Three Secret Ingredients of the Most Efficient Portfolios

Advanced, Featured, Theory

December is often the time of retrospection and yearly wrap-ups, with stories recapping events of the last year and looking forward to new opportunities. In the finance space, you’ll find endless collections of the top performers of the year and forecasts for the one to come. While that’s all interesting and comforting in its own ritualistic way, this holiday season I decided to revisit a bold question that’s much bigger than short-term market news cycles:

What do the most efficient portfolios in history have in common?

Truly understand that answer, and much of the market noise that worries you from day-to-day and year-to-year loses its power over not only your emotions but also your account balances. So if you’ve ever wanted to think beyond your investing assumptions and explore the data for proven ways to approach timeless portfolio problems, grab a cup of coffee and pull up a chair. This article is for you.


Exploring this topic requires studying a huge amount of data at once, and I’m going to make liberal use of a chart found in the Portfolio Finder.

For those not familiar with the tool, the Portfolio Finder calculates the risk and return of hundreds of different portfolios simultaneously and plots them all on the same chart. For example, the above image shows every possible equally-weighted combination of up to 10 unique assets including different types of stocks, bonds, and real assets like commodities and real estate. That’s 637 unique portfolios.

A Nobel-winning economist named Harry Markowitz first used a similar chart to study what he called the efficient frontier – the border of points to the top-left that represents the best balance of risk and return. Lots of people have built on that concept over the years while exploring the same core insight of finding the most efficient portfolio option, and they’ve brought different ideas to the table like using expected returns instead of historical averages and studying a few different assets beyond the original options.

My own version follows a similar approach to what you’ll find in many efficient frontier analyses, except I consider way more asset combinations than most people and I use different definitions for both risk and return. For full explanations, be sure to read these articles about the Baseline Return and Ulcer Index. But here are the high points for why they’re important here:

Baseline Return

The 15-Year Baseline Return solves a major problem with most efficient frontier calculations where the results vary wildly by the timeframe studied. It looks at all 15-year timeframes since 1970 simultaneously and reports the 15th-percentile inflation-adjusted CAGR rather than simply the always-shifting numbers over a single period. Basically, it accounts for the return risk that people always talk about but gloss over with an average. It presents a more honest number of something to safely plan around, and it’s my favorite measure of a conservative long-term return using historical data.

Ulcer Index

In my opinion, standard deviation is a particularly unintuitive and deceptive measure of risk that focuses too much on mathematical distribution of returns and not enough on the actual investing experience. The Ulcer Index, on the other hand, is a composite number that accounts for the depth, length, and frequency of portfolio drawdowns. I like how it better captures the feeling of a particular portfolio choice when things go south, and it’s my metric of choice for comparing the relative pain between two portfolios.

Put those two numbers together, and you get a nice feel for the true performance of a portfolio not just on average but in the tougher times when markets don’t cooperate on your own investing timeframe. And when mapped on the chart, the options closest to the top-left are the most desirable because they have consistently offered most dependable returns with the least amount of painful tradeoffs.

More power!

While looking at hundreds of portfolios at a time is pretty interesting, for the purposes of our question that still feels quite limited. This topic burrows deep into the data rabbit hole to the point where the calculations exceed the practical limits of the site tools, so I’ve taken the time to do a bunch of number crunching that greatly expands their native capability.

Instead of looking at only 10 assets, let’s try 20 covering every major unique domestic and international asset option for US investors. Have you ever wished you can set the Portfolio Finder settings to look like this? Well I’ve got you covered.

I left out TSM for the heavy overlap with LCB and BIL for the commonality with ST bonds. But this should get the job done.

In addition, the default Portfolio Finder assumption that every portfolio must be an equally-weighted combination of up to 5 unique assets is also limiting. To address that, I also updated the logic to study 20% intervals while allowing repeating assets. So for example, instead of just looking at equal allocations of 50% LCB and 50% IT, it can now look at a broader range of possibilities: 80/20, 60/40, 40/60, and 20/80.

With those two changes combined, the resulting number of portfolio options skyrocket from a quaint 637 to a hefty 42,504. The spreadsheet for all of those options is massive and slow, but it doesn’t stop me from pushing my own CPU and making some cool charts.

every possible portfolio combination

Now we’re in business!

So with a huge amount of data and the ability to filter the results, let’s stop fretting over needles one at a time and study the haystack.

