Semi-log price charts

Introduction

When we look at price charts over a long period of time, or a chart where the stock price (or index value) has moved in a wide vertical range, the common linear price chart is not as useful as the semi-log chart. The semi-log chart has a logarithmic scale for the vertical axis while the time axis is still linear - hence the chart is a semi-log chart (and not a log chart). 

Case study - S&P500

The two price charts shown here are of the S&P500 US market index. These charts show the index from 1980, through to June 2014. The strong run higher during the tech-boom of about 2000 is clear, as is the tech crash from late 2000 until the market lows in 2002. The peak in 2007 precedes the market crash of 57 percent in the GFC of 2008-2009. These charts were produced in June 2014 to consider the question: "is the US market over-bought and due for a correction?". This was discussed in the 28 June issue (#240) of the Weekly Share Market Update and Analysis email (Special Comments section).

In the first chart at right, notice how the index is rather flat for the first third or so of the chart, and then the index moves strongly higher and whip-saws violently across the right hand half of the chart. At a glance, we might think that the second half of the chart is showing muchstronger volatility than the first half. And if we want to see exactly how much the index moved in the first third of the chart, it is rather difficult to easily see the detail. 

(Toolbox Members click on the charts for a larger version)

Note that in the second chart we are looking at the same index (the S&P500), over the same time period. At a glance, we can see more detail in the early portion of the chart - the first 15 years. The 1987 crash can now be seen more clearly as it stands out from the index values in the years before, and after.

Now consider the following observations for this chart. Firstly, the index exhibited a fairly consistent uptrend over a 12 year period from 1982 (point A) to 1994 (point B) on the chart. This averaged out to about 11 percent per annum. The first 5+ years (almost 5.5 years) saw about an 80 percent increase, while the 10 years saw about 190 percent. Notice that this is much easier to see on this semi-log chart (with the logarithmic vertical axis).

On the sample price chart here there are two vertical measures drawn on the chart to indicate a 190 percent increase in value firstly over the 10 years of 1983 to 1992 (inclusive), and then again over the 5+ years period from 2009 to mid-2014. From 1983 to 1992 this index rose about 230 points (from 120 to 350, including the 1987 crash and recovery). Then from 2009 the index rose about 1290 points (from about 670 to 1960). On this semi-log chart, we can easily see the details for both time periods when the index had very different values (about 200 to 300, compared to 700 to 1900).

The other key observation on this chart is that if we take a ruler and measure the actual physical distance on the chart for each of these two 190 percent increases, we will find the distance is exactly the same. That's what happens when we use a logarithmic scale - a specific percentage price increase (such as the 190 percent here), measures the same physical distance any where on the chart.

Why use a semi-log price chart?

Just to summarise, the benefits of using a semi-log price include the following:

• It is very helpful when studying a price chart that covers a long period in time, especially where there has been a large variation in price.
• It is much easier to see the detail price movements at the lower price ranges. On a linear scaled chart the smaller price values tend to be somewhat compressed (squashed up), making it difficult to discern the detailed price movements.
• Any specific percentage price increase that is identified and measured at one point across the chart, will be exactly the same when measured elsewhere on the chart.

More Information

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© Copyright 2014, R.B.Brain - Consulting (ABN: 52 791 744 975).
Last revised: 28 June, 2014.