# Logarithmic Charts Should Be The 'Apple' Of Your Eye

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by: Gary Jakacky

Odds are you haven't used logarithms since your teacher introduced them to you in high school mathematics, if you can remember back that far. But for investors who count on price charts to gauge stock performance and use technical analysis, logarithmic charts are an essential tool that must be understood.

There are two basic scales for price on the vertical axis in stock charts: a linear scale, and the logarithmic scale. A linear scale assigns equal vertical distances to dollar changes in price; a logarithmic scale assigns equal vertical distances to percentage changes in price. This is not a small detail long term investors can overlook. Since it is percentage gains which investors use to gauge performance, the latter scale should be used in many cases.

Consider the two charts below which show the price of Apple Inc (NASDAQ:AAPL), one of Wall Street's darlings for the last decade. The top chart is a linear scale, the bottom chart a logarithmic one.

The chart clearly shows that AAPL was a superb investment over this period. What catches your eye immediately are not only the surge in price that began after the 2009 crash, but also the huge spike in the last six months or so. In contrast, AAPL sure looked like a boring holding through most of 2002 to 2005!

But looks are deceiving, as the logarithmic chart below makes clear.

It turns out the surge from \$6 a share to \$200 a share in the previous decade was far more important and profitable to investors than the recent strength after the crash. And that pop in 2012? It looks almost insignificant relative to some past action. Yet how many investors would boast about the huge price increase in AAPL since the beginning of this year?

On a logarithmic chart, a price change from 2 to 4, from 20 to 40, or from 200 to 400, all have the same "size" on the vertical axis: and thus the investor is not deceived by the large dollar amount of the latter change.

For long term investors the scale issue is more than just a stylistic one. With a linear scale the eye is drawn only to recent price movement: where the action appears to be. This tempts the investor to over emphasize short term, and recent, price swings. Conversely, price changes a decade or more ago are some compressed and invisible: it looks like there were no returns on your investment or holding the shares was "dead money."

Furthermore, the greater the long term gains in holding the stock, the more pernicious this short term focus and bias becomes! Look at a linear chart for Priceline (NASDAQ:PCLN), another one of Wall Street's star performers. After six years of desultory price action, it appears that aliens landed near the end of 2008 and started buying the shares:

But looking at the logarithmic chart, it becomes clear the PCLN was a superb investment in the early years of the previous decade, as well. You didn't have to be "lucky enough to get on board" in 2009. The gain from 2003 to 2008 was substantial and meaningful.

Logarithmic scales have other advantages as well. Returning to the APPL charts above, it is impossible to imagine drawing a trendline connecting the series of lows in 2003 on up through 2008. In contrast, on the log chart, a trendline connecting 2003 and 2006 lows is very meaningful: It was touched in 2008 and broke later that year, showing just how significant the 2008 financial crisis was. Similarly, on the linear chart the 2012 surge has made a trendline connecting dips of the last few years hopelessly out of touch. In contrast, on the logarithmic chart that trendline very much in play as a source of support or a matter of concern were it to break.

All this is not to say that there is no place for linear price charts. But their use should be confined to short periods of time, to narrow fluctuations in price, or both. Investors concerned with long term performance and returns should use logarithmic charts to gauge past performance and estimate future results

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.