# A Disturbing Chart, from Bruno Ombreux

December 2, 2014 |

A disturbing chart: "This is Probably the Second Worst Time in History to Own Stocks"

## Bill Rafter writes:

The trouble with the chart is that the regression fit was done cumulatively, resulting in older data being subject to look-ahead bias. Thus only the current values are useful, and one wonders exactly how useful. As Steve has commented, the way to foil that is to use a moving regression fit in which the values are static over time, always taking the last point in the fit. Thus all data, past and current are relevant and can then be used in statistical studies.

The question that then comes up is which lookback period do you use. Wherever possible all lookback periods should be adaptive, the question then being to what input. In shorter term price data the market will tell you the relevant lookback period. I have never tried determining lookbacks for longer term data because (a) I don't expect to live long enough to take advantage of it, and (b) too many things can happen in the short run to screw up a good plan. Most people don't marry someone in their 20s based on the supposition that (s)he will look good in their 70s.

I also question the use of any equity or debt data prior to 1972. If you don't know why, ask Stefan. **That's one of the great things about the list; there are sources for just about everything.

Several moving functions you should consider:

Moving linear (i.e., regression) fits and their slopes.

Moving parabolic fits and their slopes. Since most economic and price data are parabolic, this is the better of the two. There is also something to be gained in the difference between a parabolic fit and a linear fit. Fitting parabolas is quite tricky, and it took us a while to code it. If you try to do so and want a check on your efforts, try fitting a parabola to a straight line. If the result is ludicrous, try a different method.

Moving correlations are particularly interesting between markets that might be alternatives to one another. Moving correlations between stocks and bonds (levels to levels) are something we have used for years and continue to do so. I thank Gibbons for his comment that Colby & Myers recommended them, as I had not been aware of that. (I'm not a fan of C&M.)

## Gyve Bones responds:

Colby and Myers didn't recommend the linear regression study per se… the empirical analysis simply showed that study to perform best with a fixed loopback parameter over NYSE index returns data over a long period of time compared to other trend following signal generators. This book was an early attempt to quantify different approaches to see how they performed trying as best as can be done to compare apples to apples. In the mid-to-late 80s, it was the best thing that had been done like that since Dunn & Hargitt's study using punch card futures data in the late 1960s (which found that the Donchian Four Week system was best, the system which launched a thousand CTA, including the Dennis Turtles and their spawn.) Another similar study was done in the 90s by Jack Schwager and another fellow whose name escapes me at the moment which was well done.

A question: when was the regression line fit? Today? 20 years ago? 50 years ago? The slope will change based on your starting and end points. How overbought or sold is a function of this. A more careful analysis would either apply this same "method" every year with a set of rules (i.e sell above x% overbought) or would do the same thing on a rolling window basis. It's an interesting chart nonetheless and gives one pause, but I would suggest it lacks a certain amount of rigor.

## Gibbons Burke writes:

It seems to me that this is a flawed chart to look at historically to make rules from because the trend line drawn into the past contains information about the future. The line is drawn using the linear regression of the entire data set so, for example, the line segment covering 1998-1999 "knows" about what happened in 2014. Very deceptive and misleading to make a rule based on the relationship of the data to the trend line.

The disturbing chart is a case study of why charting is so misleading because of the regression bias and also at the variance of a sum is the sum of the variances.

## Steve Ellison says:

Here is the way to solve the problem of the regression line incorporating future data. Attached is a graph of a "moving regression", as Dr. Rafter calls it. For each date, the red point is the last point of a 30-year regression of the S&P 500 as of that date (the graph is from 2010).

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