Thinking beyond old-school stocks and bonds

As a starting reference point, I think it’s helpful to see where the most popular portfolio ideas fall in the cloud of potential options. So let’s begin with what many investors consider the pinnacle of US stock diversification — a good old large cap blend index fund.

See that green dot? That’s where your typical US large cap fund fits on the chart. The pain is quite high, and the return is a lot lower than you probably expected based on the standard literature. That’s the result of the inflation-adjusted baseline return that we talked about that adjusts for return variability and looks not at the average but at the lower-end 15 year outcomes on record. Clearly volatility has a very real tradeoff and it involves more than just your emotions. We’re talking real dollars and long-term savings goals possibly not meeting expectations.

Also note that virtually any combination of other assets is likely to have a result above and/or to the left of large cap blend alone. For all of its rightfully-earned praise in efficiently tracking the US stock market, a LCB index fund by itself is not a particularly efficient allocation of resources in terms of risk and return.

Next, let’s look at different mixes of large cap blend and various types of treasury bonds.

Adding short term bonds to stocks accomplishes what most people expect and reduces risk, although down to about 60% stocks the baseline returns are actually pretty flat. Contrary to what many people believe about risk and return, the relationship is not necessarily linear — especially once you actually account for the risk and look beyond averages. Switching to intermediate bonds adds an interesting bump in the curve with a peak at about 60% stocks, which speaks well to the relative bang for the buck of the Classic 60-40 portfolio.

Pay close attention to the curve with long term bonds, though, as it demonstrates an interesting phenomenon where anything above or below 40% stocks is both higher risk AND lower return than the right combination of the two assets. Both stocks and long term bonds are relatively undesirable in isolation, but the combination of the two moves the portfolio point dramatically in the right direction.

It’s that lesson that really unlocks the power of understanding modern portfolio theory. Combinations of volatile complementary assets can have much more desirable performance than any one asset by itself.

Diversification from the ground up

So if a simple large cap blend fund is comparatively pedestrian and mixing in bonds only starts to expand the outcomes a little, how does one effectively move their portfolios to the more desirable corner of the cloud?

Let’s start by adding the options for all types of US stocks including every combination of large/small and blend/value/growth funds.

every combination of us stocks

Opening up the various size and valuation factors clearly improves the options in terms of both risk and return. In fact, do you want to guess what portfolio owns the desirable spot at the top-left?

That’s 100% small cap value. Factor diversification really is a legit stock strategy, but there’s still a lot of cloud to explore.

What if we also include all types of US bonds?

every combination of US stocks and bonds

Now we’re getting somewhere. Once you think beyond a single type of stocks and one bond fund at a time, investing gets a lot more interesting. But let’s not stop there. What happens when we open it up to international stocks and bonds as well?

every combination of US and international stocks and bonds

Hmm. That filled in the middle and expanded south, but honestly did very little to unlock the most desirable portfolios. To close that gap, you need to expand your mind beyond factor and country diversification to assets beyond stocks and bonds entirely. Let’s step through the remaining options one at a time — REITs, commodities, and gold.

REITs mostly fit in with the other stocks as one might expect. Commodities start to move the needle a little. But it isn’t until you consider the portfolio-boosting power of gold that the most efficient options become available. It really is a unique asset for how it’s able to mitigate the downside risk of certain portfolios without sacrificing baseline returns.

All that glitters is not a good investment

Before you rush out and buy as much gold as you can afford, allow me to share one more chart for context. This one shows all portfolios that include some amount of gold, and I’m going to need to zoom out.

every portfolio that includes gold

Do you see that lonely point at the far bottom right that not only was insanely painful to own but also had large negative real returns for a full 15 years? There’s a reason I cropped the charts to ignore it. Why on earth would any rational investor touch that with a 10-foot pole?

That’s the portfolio with 100% gold.

So two things can be true at the same time:

  1. An asset is a critical component in many of the most desirable portfolios.
  2. The same asset is disastrously undesirable when studied only in isolation.

Do you like salt on your food? Can you eat an entire box of it in one sitting without getting extremely sick? Same concept.

Incidentally, I share this chart not only to provide balance but also to demonstrate an important point about the metrics being measured. While some of you reading this may have a natural reflex to assume that the data for certain assets like gold is cherry-picked or skewed by unique historical events to make them look better than they really are, this clearly proves that it’s not the case. The chart deliberately seeks out the not-so-good timeframes that the fund marketers don’t dare mention, and in that context the numbers for gold are brutal. But the thing is, the same image also demonstrates that it doesn’t matter. It’s the portfolio that counts.

