# Use of charts and statistics to identify bubbles

Portfolio management

#### Taming and giving meaning to masses of data

Jeremy Grantham, Chief Strategist and Chairman of Grantham, Mayo, Van Otterloo, now known as GMO, has explored the idea of defining a bubble as an increase in the price of an asset to more than two standard deviations above the trend, taking inflation into account. Or, it may simply be used as a warning sign.

It will all make sense

Since this will be Greek to most readers let me introduce the idea of linear regressions and make some further comments about using standard deviations in charts of linear regressions.

A linear regression is a line on a chart of stock prices between two dates that best fits the trend of the prices. It is calculated using the ‘least squares fit’ method. Essentially, it minimizes the distance between the prices and the trend line. In some ways it is like a moving average and in some ways it is like drawing a down sloping trend line by drawing a line through a series of down trending tops, or drawing an up sloping trend line by drawing a line through a series of up trending bottoms. The linear regression line does not show as much delay in suggesting a change of trend as a moving average. Hold this thought. We will see an example below.

The linear regression line can be combined with a standard deviation channel. Standard deviation is simply a statistical measure of volatility. Charting software will do all this for you. The standard deviation channel is simply two parallel lines above and below the linear regression trend line plotted one or two standard deviations away from the linear regression line.

So, the linear regression line essentially draws a line through the middle of a data series. The software then plots a two standard deviation channel on either side of this line.

This is shown on the following chart plotted using Metastock software. This plot shows a hindsight view. That is, even though we are looking at the period of the late 1990s, the prices are shown through 2014. That is, we are looking backwards from 2014, hindsight. The S&P 500 appears to cross through the two standard deviation channel in mid-1996. If we use a breach of the two standard deviations channel as a definition of bubble, this is when the bubble begins. If we use the breach simply as some evidence (as I suggest is the correct approach) we would be saying at that time there is some evidence of a bubble.

This timing is roughly consistent with Alan Greenspan’s famous December 1996 comment regarding ‘irrational exuberance’. It is also consistent with Andrew Sarlos’ book, Fear, Greed and the End of the Rainbow, offering a clear opinion that American stock markets were in a bubble.(Sarlos, 1997).

S&P 500 with linear regression and two standard deviation channel

Statistics tells us that approximately 67% of the price data shown are within the two lines forming a one standard deviation channel and that approximately 95% are within the two standard deviations channel. In a sense, the GMO definition of a bubble says that 5% of the time we are in a bubble. That would be one year in twenty.

Plotting a two standard deviation chart is quite sensitive to the starting date and ending date. The chart covers the period from 1980 to 2014. In 1997 an investor would not have been able to plot future stock prices. In a stock market where prices are increasing quite smartly the regression line, and thus the channel, move up as prices go up and so tends to be a lagging indicator.

For readers unfamiliar with charting software this is difficult to understand. The idea basically is that if you plot a chart in 1998 the data only go to 1998. If you plot with the same data series in 1999 and prices have gone up significantly, the slope of the trend line, here, the linear regression, will have increased. In the same way, the starting point of the trend, whether in 1985 or 1995 influences the slope of the trend line. If it starts lower the slope is greater. If it starts higher, the slope is lower.

This is only the start of how we identify and deal with bubble. See below for more reading.

Individual stocks can go into their own bubble even if the overall market is acting normally. Today one might use these tools, including the exponential rise in semi-log plot charts discussed in my last post, to look at some rapidly advancing stocks like Tesla or Apple. I use linear regression and two standard deviation channels for all stocks I own or am interested in. One inspects the charts not for any definitive signal but to gather evidence.

Conclusion

Like many chart indicators a two standard deviation channel can be helpful. But it must be used with care and common sense. Sometimes it will give a false positive signal and sometimes it will give a false negative. In the first case it may give a bubble alert when there really isn’t a bubble. In the second, it may not be indicating a bubble even though there really is one.

For readers wanting to learn more about identifying and dealing with bubbles, take a look at Part 5: Asset Management and particularly Chapter 29. Bubbles, crises, panics and crashes and:

Section 29.05 Identifying a bubble

Section 29.07 Which market?

Section 29.08 GNP indicator

Section 29.15 Frauds and swindles

And then the all important Section 29.17 Picking the time to go to cash

But, to put all in context, read Part 5: Asset Management and particularly Chapter 28. Asset allocation