The graph below, published by Deutsch Bank recently, shows that the market is pricing in less than a 10% probability of a 20%+ drop in the S&P 500 Index in the next 12 months. This is the lowest probability since the outbreak of the financial crisis, back in 2008. So, just how optimistic are investors, right now?

**Counting bears**

To answer this question, we have to study the history of bear markets. How often do stock market corrections with a magnitude of 20% or worse happen? Well, it depends on your definition of bear market. For example, one definition of a bear market is, the period between the moment the index drops 20% from its last record high, until the moment the lowest level from there is reached. Most bear markets don’t end at exactly 20%, obviously. Using this definition of a bear market implies a bull market is the period between the moment the index has reached its lowest level, after the market is down 20% from its last record high, until the moment a new high(!) is reached. This is visualized in the graph below.

A quick look at the graph learns that, by these definitions, there have been only eight bear markets since 1929. That’s less than one bear market per decade! That doesn’t feel right, and it probably isn’t. The definitions used above work heavily in favor of bull markets. Let me explain this using an example. During the Great Depression (1929-1932), the S&P 500 Index fell by more than 80% to a level of just 4.4. It took until the middle of the 1940s until the index managed to break above its previous high. Only then, a new bear market became possible, which eventually occurred in 1947, fifteen years after the previous bear market.

This methodology does not take into account, however, what happens in between. And that can be quite a bit. From 1932 to 1947 the S&P 500 Index dropped 20% or more no less than seven times (it also gained 20% of more seven times). But since the index never fell below the low of 4.4, reached in 1932, these seven 20%+ corrections are not considered a bear market. I don’t believe investors can relate to that.

Hence, the table above shows all periods in which the S&P 500 Index fell by 20% or more. For clarification, whenever the index rose by 20% or more (a bull market) following a bear market, and then dropped another 20% or more, two bear markets are counted. This way we can determine the maximum number of bear markets since 1929, which is 25. The number of bear markets has tripled, indicating one each 3.5 years on average.

**It has been a while**

Now, let’s link these findings to the first chart. It has been over eight years (2009) since we last experienced a fall of the S&P 500 Index of 20% or more. That’s more than twice the average period between bear markets since 1929. The fact that markets only price in a 10% chance of a 20%+ correction in the next 12 months implies investors are very upbeat about equities.

It’s probably fair to say that this conclusion is partly influenced by the volatile period between 1932 and 1947, already mentioned above. If we only look at the period after WO II, the frequency of a bear market increases to once in almost six years. Even then a new market should be around the corner if history is any guidance.

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