## Recovery inside a recovery

##### Apr 30, 2009

While reconstructing the Dow price chart (here), I noticed that there was some dubious statistics going on behind the scenes.  The chart made the point that the 1929 bear market took over 20 years to recover to its peak value.  The mystery wrapped in the enigma is the existence of the time series for a 1937 bear market and a 1939 bear market.  This could not happen unless there were bears within bears and recoveries within recoveries.

The uncomplicated time-series view brings this situation out more clearly:

This is a sobering picture in the face of all the talk about "green shoots" and "bear market rallies".

From a statistical perspective, the 1937 and 1939 bear markets cannot be interpreted without noting that they happened inside of a larger bear market.

That IS a sobering chart, but it leaves me with a question:

I'd be interested to see the graph of "how many days since it was last this low? (or this high?)"

At any time the price will be either rising or falling, so the answer to one of those two questions is always zero, but they can alternate frequently. the "days since low" can be plotted below the baseline while the "days since high" could be plotted above the baseline. Every so often the number of days increases discontinuously, as a recent record is breached, so the history reaches suddenly much further back. .

Derek: in order to execute your idea, we would need to agree on the definition of "high" and "low". The problem is one needs a long view to establish a real low as opposed to a transient low. Take a look at the absolute low in the chart above; not many months later, another "low" was reached; it would seem odd to reset the count at that point.

Sorry, I wasn't clear: I didn't mean "days since last peak/trough", which would require a definition of peak or trough. I meant "days since the curve was last this high, or low," which is unambiguous: you simply draw a horizontal line backwards in time until it stops floating in air and hits a previous portion of the curve.

If the curve is exactly flat locally, the value is zero. If it's rising locally, the "next" (backwards in time) time a horizontal line hits the curve will be the "days since last this high" value. If it's falling locally, the "next" time a horizontal line hits the curve will be the "days since last this low" value.

It's definable without disagreement or need for definitions, and it is describable in a plain English sentence, "the last time the stock market was this low was ten years ago!" That doesn't mean there was a trough ten years ago; in fact the market was probably rising at the time.

A time series of such values will be characterised by slow increases in value, punctuated by discontinuous increases (as old peaks and troughs are surpassed) and sudden falls to zero (as the curve changes direction and "days since" starts again from zero.

The high or low distinction can be encoded by colour, or by which side of the axis it's plotted.

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