5 Ways to Plot Returns

There's an infinite number of ways to plot financial time series, let's look at the main ones.

The most basic way is just plonking returns on a plot.

This has one very nice feature. The returns are comparable across time, which makes a lot of sense, right? A return at the beginning of our backtest should probably be as important as one at the end.

The big drawbacks are twofold.

Firstly humans like smoothness, spikey returns are hard to decipher.

Which leads us to the second point. People love telling stories. Storytelling is what finance really is (a collection of models or anecdotes) but it can be dangerous as well. The plot doesn't tell a good story.

The cumulative plot is the most popular graph.

It tells a story, but only one story well, the plot starts at zero and ends at the cumulative return.

No point plotting a chart like this when a single return figure will suffice.

Returns are not comparable over time. Returns from the sixties look minuscule next to those from the past decade

For fun, try to find the crash in '87, hard to spot eh?

Another favourite chart is the venerable moving average.

One big plus, returns are comparable over time.

A humungous disadvantage is that the moving average 'returns' aren't real. They are dampened, things look a lot less volatile than reality.

Depending on the moving average period you define, you can start to tell a riveting story. Problem is, the story you end up telling may well have little to do with reality ('87 doesn't look very familiar?).

A demeaned cumulative plot tells a story, plus you can make intertemporal comparisons.

At least to a certain degree. By its nature the time series begins and ends at 0, so any massive jumps or drops close to the beginning or end of the time series are going to look a little smaller than those in the middle.

But now you can pick out the drop in the last quarter of '87 pretty handily, not only that but other less familiar large drops pop out. E.g. the massive drop in the '70s when the Middle East hiked oil prices.

While the usual cumulative plot tells you one figure (cumulative return) this plot gives you a richer understanding of volatility over time while also giving you a story to tell.

Moreover, the data is 'real', we only took a constant average return away from each return.

My favourite graph however is the humble histogram.

The biggest problem with the histogram is that it doesn't tell a story, because fundamentally it's about forecasting the future. In this case it gives us an idea of what might happen in the next quarter.

Generating future parallel universes is what everyone should be doing, rather than trying to replay history.

Conclusion

The tendency for financial analysts to use many types of plots simultaneously, is, as one old colleague used to call it - the 'airplane cockpit syndrome' - which cause more headaches than anything else. Personally I'd take a 'demeaned cumulative' plot over using both 'returns' plus regular 'cumulative' plots together.

And... as tempting as it is to tell stories, perhaps we should begin to shun them, more often than not they are beguiling rather than instructive.

If I have missed any good plots, be sure to get in touch!