Swedroe: Moderate Your Market Expectations

‘Bootstrapping,’ a statistical analysis method, suggests we’ll see lower returns going forward.

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

My colleague, Jared Kizer, who serves as chief investment officer at Buckingham Strategic Wealth and The BAM Alliance, recently examined the performance of the S&P 500 Index from March 2009 (the bear market ended on March 9, 2009) through October 2018, a period ending shortly before a spate of market volatility in December that saw the index record some dramatic declines.

Using a common statistical analysis referred to as “bootstrapping,” he shows how “otherworldly” the returns to that asset class were over the past decade. Importantly, he also shows that other “alternative universes” might have shown up.

The message for investors is that they should not make the all-too-common error of recency bias and become performance chasers. The outstanding returns provided by the S&P 500 also led to much higher valuations. While that doesn't forecast a bear market, it does mean investors should not expect a repeat performance, and that return expectations should now be well below historical levels. Following is his analysis.

The S&P 500 was up 352% from March 2009 through October 2018, while international developed stocks, emerging market stocks and bonds were up 140%, 142% and 39%, respectively.

Massive Understatement

What you might be surprised to know, though, is that it’s almost impossible to simulate another same-length period where the S&P 500 had better risk-adjusted returns. In other words, saying the S&P 500 has done well during this period is a gargantuan understatement. As we will see, it’s done so well that it’s reasonable to ask whether anyone alive will ever experience a better performance period for U.S. large-cap stocks.

The last sentence may sound extreme, but returns data for the S&P 500 illustrate just how mind-blowingly astounding the post-global financial crisis (GFC) returns experience has been. Using a bootstrapping technique (also referred to as “resampling”), you can take the entire historical returns history for any asset class and build out an extremely large number of alternate histories of any length.

For example, you can use the entire monthly returns history of U.S. small-cap stocks to build out 100,000 unique 10-year-length histories to get a sense of what’s theoretically possible, performancewise, over a 10-year period.

Widely Used Method

As you might guess, bootstrapping is very similar to Monte Carlo simulation; the key difference is that bootstrapping directly uses historical data as opposed to simulating returns according to a particular distribution (e.g., the normal distribution).

Bootstrapping is widely used in a variety of other fields outside of finance (and was recently used in a paper by professors Gene Fama and Ken French), and there are a multitude of online resources you can check out if you want to more deeply understand the procedure.

For most, though, all you need to know is that it’s a great way to get a sense of the possible range of outcomes you can then use to compare to specific, actual historical periods of returns data, as we’ll do here.

From a financial market point of view, it’s been about 116 months since the official end of the GFC. This period covers March 2009 through October 2018. In years, this is just shy of a decade. Over this period, the S&P 500’s excess return, i.e., the return in excess of the Treasury bill return, has been 16.5% per year (or 1.35% per month). In terms of the growth of a dollar, $1 invested in the S&P 500 had grown to $4.52 by the end of October.

Most impressively, however, the S&P 500’s excess return achieved a Sharpe ratio of almost 1.30. While Sharpe ratios are generally a bit harder to interpret than the growth of $1 or annualized returns, this Sharpe ratio is about three times higher than its long-run historical value. In other words, not only have raw returns been astounding in the post-GFC period, but the risk-adjusted returns (i.e., Sharpe ratio) have been otherworldly.

Using bootstrapping, we created 100,000 other 116-month returns histories for the S&P 500’s excess return and analyze them below. The excess returns history we used for this bootstrapping procedure encompasses the complete history of January 1926 through October 2018.

Let’s first look at a histogram of the average monthly excess return across each of these histories. Data are from Bloomberg and Ken French’s data library.



Notably, the graphic shows that a wide range of outcomes is possible over a decade, a good lesson in and of itself. We see a significant number of 116-month periods where the average monthly excess return was 0% or less. The average 116-month period achieved an average monthly excess return of 0.67%.

It also shows, however, that an average monthly return of 1.35%—what the S&P 500 actually achieved from March 2009 through October 2018—is an outlier outcome. Less than 10% of the 100,000 samples achieved monthly returns higher than what the S&P 500 has recently achieved.

You might say this is noteworthy, but not overly impressive. It’s been a great run for returns, but there are at least a significant percentage of bootstrapped histories that exceed the March 2009-October 2018 result.

Different Angle

The picture changes when we look at risk-adjusted returns. Figure 2 is a histogram of the Sharpe ratios across all 100,000 samples. Again, data are from Bloomberg and Ken French’s data library.



As it turns out, a Sharpe ratio of 1.30 or higher was achieved in less than 1% of the 100,000 samples. The actual percentage of samples with a Sharpe ratio higher than what the S&P 500 achieved was 0.57%.

In other words, the risk-adjusted returns the S&P 500 actually achieved from March 2009 through October 2018 are almost outside the range of the possible. In fact, in looking at calendar year returns, S&P 500’s excess return of 16.5% from March 2009 through October 2018 is greater than any decade-long period I could find—from 1950 through 1964, the S&P 500 produced an excess return of 16.2%.

The practical lesson here is that the returns the S&P 500 achieved relative to the volatility investors experienced is virtually unparalleled and may not repeat for many decades to come. This result also lends strong support to expectations for very modest returns going forward.

It’s hard to imagine how the S&P 500’s excess returns, or certainly risk-adjusted returns, could be anywhere near as high over the next decade as they had been recently. Wise investors should maintain a globally diversified approach and appreciate that at least some portion of their portfolio benefited from that historically great run for the S&P 500.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.