Gold is the ultimate example of the same risk-bending phenomenon that we saw with mixes of stocks and long term bonds where it only makes sense in certain amounts. That disconnect between the individual asset and the overall asset allocation is why some people can’t get over owning any gold in a portfolio, and it’s also why the concept of mixing volatile assets to cancel the noise can seem completely out of reach for investors of a certain mindset. If you fixate on the fundamentals of each portfolio ingredient, you’ll never see the full potential of the recipe.

So let’s cut to the chase and talk recipes.

Exploring the efficient frontier

If you’ve been paying attention to the breadcrumbs along the way, you probably already have a decent guess as to the types of portfolios occupying the top-left portion of the chart. But in case it isn’t obvious, here are all of the portfolios that contain at least 20% each of small cap value, long term treasuries, and gold. The green dots leave the other two spots open for any other option, while the navy dots focus exclusively on the big-3.

That’s a pretty compelling grouping.

The only point that looks a little weak (down at about a 1.4% baseline return) is predictably the one with 60% gold and the minimum amount of the other two. As we’ve seen, too much gold gets rough pretty quickly.

And since I’m sure you’re wondering, the top-2 navy portfolios right at the sweet spots of the efficient frontier are: (60% SCV, 20% LT, 20% GLD) and (40% SCV, 40% LT, 20% GLD). That’s a remarkably clear illustration of how well the assets work together, but look at all of the other green dots and you can see that it’s definitely not an exclusive 3-asset party. Other assets also mix in quite well, and one notable example is the Golden Butterfly.

The orange circle is a close representation of the Golden Butterfly with equal parts large cap blend, small cap value, long term bonds, short term bonds, and gold. So if you’ve ever played with the charts and wondered why the Golden Butterfly is so hard to beat in terms of consistency, this helps explain the challenge. It’s already right along the efficient frontier for all possible combinations of assets. And the data indicates that it can largely thank its allocation to small cap value, long term bonds, and gold for the honor.

So no matter how you personally invest, if you’re looking to boost baseline returns and reduce painful investing experiences then there’s a particular 3-asset mix that you should probably take a look at. Small cap value, long term treasuries, and gold. For the purposes of discussion, let’s call them the Frontier-3.

Stuff to think about

To be honest, I struggled for a while on how to present this information because it starts to tread dangerously close to something I’m fundamentally against — pushing people towards a particular way to invest. And to be very clear, I definitely do NOT recommend that you all go out and sell everything to load up on the Frontier-3 assets. Picking the right asset allocation for your own life savings is about so much more than simply optimizing one chart, and it takes careful consideration from lots of different angles.

But I do find the data from this perspective thought provoking, and I imagine it might encourage a lot of people to reconsider their assumptions that determine how they invest their money. So rather than pitching one single solution, here are a few things to think about based on what we’ve covered.

There’s nothing magical about the assumptions

While all of the charts I’ve shown focus on 20% increments of 20 different US and international assets, there’s nothing particularly special about those numbers. Smaller portions or portfolios containing more than five assets can be great options as well. I had to make certain assumptions simply to limit the possibilities to a number that could be calculated at all, so it’s better to consider it as a starting point for exploration rather than a final say.

For reference, here’s how all of the portfolios on the site map to the same chart.

To see where your own favorite asset allocation stands, the easiest way is to use the Risk and Return chart. You won’t see the full gray cloud, but the default settings use the same metrics and you can quickly compare your ideas to the other professional portfolios. And to try the same analysis with different assets, fire up the Portfolio Finder and lose yourself in the options.

By the way, that advice is especially important for investors outside of the United States because the results may be very different for you. This is admittedly a US-centric analysis by default, but the Portfolio Finder is capable of running the numbers using your own unique asset options, currency, and inflation. So don’t just take my word for it and assume the same conclusions also apply to you. Test it for yourself and plan accordingly.

One step at a time

Let’s say that you find all of this information truly eye-opening and are fully convinced that buying small cap value, long term bonds, and gold is something you want to do. I know it’s tempting to go nuts and change everything, but there are other ways to look at it.

First, perhaps consider the Frontier-3 as a package deal similar to the holy trinity of onions, celery, and bell peppers that serve as the foundation of Cajun and Creole recipes. From étouffée to gumbo and jambalaya, a bunch of awesome dishes share a common base. So rather than just eating only three ingredients, take the time to think about how they might incorporate into other things you already own and like.

