A Log In Your Eye

Even stocks crushed to a fraction of their all-time highs can come back from the dead. But you can miss signs of life if you rely solely on linear charts. To sharpen your diagnostic vision, eyeball stocks using logarithmic charts.

A great example is MicroStrategy (MSTR | Quote | Chart | News | PowerRating). On Friday, the stock jumped 18 1/8 to 62 1/4 on widespread rumors the customer-management software company is close to securing $100 million through a private placement.

That marks a fourfold advance from the stock's May 16 low of 16 9/16. Yet this explosive advance barely registers on a linear or arithmetic chart. To the eye, MicroStrategy's recent price progress appears minute in comparison to the preceding crash in the stock.

Now let's check out a MicroStrategy chart drawn over the same time frame but on a logarithmic scale. As you can see, the advance off the bottom stands out bright as day.

So which chart is more accurate? Neither. Each faithfully depicts price according to its scale. The problem lies in how we interpret charts.

A linear scale portrays simple arithmetic price moves. For instance, the vertical distance from $10 a share to $20 equals the vertical distance between $100 and $110. That makes perfect sense in an absolute sense. Each visual span on the chart covers an equal arithmetic price change of $10.

But in relative terms, the two price moves are very different. A price increase from $10 to $20 represents a gain of 100% while a price increase from $100 to $110 spells a 10% return. Which stock would you rather own?

On the downside, a price decline from $20 to $10 translates into a 50% loss. A price decline from $110 to $100 comes to a 9% loss.

Log charts depict percentage or relative price moves rather than arithmetic price moves. The same vertical distance measured anywhere on a log chart spans the same percentage gain or loss.

Linear charts work fine over short time frames. But a visual distortion creeps in as you plot big price moves over longer time frames.

In a linear chart, a long-advancing stock will appear to make greater and greater gains, causing the price to curve increasingly upward, like a jet aircraft pulling its nose ever higher into the sky. This can occur even if the stock's percentage rate of increase remains unchanged.

The opposite occurs when you depict a long-declining stock on a linear chart. The price declines become smaller and smaller, visually speaking.

You can see this on the linear-scale MicroStrategy chart. Shares entered a decline after peaking at 333 a share on March 100. The stock gapped below its 50-day moving average on March 20, losing more than half its value, after the company restated its financial results.

The changes reduced MicroStrategy's 1999 reported revenue from $205.3 million to between $150.0 million and $155.0 million. The bottom line changed from previously reported earnings of 15 cents a share to a loss ranging between 43 to 51 cents.

From there, stock tried to rally, stalled below its 50-day moving average, then rolled over. As you can see, the price bars become increasingly compressed on the linear chart, creating the visual impression of progressively smaller price declines. The decline appears to decelerate. And the rebound off the May 16 low looks skimpy by comparison to the preceding sell-off. You form the impression that the stock has barely budged.

Viewed on the log chart, you can see that MicroStrategy's percentage rate of descent was constant from March 10 peak over the next seven weeks. And the rally off the May 16 low comes through loud and clear.