With the subprime-induced global financial meltdown of 2008 and 2009, along with the dotcom implosion in the early 2000s resulting in the NASDAQ dropping by approximately 80%, it’s not surprising that most investors are constantly on guard against the bursting of bubbles and crashes ensuing. If one takes a step back, however, and studies global financial markets over a long period of time, just how common are bubbles and ensuing crashes?

## Bubbles Are Booms That Went Bad

I occasionally like to bounce around the National Bureau of Economic Research’s very interesting site which houses all of its research papers as well a treasure trove of historical economic and financial data. I came across a recent research paper by William N. Goetzmann who is affiliated with Yale’s School of Management and one who is quite a prolific contributor to NBER research. He released a working paper in October 2015 called *Bubble Investing: Learning from History*.

Goetzmann states that “[i]n simple terms, bubbles are booms that went bad but not all booms are bad.” What conditions are required to be a bubble? He has two categories of bubbles. The first is, at least, a 100% gain (cumulative return) in a one year period of time and the second is, at least, a 100% gain over a three-year period of time. The second definition was chosen so that the booms of the 1920s and 1990s would be included.

## What Constitutes a Crash?

What constitutes a crash? The first is a drop of at least 50% in the following year and a drop of at least 50% over the next five years.

The author used databases going back to 1900 for 21 global markets. Here are the findings presented in table form:

**100% Real One-Year Price Increases**

T +1 | T + 1 | T + 5 | T + 5 | |

Count | Unconditional Frequency | Count | Unconditional Frequency | |

Market-Year Counts
| 3308 | 100% | 3122 | 100% |

Double in Value | 68 | 2.06% | 803 | 25.72% |

Halve in Value | 73 | 2.21% | 197 | 6.31% |

The first observation is that bubbles and crashes are pretty rare events over one year periods with a frequency of 2.06% for doubling and 2.21% being cut by at least half. Thus, there’s a relatively equal chance of both extremes occurring based purely on historical data. Not surprisingly, when the data analyzed expands to five years later, the probabilities increase significantly, but much more so for a doubling of value. Its probability shoots up to 25.72% while the probability of a drop in excess of 50% nearly triples but to a far smaller 6.31%.

Now that the author has quantified his best estimate of historical probabilities, how frequent are crashes after booms? Let’s turn to another table for the results.

**100% Real One-Year Price Increases**

T +1 | T + 1 | T + 5 | T + 5 | |

Count | Conditional Frequency | Count | Conditional Frequency | |

Years with a 100% real price increase
| 72 | 72 | ||

Counts of Doubling | 6 | 8.33% | 19 | 26.39% |

Counts of Halving | 3 | 4.17% | 11 | 15.28% |

Years with a 50% real price decrease
| 76 | 75 | ||

Counts of Doubling | 10 | 13.16% | 27 | 36.00% |

Counts of Halving | 5 | 6.58% | 7 | 9.33% |

Although the probability of a crash is quite a bit higher after a big run up the probabilities are still relatively low within one year (4.17%) and five years (15.28%). The chances of doubling yet again are higher for each cohort than the crash probabilities (8.33% and 26.39%) respectively. The chances of doubling go up quite a bit after a 50%+ crash as compared to crashing again for both the one year and five year time frames (13.16% vs. 6.58% for one year and 36.00% vs. 9.33% for five years). This shows the natural bias of markets to rise. Even after doubling the chances of doubling again are higher than crashing and when a crash does occur the chance of markets doubling are quite a bit higher than crashing again.

This is how the author puts it:

“Thus, a boom

doesincrease the probability of a crash, however, the crash probability is low. A rapid boom is not a strong indicator of a bust – probabilities move from 2% to 4% at the one-year horizon and from 6% to 15% at the five-year horizon. The significance of this shift depends of course on investor risk aversion. From a historical perspective, it is important to recognize that the overwhelming proportion of booms that doubled market values in a single calendar year were not followed by a crash that gave back these gains.”

The same results hold for booms that took place over three year periods of time as well as the following table shows.

**100% Real Three-Year Price Increases**

T +1 | T + 1 | T + 5 | T + 5 | |

Count | Conditional Frequency | Count | Conditional Frequency | |

Three Year Periods with a 100% increase
| 460 | 451 | ||

Counts of Doubling | 17 | 3.70% | 98 | 21.73% |

Counts of Halving | 21 | 4.57% | 47 | 10.42% |

Three Year Periods with a 50% decrease
| 178 | 179 | ||

Counts of Doubling | 15 | 8.43% | 85 | 47.49% |

Counts of Halving | 6 | 3.37% | 14 | 7.82% |

This is what the author says about the three-year booms:

“After a three-year run-up, markets subsequently halved in the following year 4.57% of the time. This is about twice the unconditional probability of a one-year having event, but it is still rare. At the five-year horizon, the probability of the market value declining by a half after five years is 10.42%, which is higher than the unconditional probability of 6.31% but not dramatically so.”

What the author doesn’t state above, however, is that the probability of the market value, at least, doubling after five years after doubling is 21.73%, more than double the chances of halving. The probabilities increase dramatically for a boom after the market has halved after five years. The probability goes from 8.43% after one year to 47.49% after five years, while it increases from 3.37% for halving after a year to 7.82% after five years. It looks like it pays to be aggressive after a market has been cut in half as the chances of a further crash are quite low relative to the potential for a boom to ensue.

Although I am by no means an expert in statistics, this research would suggest that investors may be too risk averse in terms of fearing a crash not only after a big run higher but particularly after a big downturn. This shows just how difficult market timing can be as it is logical to believe that being in at the top after a big run-up exposes oneself to a terrible risk of a permanent loss of capital. We all know how adept Warren Buffett has been in terms of avoiding getting sucked in at the top. On the other hand, this research seems to show that not all bubbles are homogeneous. They may climb a wall of worry or come from a deeply oversold and undervalued starting point to a new level that may still reflect fair value. In addition, it’s also very difficult for most people to invest when fear and pessimism are at their extremes, which are obviously hallmarks of bear market bottoms.

If one has the inclination and ability to pay close attention to and analyze sentiment, public participation, margin levels, and media coverage with some understanding of fundamentals, then one can at least make some sort of concerted effort to try to see how much greed is driving the boom versus improving fundamentals and something more secular in nature. There is no easy way. It is very, very difficult to ascertain whether the light one sees is an opening to more daylight or the train coming at you. Bubbles often go far beyond what most people can imagine so we’re prone to getting out too soon or eventually we throw in the towel because we see how well everyone else is doing and our envy of others and fear of missing out lead us to get in at the top which ends up leading to disaster.

It’s been said that “Eternal vigilance is the price of liberty.” I think history (and research) would show that it is a price of wealth too if one wants to keep and grow one’s capital. What is clear, however, is that not all bubbles are created equally. Some can lead to a catastrophic financial loss while others can be the springboard for even more significant gains.

Nobody said that making money was easy….except those who are trying to separate you from yours.

**Over to You:**

**Do you agree that bubbles go far beyond what most people expect or imagine? Do you go out of your way to avoid bubbles?**

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