Oct

11

The Stats, from Kim Zussman

October 11, 2008 |

Everyone knows last week's 18% drop was the worst in DJIA history (10/28-present). Here are the stats excluding that week (but including Great Depression weeks):

Descriptive Statistics: week ret

Variable     Mean    SE Mean   StDev     Minimum  Median Maximum
week ret   0.0012  0.00038  0.02442  -0.1554    0.0025  0.1821

So last week's return (return?) of -0.18 was about 7.4 STDEV below the mean.

Not only not normal, but where to look for example periods to model quant strategies? We now see it was a mistake to exclude 00-02. Even 29-40. What about the KT boundary?

In honor of this occasion, one will ditch the clever-as-if-it-was-known tone of this web site, and offer an opinion:

There are periods when markets behave well and are amenable to characterization (quantitative or otherwise). And there are periods when they are not. If you could know this with any precision, you would be extremely wealthy; which by design makes it about impossible to know.

Markets wouldn't trade actively if there weren't opportunities, or if it were easy to tell genius from luck.

There are periods when markets behave well and are amenable to characterization (quantitative or otherwise). And there are periods when they are not. If you could know this with any precision, you would be extremely wealthy; which by design makes it about impossible to know.

Markets wouldn't trade actively if there weren't opportunities, or if it were easy to tell genius from luck.

Rich Bubb responds:

So this "characterization" could be a 3×3 cube plotted representation (albeit this might be a little simplistic for most of the SPEC-Listers), with axes listed, in no particular order:

x aka a bubble exists in sector/commodity, scale might read: "no chance" at far left end; hysteresis happening and/or lobagola should happen or just did happen being in the mid-zone/s; and price/cost up n% in m-time meaning "here there be the bubble monster" and tread lightly or get out as fast as feasible.

y aka the interest rate du jour… scale trending down means economy &/or mkt trending down; scale trending up means economy &/or mkt trending up… but the scale would be visually represented by an upside down bell curve. So, for example, if fed rate is trending down, then the might be converted to a z-scale transformed scale with 0 in the mid of the scale, +3 on high end of scale, and -3 (std devs) at the low end.

z aka axis might be volatility or put-call ratio, or money supply, or OBOS%, or your indicator of choice.

With enough data points one might be able to observe the rate of change in 3D as things (x, y, z) move about.

I think this could be done with the charting tools in Excel…

Phil McDonnell observes:

The analysis Rich Bubb has described is essentially a 3D scatter plot. There are many examples of 2D scatter plots in Education of a Speculator and Practical Speculation as well as any introductory stat book that covers regression. The 2D plots relate to regression of one variable in an attempt to explain or predict another. The 3D case would relate to the case of using 2 variables to explain a third one. The regression would be of the form:

Z = a * X + b * Y

The usual caution is to avoid variables which are serially correlated. Usually price CHANGE variables are not correlated because an efficient market will remove any such correlation. By the same token price LEVELS are always highly correlated. One notes in passing that interest rates are a kind of reciprocal of the price level of the underlying debt instrument. Thus interest rates would be expected to be highly correlated but CHANGES in interest rates or prices would not be correlated.

Volatility is a more interesting animal. Volatility and therefore Vix levels are highly correlated. Again it is probably better to use changes in Vix than levels.

A final note is that one can perform a two variable regression of the above form even in Exc3l. To do that you need to have the Analysis Tools Add-In loaded. The data columns should be right next to each other (vertically). Then the regression analysis can be performed by clicking 'Tools/DataAnalysis/Regression'. 


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