Exchange-traded fund providers have flooded the market with all sorts of novel assets and strategies: single-stock ETFs, leveraged and inverse ETFs, and even spot bitcoin ETFs can be accessed through your brokerage account with the click of a mouse.
You don’t need any of it. Basic stocks and bonds are still the workhorses of real long-term investments, and access to them through tax-efficient ETFs has never been easier or cheaper.
Combining them in the right proportions can be another sticking point. Complex mathematical models that solve for an “optimal” portfolio look like one remedy. But they can create a false sense of security because the future is so difficult to predict with any degree of accuracy.
These complex tools still provide some insight. They demonstrate some simple and timeless principles that every investor should understand. Portfolio construction ultimately rests on a few basic ideas that have withstood the test of time. Investors need to incur enough risk to achieve a rate of return that will allow them to meet their goals. And they have two asset classes to help dial in the right amount of risk and return: high-risk stocks and low-risk bonds.
Smart People
Portfolio construction is ultimately about combining different assets to achieve a desired rate of return, level of risk, or both. In its ideal form, it tries to minimize the amount of risk necessary to achieve a desired rate of return or maximize the amount of return for a given level of risk.
Diversification plays a big role in achieving that objective. Diversifying a portfolio means holding multiple assets that perform in unrelated ways so that one won’t wipe out the entire portfolio when it goes through a rough patch. The trick lies in figuring out how much of each asset is necessary to realize the greatest benefit.
Harry Markowitz, the late Nobel Prize-winning economist, is credited with formalizing the mathematics behind portfolio construction. His model, still used by many financial professionals, calculates the precise weighting of stocks and bonds necessary to achieve an ideal portfolio—one that maximizes the rate of return for a given level of risk.
The math behind Markowitz’s framework is complicated—too complicated for most to comprehend. But it’s built on some simple concepts that can help any investor make better long-term investment decisions.
Exhibit 1 illustrates the output of Markowitz’s model, a chart commonly referred to as an “efficient frontier.” The plot shows various mixes of US stocks and bonds that produced the highest level of return (the vertical axis) for a given amount of risk (the horizontal axis). The point at the left end of the chart represents a low-risk portfolio of 100% investment-grade US bonds (proxied by the Bloomberg US Aggregate Bond Index), while the high-risk portfolio at the right end held only US stocks (proxied by the S&P 500). The points in between represent various mixes of those two assets.
There’s an easy conclusion to draw without reading too much into the numbers. Higher rates of return require taking on more risk. That means owning more stocks and fewer bonds. And there’s some nuance at the extreme ends of the chart. The least risky portfolio wasn’t the one fully allocated to bonds. It had a small investment in stocks, so the most risk-averse investor can further cut back on risk by owning some riskier equities. At the other end of the chart, the most aggressive investor can make a meaningful reduction in risk with only a modest hit to their long-term total return.
Some caution is necessary in drawing more precise conclusions about the exact allocations. It’s easy to assume that the elegant mathematical formulas and precision of the allocations it spits out are leading to an accurate solution about what the future holds. They don’t.
Garbage In, Garbage Out
First, consider what’s going on behind the scenes. Exhibit 1 was generated using historical numbers, and the future is unlikely to look exactly like the past. Rates of return, volatility, and how stocks and bonds move relative to one another change over time. Their dynamic tendencies move the optimal allocation around, sometimes dramatically. Exhibit 2 shows that the efficient frontier can change substantially from one decade to the next. So using past data to forecast an optimal allocation for the future can be disastrous.
Precision isn’t the strength of Markowitz’s model. Does that make it completely useless? Hardly. It still provides valuable insights for constructing a long-term investment portfolio.
First, stocks and bonds behave differently from one another. Their correlation coefficient (a measure of their relationship to one another) was about 0.24 over the full period in Exhibit 1 (January 1976-October 2023). For context, a coefficient of 1 would imply that they moved in lockstep, while 0 would mean their movements had no measurable relationship. Assets with low correlations are desired, as they’re what lead to a diversified portfolio.
Those conclusions aren’t likely to change much if more asset classes were included, such as international stocks. Exhibit 3 shows the correlations across four major asset classes between January 2001 and May 2024. Stocks, whether domestic or international, were closely tied to each other, with correlations ranging between 0.7 and 0.9. Bonds, on the other hand, tended to behave in a very different way. Their correlations with all three regional stock markets were much closer to 0.
What does that mean? Allocating to different regions of the global stock market didn’t provide much diversification benefit. Stocks from international markets move in the same direction as US stocks most of the time. Bonds, on the other hand, were the only true diversifier. In other words, the amount allocated to stocks and bonds will likely have a larger impact on your portfolio’s long-term risk and reward than the amounts allocated to foreign and domestic stocks.
Don’t Overcomplicate It
The ideal portfolio is impossible to achieve because the future isn’t known with a great deal of accuracy. Markowitz’s optimization model works great as a way to understand the mathematical side of diversification. Its weakness isn’t the mathematics. The model’s ability to correctly determine optimal allocations directly depends on the accuracy of the predicted inputs.
Investment portfolios are almost always constructed to achieve a certain goal, which dictates the required rate of return and the amount of risk required (or allowed). For this reason, everyone will have different preferences and different mixes of stocks and bonds based on their own circumstances.
Along those lines, Markowitz left us with an invaluable nugget of insight when he described how he approached his own portfolio:
“… I should have computed the historical covariances of the asset classes and drawn an efficient frontier. Instead, I visualized my grief if the stock market went way up and I wasn’t in it—or if it went way down and I was completely in it. My intention was to minimize my future regret. So I split my contributions 50/50 between bonds and stocks.”
Markowitz had enough humility to foresee his behavioral weaknesses, and he chose his allocation to stocks and bonds accordingly, despite his deep understanding of the mathematics behind portfolio construction. That may be his most important contribution to finance. The correct portfolio is the one that achieves our goals and allows us to sleep at night, regardless of the mathematical formulas.