by looking ahead to count the number of days that the market was in bear mode, beginning with today’s price and ending when the market makes its next new high.

Table 2.  Maximum DD from today forward

We see that the answer is similar to the previous count. The odds of the market being in bear mode are still 1-in-3. At this point we know one thing: on any given day, there is a 1-in-3 chance that a bear market is coming before the market makes its next new high.

The next step is to narrow our focus to just the next 12 and 24 months. This is what the client wants to know, and we can calculate a reasonable estimate using Bayes’ Theorem. We begin by looking at Tables 3 and 4, which show the odds that a bear market is coming sometime between today and 12 months from today (Table 3) or 24 months from today (Table 4).

Table 3.  Maximum DD next 12 months

When we narrow our focus to what is likely to happen within the next 12 months, the odds of a bear market drop considerably. Instead of a 1-in-3 chance, we now have a 1-in-9 chance. This makes sense, because bear markets don’t follow a schedule. It takes some of them much longer to play out than others.

Table 4.  Maximum DD next 24 months

If we expand the time frame to 24 months, we increase the odds from 1-in-9 to 1-in-6. This also makes sense, because we’ve given the bear market twice as much time to develop.

This is where things really start to get interesting. (Well, maybe not for you, but definitely for a stock market nerd like me.) The next step places a new condition on the process by limiting the 12 and 24 month bear market counts to just the ones that start from a new high.

Table 5.  Maximum DD next 12 from new high

This changes the odds quite a bit. In fact, it’s extremely unlikely that a bear market will hit within 12 months of the most recent new high.

Table 6.  Maximum DD next 24 from new high

Even if we double the time period to 24 months, it’s still only a 1-in-106 shot for a new bear. But a word of caution: this does not mean that investors are safe whenever the market makes a new high. These tables are the conditional probabilities of a bear market. We still need to run these numbers through the Bayes machine to come up with the posterior probabilities. Those are the ones that really matter.

Here’s a simplified version of how the Bayes machine works. We start with a prior probability that a bear market is coming. This is just our “best guess” which is based on our assumptions and beliefs. Then we look at the numbers, which is what these tables represent. These are the conditional probabilities. Finally, we use the conditional probabilities to adjust our estimates so that they include the new information we collected from the tables. I will go into more detail about this in the next installment.

We can get a sneek peek at the final results by looking at Table 7. The numbers in this table are not perfect, but they do get us in the ballpark. It looks at only the 1,066 days out of the 19,800 days in our dataset, and counts the number of new high days that ended in a bear market before the next new high day.

Table 7.  Maximum DD from any new high (1,066 observations)

How do we make sense of all the different day counts and probabilities from these tables? That’s where Bayes’ Theorem comes in. We’ll address that in the next installment of this study.

Next time on Bear Markets

According to Bayes’ Theorem, there are three types of probability: Prior, Conditional, and Posterior.