Back in college my favorite engineering professor liked to repeat an adage that I bet everyone has heard at some point:

There’s no such thing as a free lunch

I believe the first time I heard that phrase it was in reference to a literal gathering where they were enticing students with free pizza, and my professor astutely noted that, make no mistake, you were going to pay for it in some way. Nothing is ever truly free, and there was bound to be a call for your time or money as part of the deal. Of course he was right, as the string attached to that pizza was an eye-rolling sales pitch I really could have done without.

The phrase was important to my professor not just to be cynical but to teach a very important lesson to a young engineer — everything has a tradeoff, and usually the larger the reward the greater the required payment. He did a great job as the memory has stuck with me to this day, and the idea of balancing tradeoffs has helped me in all aspects of life from how to judge the true worth of a “free” slice of pizza to how to get a new product to market.

Tradeoffs are a core topic not only in engineering but also in investing, and reams of books have been written on balancing the risk of an investment with the expected return. One recent post by Zach at Four Pillar Freedom particularly got my attention, as he did a very impressive job of summarizing the average return and standard deviation of every portfolio on Portfolio Charts. By mapping the risk and return of each portfolio option, it’s really easy to get a feel for the tradeoffs involved.

I’ve also been known to use similar charts to make a point, and I know first-hand how much effort goes into making them. So inspired by Zach’s work and similar charting gurus that paved the way, I thought it would be helpful to make a new tool to generate them automatically. I call it the Risk and Return chart.

The Risk and Return chart takes the traditional idea of mapping different asset allocations by their average return and standard deviation and adds quite a bit more functionality. From a customization perspective, I’ve included the ability to not only dynamically visualize your own portfolio on the same chart but also to choose from a wide variety of different risk and return metrics that may be important to you personally. You can think of it as a mashup of the Portfolio Finder’s ability to map the risk and return of many different portfolio types simultaneously, the metric diversity of the Portfolio Matrix, and the quick computation ability of the My Portfolio tool.

(As a quick aside, one of the very cool unexpected bonuses of creating this tool is that a portion of it was easy to translate to other calculators. So in addition to the Risk and Return chart, take a moment to try out the Portfolio Matrix that now also has the ability to add your own portfolio to the rankings.)

From my perspective, the most unique and helpful feature of the tool is the ability to choose your own risk and return metrics. Any long-time reader of Portfolio Charts knows that average return and standard deviation really don’t tell the whole story about the full investing experience, and having the ability to quickly modify the chart to study other useful measures may challenge many of your core assumptions about the nature of risk and return rooted in “common knowledge”.

As an example, let’s start with a standard version of the chart showing the relationship between standard deviation and average return. I’ll crop out the asset allocation section to save space, but for these examples the “My Portfolio” option is a simple 80% total stock market / 20% intermediate bonds portfolio.

That’s a classic distribution found in many different academic studies that is used to illustrate the proportional relationship between risk and returns. The Total Stock Market portfolio has the highest average return and also the highest standard deviation, while other more diverse portfolios fit somewhere lower in both metrics along the spectrum. Students of Markowitz may find it interesting that the Golden Butterfly and Pinwheel Portfolio lie along the efficient frontier of these options, which is an indicator of their ability to generate maximum returns with minimum risk.

Speaking of risk, here’s a pop quiz — is a standard deviation of 10.5% good or bad?

You probably have no idea, and it’s really not your fault. Standard deviation is a statistical measure that’s popular at least in part because it’s easy to calculate but honestly is not that useful for normal people. Personally, I prefer something called the Ulcer Index, a composite measure of the depth, length, and frequency of every portfolio drawdown that more accurately represents the degree of portfolio pain.

As you can see, using the Ulcer Index as your measure of risk doesn’t completely change the order of portfolios but it does spread them out a bit. Rather than being only twice as volatile as the Golden Butterfly measured by standard deviation, the Total Stock Market is about 7 times as painful measured by the Ulcer Index. For risk-averse investors, that bit of info alone may change the point along the efficiency curve where you prefer to operate.

But where it gets really interesting is when you start thinking beyond the average return. You see, the average return is also easy to calculate but as a statistic it completely ignores a very important financial risk — the uncertainty of sequence of returns and how it affects your compounded account balance. Not every portfolio is particularly accurate at hitting its average return on your own personal timeframe, and when you start looking at reasonably conservative historical outcomes the results may surprise investors who only think in terms of averages. My favorite metric here is what I call the Baseline Long-Term Return. The long story is that it’s the 15th percentile 15-year inflation-adjusted compound return for every rolling investing period we have data for. But in layman’s terms, its a reasonably conservative real-world long-term return excluding the worst outliers.

Talk about inverting expectations! Accounting for both investing uncertainty and the effects of compound returns, betting on the higher risk of the Total Stock Market rewarding you with superior long-term returns is no sure thing. In fact, even over long 15-year periods that would stretch the patience of even the most stoic investor, the highest-risk portfolios like the Total Stock Market have sometimes lagged even the lowest risk options such as the Permanent Portfolio. Once you think beyond over-simplified mathematical assumptions, the relationship between risk and return gets a lot more complicated.

Of course, the Risk and Return chart doesn’t stop there and you can play with lots of different performance metrics. For example, have you ever wondered how safe withdrawal rates are related to longest portfolio drawdown?

That’s a surprisingly strong correlation which provides a valuable reference point for the best way to build a retirement portfolio to last. Perhaps the name of the game isn’t maximizing returns but minimizing the length of drawdowns. By looking at different risks and returns your entire perspective changes.

With many different metrics and your own portfolio ideas to add to the mix, the Risk and Return chart is a flexible tool suitable for lots of different types of exploration. Not only will it help you navigate the various risk and return tradeoffs of a particular portfolio idea, but it can also help you avoid the very significant cognitive tradeoff of missing very important data points by only looking at standard deviation and average return. Mix up the metrics and you’ll paint a much more colorful and nuanced image that will make you think and help you settle on something you’re truly comfortable with.

There’s no such thing as a free lunch, but in this case there really is such thing as free data. Happy portfolio hunting!