A Picture Is Worth A Thousand Calculations

Beginner, Theory

Perhaps you’ve noticed the tag line for Portfolio Charts:


A Picture Is Worth a Thousand Calculations


While obviously a play on words to a common phrase that figuratively captures the descriptive power of images, some may not be aware that in the context of the site it is actually quite literal.  Lots and lots of calculations go into every image, and I thought it might be fun to illustrate just how deep the rabbit hole goes.  

To start, let’s look at one of the most common charts in finance — a compound returns chart. 




This illustrates the inflation-adjusted compound growth of a portfolio over time, and you’ll see these everywhere from fund summaries to message board debates.  While it is perfectly factually accurate, to be very honest I think this particular chart is the source of so much disinformation that it’s one of my biggest pet peeves in finance.  To illustrate why, let me offer an extremely common extrapolation of this chart and ask a simple question:


Which portfolio would you prefer?



Obviously the red line is the same portfolio as before.  The purple one ended with significantly more money, while the blue one ended with significantly less.  So the best portfolio seems pretty obvious, right?

Well, it’s a trick question.  The three lines represent the exact same portfolio.  The only difference is the start year.  The red line represents the most recent 30-year period beginning in 1987, the purple line represents the best timeframe (since 1970) starting in 1975, and the blue line represents the worst timeframe starting in 1973.  Yes, you read that right — only a two-year difference in start date resulted in a 2x difference in end portfolio values.

So you can see how that might quickly become a problem when comparing portfolio options.  Start date and overall investing duration have a huge impact on the apparent attractiveness of a portfolio, and most investors are blissfully oblivious to that fact. Whenever I see a portfolio debate reference a simple long-term average or a chart with a single line (or even worse, competing charts with different start dates), I usually get a bit frustrated.  Too much valuable information is being excluded to have a truly informed discussion about the highs and lows one may realistically expect.

But I’m not one to sit back and complain, and Portfolio Charts is my effort to expand the conversation to something more thorough and meaningful.  For example, rather than showing a single line or even several, the Portfolio Growth chart displays all 47 possible lines using every annual start date since 1970.




Now that’s a lot more interesting!  By displaying the full collection of historical paths, one can get a much better idea of the risk and uncertainty involved in any portfolio selection.

To illustrate the difference in information contained in each chart, let me reduce the original traditional line chart down into an icon.




Think of this as a single compound return that you can use to evaluate a portfolio.  You can also think of this as a single historical simulation run through one of many portfolio tracking tools around the web.

The number of similar calculations contained in a Portfolio Growth chart looks like this:




That’s 47 individual growth paths in one chart.  That alone would save tons of time cranking through traditional calculators, but it only scratches the surface of the data contained in other Portfolio Charts tools. For example, the Withdrawal Rates calculator evaluates 322 growth paths (each individually iterated hundreds of times)  to find the safe and perpetual withdrawal rates:




The Heat Map calculates even more returns:




That’s 1128 total returns — one for every colored cell on the chart.  But believe it or not, that doesn’t even come close to the site record.  That belongs to the Portfolio Finder:




While you may not realize it looking at the final chart, the Portfolio Finder makes 21,021 growth path calculations to find the minimum 15-year real CAGR for every possible combination of the 10-asset limit.  And that doesn’t include the extra drawdown calculations!

As an aside, some people occasionally ask me why I don’t simply calculate every possible portfolio and filter down from there.  This may help explain the problem.  The above image shows all of the calculations involved for only 10 assets at a time. To run all 28 current assets would require over 4 million calculations.  That’s one for every single pixel in your HDTV — times two!  I’ll save you the bandwidth from downloading an example, and also me the computing power to make it happen.  It’s in my eventual roadmap, but that’s a long-term goal.

Now don’t get me wrong — sheer data volume does not necessarily make an analysis more accurate.  I’ve seen plenty of deep calculations with very interesting results that are ultimately based on faulty assumptions, so methodology matters.  But hopefully this gives you a bit of insight into the depth and richness of data contained in the many charts on the site.  The apparent simplicity masks a lot of sophisticated calculations, and soaking in all of the information may take a little more time than you may be accustomed to with other tools you may enjoy.  It’s been worth the effort for me, and I hope it is for you as well.

So the next time you see a line chart or a single average return in an investing example, don’t simply rush to judgment.  Take a moment to consider the information that is left out, and think about how looking at the same portfolio through multiple lenses — even thousands of lenses simultaneously — may change your perception.  Portfolio Charts offers many tools to help with that process, but the ultimate responsibility belongs with you.

How well do you really understand your portfolio?