Using a Chain Index to Visualize Growth

A chain index is an index number in which the value of any given period is related to the value of its immediately preceding period (resulting in an index for the given period expressed against the base period = 100).

This index type is called a chain because individual values can be linked with previous values all the way back to the base value, thus converting them into a series of indexes with the first reference period. This way, the consecutive values of the index numbers form a chain, as it were, from the first (reference) to the last period in the series.

For example, the following table gives the financial metrics for a major consumer products company, Procter & Gamble (PG, Financial), over the last 10 years expressed on a per-share basis.

The following chart illustrates the above metrics. While useful, it is a bit difficult to interpret given the different scale and starting points of the data.

We can think of the above series as horses running on a track (time being the track). Currently, they are all running independently. However, if we can line them up at a common starting point and then compare them to each other as they run, over time, the data becomes much more interesting.

We can do this by constructing a chain index with each of the series. The base of the series will be the first number of the series. For instance, the earnings per share series will be June 2012 at $3.66. This will be index "100."

The index for June 2013 is calculated as: 3.86/3.66 * 100 = 105.46.

For June 2014: 4.01/3.66 * 100 = 109.5

And so the trend continues.

Using this technique, the data has been converted to the following array expressed as a chain index. Each series is chained to June 2012 (note that the values have been rounded).

We can look at the above array graphically after plugging the data from GuruFocus into an Excel spreadsheet. The chart is much easier to interpret as all the numbers are expressed on a common scale and begin at a common starting point.

For example, we can see Procter & Gamble's share price has outpaced its revenue and earnings per share by a wide margin. Earnings per share is up 50% in 10 years while the stock is up 132%.

We can also compare the chain indexes of different companies. Below is the one for 3M (MMM, Financial).

I can now see that 3M's fundamental performance is better than that of P&G over the past decade. Also, 3M's price is more consistent with fundamental performance while P&G looks overvalued. This indicates I should be thinking of overweighting 3M and underweighting P&G in my portfolio.

Conclusion

Converting data series into chain indexes and comparing them to each other is a way to analyze data visually. We can uncover insight into the company's strengths and weaknesses as well as make decisions on valuation and asset allocation. While the above can also be done using percent change, an index is more intuitive (at least to me) and it's the same amount of work. This technique is commonly used in macroeconomics. For example, the Consumer Price Index is a chain index.