# Telltale chart

The Telltale chart is a term popularized by John Bogle for a chart which compares the performance of one security to another.[1] It is also known as a "price-relative" or "relative strength" chart.[2]

## Background

In June 2002, John Bogle published his seminal article titled "The Telltale Chart". In this article, he began by:[1]

...criticizing the vastly over-simplified but typical way we look at long-term results. We hear, for example, that "small-cap stocks outperform large-cap stocks by almost two percentage points a year," [...] without acknowledging that each and every comparison we see is period-dependent. Whether or not the period has been selected to prove a point, neither the starting date of a comparison nor its concluding date are random.

He was referring to typical growth charts, which are indeed very sensitive to start and end dates, and tend to hide the periods of time that make a big difference to the trajectory.[note 1]

He then suggested the following:[1]

[...] that imposing chart... conceals more than it reveals. I would strongly urge you to not accept that conclusion without transforming it into the telltale chart that is devised simply by dividing the cumulative returns of one data series into another, year after year - in this case dividing the cumulative large-cap stock return into the cumulative small-cap return.

In other words, a telltale chart shows the aggregate growth of one or several investment assets (e.g. portfolio, fund, individual stock) divided by the aggregate growth of a benchmark asset.

Mathematically speaking, this is a simple way to normalize performance and to display it in a relative manner. Practically speaking, this type of chart can provide remarkable insights, showing the dynamics year over year in a much more effective way than a growth chart.

Telltale charts were originally used by John Bogle to illustrate his strong belief in Return to the Mean (RTM) properties, also known as mean reversion.

## Overview

Here is a growth chart comparing US Total Stock Market (TSM), US REITs, Total-International, and US Total-Bonds (TBM) from 1972 to 2016, using historical total returns from Vanguard funds and corresponding indices. The investments start with an initial value of \$100. Note that the vertical scale uses a log scale, which is more appropriate for displaying absolute (growing on average) performance.

We can clearly see that REITs overall performance was impressive, while TBM and International lagged, and that TBM displayed a steady (albeit lackluster) growth. This might lead a casual observer to jump to conclusions, though.

Here is the same information, but using a telltale chart with the US Total Stock Market (TSM) as a benchmark (baseline). This chart displays US Real Estate Investment Trusts (REITs), Total-International (ex-US), and US Total-Bonds (TBM) from 1972 to 2016, using the same returns as for the growth chart. Note that the vertical scale uses a linear scale, not logarithmic, which is more appropriate for displaying relative performance.

First, let's get acquainted with the mechanics of a telltale chart.

The numbers on the vertical scale quantify the relative performance (REITs grew roughly twice as much as TSM by the end of 2010, on our example chart).

When a line goes up for a period of time, this means that the asset grows significantly faster than the asset used as the benchmark. When a line goes down for a period of time, this means that the asset's performance is lagging compared to the performance of the benchmark, but this doesn't necessarily mean that the growth of the asset is negative - the benchmark could also be growing at the same time.

When a line goes sideways, even if it's positioned significantly higher (or lower) than the benchmark, this means that the growth (or lack thereof) of both the asset and the benchmark are similar, for this period of time.

Telltale charts are very handy because they allow to see on the same visual the overall cumulative trajectory (from start to end) AND what is happening year over year, therefore allowing one to grasp the big picture as well as the underlying dynamics.

Now, back to our example. The telltale chart exposes the following performance that is not evident in a growth chart.

• Bonds (TBM): We clearly see the changes in directions (relative to TSM) during the major crises (e.g. 1973, 2002, 2009), while the big picture, otherwise, is a lagging performance compared to stocks.
• REIT: We clearly see that the impressive overall performance is mostly due to two 'spurts of growth' (early 80s and early 2000s), while performance has been very poor (relative to TSM) for 15 years (1985 to 2000). Successfully investing in REITs would have required strong nerves and patience.
• Total-International: It goes up and down and up and down, relative to TSM. This really puts in perspective the lackluster performance of the last 10 years.

## Application

The Simba's backtesting spreadsheet was developed for the purpose of analyzing a portfolio based on historical returns.

John Bogle stated:[3]

A telltale chart is devised simply by dividing the cumulative returns of one data series into another (the benchmark).

In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.

Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.

It is interesting to observe that growth charts are actually a special form of telltale charts, and can be generated by the same tool.

A telltale/growth chart is provided in the Compare_Portfolios worksheet and can be used in multiple ways:

• If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).
• If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).
• If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.

Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: Telling Tales – 2017 update.

## Notes

1. A growth chart shows the change in value of an investment over time. For example, the "Growth of 10k chart" compares investments at a starting value of \$10,000. See: Growth Of 10K, Investopedia.com, viewed August 04, 2017.

## References

1. The Telltale Chart, John C. Bogle, Vanguard.com (Bogle_site), June 26, 2002.
2. Price Relative / Relative Strength, stockcharts.com, viewed August 04, 2017.
3. The Telltale Chart, John C. Bogle, Vanguard.com (Bogle_site), June 26, 2002.