Confronting Reality Head-On

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On page 40 of his seminal work, Technical Analysis of the Financial Markets, John Murphy offers a graph that concisely illustrates the difference between an Arithmetic and a Logarithmic Scale. Applied to chart analysis of stocks, the key difference is that the vertical, or Y-axis, on an algorithmic price scale shows an equal distance for each price unit of change. In essence, each point on the arithmetic scale is equidistant. Most of the charts we look at use an arithmetic scale, and that is perfectly fine.

When looking at a longer-term chart, though, particularly one where price has made a dramatic move in the given timeframe, it is more appropriate to use a semi-logarithmic scale. Logarithmic scales do a better job of capturing the essence of larger percentage moves, since the percentage increases get smaller as the price scale increases. The points along the vertical axis on a logarithmic scale are not equidistant like that on the arithmetic scale.

That may sound like a bunch of technical mumbo-jumbo, so let me give you a practical and familiar example. Green Mountain Coffee Roasters is a stock that I profiled several times last year, all using an algorithmic scale. The theme of my posts was to analyze the bearish nature of the price action in the latter-half of 2011. While I probably could have used a semi-logarithmic scale to argue against my thesis that GMCR has formed a parabolic blow-off top, the reality is that the latter type of chart actually presages an even steeper drop ahead for the trendy coffee machine and K-cup maker. So, if anything, I was holding back from driving the bearish thesis home.

Before I delve any further, note that both charts I present below are identical in terms of issue (GMCR) and timeframe (monthly). The difference, of course, is the scale I use for each. As you can see on the second chart below, the logarithmic scale sees our parabolic blow-off top vanishing. However, on the broad, multi-year look that this monthly chart offers us, the trend could only now just be coming apart. In other words, parabolic blow-off or not, Green Mountain has much further to drop. If anything, the logarithmic scale magnifies the room the stock has to go lower, if indeed this major trend change starts actually rolling down the other side of the now-red mountain. Note that the volume pattern certainly seems to suggest that, with the huge level of selling bars to close out last year.

Interestingly, the algorithmic scale, the first chart below with the same monthly timeframe as the second chart, gives the appearance that GMCR has already crashed and is basically done going lower. Again, compare that algorithmic look of the “already crashed” Green Mountain to the logarithmic scale, where the bears are just getting warmed up here. So, if you think using a logarithmic scale to eliminate a blow-off move is a sneaky way to add points to a given bullish thesis, think again. The value of using the logarithmic scale for longer-term charts where price has rapidly appreciated is only captured by confronting the reality of the technicals as objectively as you can.

In some cases, it may very well be true that using a logarithmic scale that eliminates a parabolic move on an algorithmic scale is bullish. Indeed, the more objective interpretation in that case would be that the stock simply saw a secular breakout. That may be true for a stock like Apple, but in my view it is not correct for Green Mountain Coffee Roasters. For the foreseeable future, I would avoid GMCR for anything more than a quick trade.

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