Taking the food metaphor one step further, another way to approach it is to think of the Frontier-3 as a diversified add-on like seasoned salt that pretty much makes everything taste better. For example, let’s say you’re sitting on a large cap blend stock fund and are looking to improve the risk and return of your investments by adding something new. The standard advice is to perhaps allocate 30% of your money to intermediate bonds. But what if you instead allocated 10% each to small cap value, long term bonds, and gold?

Both options are clear improvements, but one arguably goes farther towards your desired goal even if the ingredients are a little counter-intuitive. And if only a relatively small allocation to those oddball seasonings can have such a profound effect, just starting there to see if you even like it may be a much better option than risking buyers remorse by going all-in from the start.

There are plenty of other options

While it’s easy to be tempted to over-concentrate into the three complementary assets, they’re not for everyone. Some people just hate gold. Others don’t trust that the value premium will last. And I see tons of investors today who are terrified by the prospect of how rising rates will hurt long term bonds. While I think there’s more to the story, I get it. And I absolutely do not recommend that you invest in something you actively fear or despise, as it virtually guarantees you’ll sell at a loss the first time the markets show signs of weakness.

Luckily, if any or all of the Frontier-3 are not for you then it’s really not necessary to invest in those assets. Study this chart one more time, and you’ll see that lots of portfolios sit in the upper-left quadrant of the cloud.

efficient portfolio combinations

If you don’t care for small cap value, note the Permanent and All Seasons portfolios well to the left. For a small and value tilted portfolio without long term bonds or gold, the Coffeehouse and Merriman Ultimate portfolios stand out. And I’m impressed by the 7Twelve and Swensen portfolios that each contain none of the three assets we discussed. There’s more than one good way to invest.

Long story short, keep an open mind but also know thyself. Theoretical optimization is only as good as your ability to stick with the plan. Choose a portfolio you believe in, and it will be so much easier to stay the course.

No secrets. Just intelligent diversification.

We’ve looked at a crazy amount of data, studied how different mixes of assets tweak performance, and talked about three particular assets that seem to work uniquely well together to create dependable investing outcomes. And on top of all that, we’ve also covered a few possible ways to use that information to responsibly influence your own investing strategy. Not bad for a day’s work.

But while things like the Frontier-3 assets are certainly interesting to learn about, the most important lesson I’d personally highlight is less about the assets themselves and more about the investing intuition that makes an article like this so surprising or controversial for many people. To put it succinctly:

Risk mitigation doesn’t always work the way you expect.

When presented with three investing options and the ability to combine them, we’re taught to expect that the performance of the resulting portfolio will fall somewhere between the asset extremes. It’s just the law of averages with some asset weighting thrown in. But once you start studying real-world portfolio performance and account for things like asset correlations, rebalancing, and the effects of volatility on compound returns, portfolio behavior is way more unintuitive than we naturally think.

asset allocation expectations vs reality

Most educated investors would scoff at the idea of adding stocks to bonds to reduce risk. But depending on the stocks and bonds you’re talking about and the percentages involved, that’s exactly what happened. And most normal people would think that it sounds crazy to invest in an asset that once lost nearly 5% a year for 15 years in order maximize the dependability of your portfolio return. But study the data and you’ll see that it actually worked. The human brain is just poorly suited to comprehend uncertainty and complex multivariable relationships, and the real world is more complicated than over-simplified mental models.

So as you process all of this information and evaluate how it may affect your own efficient portfolio design, I challenge you to really think about your own investing assumptions. What does risk mean to you? Why do you choose the assets that you do? And does the historical data support your beliefs about how the total portfolio should behave?

It’s possible that this particular cloud approach doesn’t capture those tradeoffs well enough for you and another chart does. Maybe those other perspectives even lead you to a totally different conclusion. That’s awesome! Everyone has different priorities, so dig in and make your own educated investing decisions.

But it’s also possible you’re resistant to certain portfolio ideas simply because they don’t match your expectations about how investing is supposed to work. There’s nothing inherently wrong with that, and there are all types of asset allocations suitable for different types of people. But by opening your mind to ideas that don’t always make sense on the surface, perhaps you’ll stumble into a new paradigm that changes the way you think about investing altogether.

That’s why I started making spreadsheets, and data like this is how I learned. I hope it helps you, too.

Happy Holidays!

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