Last month a regular reader emailed me with a great question about “leverage”.  The term “leverage” traditionally refers to investing with borrowed money.  I haven’t written much about leverage because it seems apparent that investing with someone else’s money is an unnecessary risk.  But investing based on how things “seem” is not particularly mindful.  So, I thought I’d take a closer look at the pros and cons of leverage.

Over the last 10 years or so the investing industry has been offering an ever-wider range of “leveraged” exchange-traded funds (ETFs).  Unlike traditional leverage, leveraged ETFs don’t require you to borrow any money to invest in them.  Instead, leveraged ETFs are designed to exaggerate the daily price changes of an underlying benchmark by using a variety of derivative products such as futures, swaps, and options.  So, an ETF advertised as “two times” (2x) the S&P 500 will generate daily price changes that are approximately twice that of the S&P 500 in both positive and negative directions.

My curious reader was most likely asking about this type of leveraged ETF product.  His specific question was:

• A mindful investor would favor a 100% stock portfolio over a long time horizon because volatility becomes less important over time.  Would you, via the same logic of volatility, recommend a more leveraged portfolio?  If so, by how much?

The volatility of leveraged ETFs is roughly proportional to the leverage employed.  For example, a 2x ETF on the S&P 500 experiences about twice the volatility of the S&P 500.  So, the question is correct to assume that mindful investors shouldn’t care much about increased volatility.  That’s because stock market prices have always risen over long periods, providing the patient long-term investor with positive returns regardless of how bumpy the ride was along the way.  By that logic, the mindful investor should be able to also endure two or three times the normal volatility in exchange for substantially higher long-term returns.

I’ve seen a lot of articles about leveraged ETFs recently, and I think it’s because many investors are salivating at the performance of some of these investment products during their relatively brief 10-year history.  This 10-year graph from Portfolio Visualizer shows an example comparing the performance of $10,000 invested in an S&P 500 index fund (SPY in blue) versus the oldest 3x S&P 500 ETF (SPXL in red) since it started.

Who wouldn’t want some of that?!  Sure, the volatility of SPXL in this period was a whopping 35% as compared to SPY’s 13.5%.  And the maximum drawdown of SPXL was nearly -50% as compared to SPY’s -18%.  But $10,000 in SPXL grew to almost $270,000, while SPY grew to a relatively meager $45,000.  All that extra volatility came with big rewards for those mindful enough to endure the wild ride.

Pros and Cons

Everyone sees this one huge pro for using leveraged ETFs, but of course, there must be some cons as well.

First, the very short history of leveraged ETFs is a clear caution.  I’ve argued on other topics that the entire 149-year history of the U.S. stock market is not a particularly long track record.  In comparison, the decade-long history of leveraged ETFs is a fleeting moment.  Two, the last 10 years were dominated by one of the most remarkably consistent, calm, and long-lived bull stock markets in history, which tells us little about how leveraged ETFs will behave during future sideways or bear markets.  Three, as an example, a 3x ETF is designed to generate 3x a daily price change in the benchmark, but those daily changes don’t mathematically equate to 3x the long-term return.  Larry Swedroe recently examined the performance of all available leveraged ETFs over the last 10 years and found that, for 3x ETFs, the 10-year annualized return was 8% to 15% less than the 3x level you might expect.  Given that the long-term annualized return of the stock market is only about 9%, missing a target by an annualized 8% to 15% is huge.

Further, almost every recent article I’ve found on this topic includes a caution about a math problem inherent to leveraged ETFs known as “reset decay”.  Here’s the basic example:

• You buy one share of a 2x ETF and one share of its underlying benchmark, both at a starting value of $100.
• On day one the benchmark goes down by 5% yielding a new price of $95.
• On day one the 2x ETF goes down by 10% yielding a new price of $90.
• On day two the benchmark goes back up by 5% yielding a new price of $99.75.
• On day two the 2x ETF goes up by 10% yielding a new price of $99.

The market has gone nowhere in these two days, but the 2x ETF investor lost 75 cents more than the benchmark investor due to unavoidable compounding math.  If a flat market like this extends for many years, the leveraged ETF investor would eventually lose almost everything.

This is pretty much where all the articles on leveraged ETFs I found stopped, which is distinctly unsatisfying.  OK, so leveraged ETFs don’t generate the full expected return, and the returns can be further eroded by compounding math.  But the stock market isn’t usually flat; prices go up 73% of the time.  So, leveraged ETF returns can still exceed the returns of their benchmark even while falling shy of the expected multiple.  And the math of reset decay tells us nothing about the probability that a leveraged ETF would make (or lose) money relative to the benchmark in any given period.  I wanted to go a step further and see if I could simulate the performance of one of these leveraged ETFs and then subject it to different potential future market conditions to see how it performs.

Methods

If you don’t care how I simulated the future performance of a leveraged ETF, and trust that I did a halfway decent job, you can continue to the “results” subsection of this post.  If you’re more skeptical or are a simulation nerd like me, then you can read a description of my methods at the end of this post under “Methods Postscript”.

In summary, I used distribution statistics on S&P 500 price changes going back to 1964 to develop a “random future market generator”.  I used historical daily price changes of SPXL to develop a simple mathematical simulation of how SPXL would react to S&P 500 price changes output from the random future market generator.

Results

Once everything was set up, I ran 100 trials of the SPLX simulation based on randomly generated future market conditions over 10-year periods.  One hundred trials seemed like enough to see any trends without getting super tedious.  I then calculated the annualized 10-year compound annual growth rate (CAGR) of both the random future S&P 500 and the simulated SPXL.  Keep in mind that these CAGRs only factor in price change growth and don’t include dividends.  Here’s a graph showing the CAGRs for all 100 trials for both the random future S&P 500 (horizontal axis) and the simulated SPXL (vertical axis).

There’s a highly predictable relationship between the simulated S&P 500 and SPXL returns.  Further, the relationship is not the perfect 3x multiple we might expect.  For example, if the S&P 500 10-year annualized return is about 10%, the SPXL return is about 25% (about 2.5x).  This skewed relationship roughly matches Swedroe’s observations about the last 10-years of leveraged ETF performance.  More importantly, the graph shows that when the S&P 500 annualized price returns are slightly positive (in the 1% to 4% range), SPXL would lose money in the same 10-year period.

We can examine the distribution of the simulated SPXL 10-year CAGRs to determine the probability of SPXL making more money than using an S&P 500 index fund.  As the graph shows, when the S&P 500 10-year CAGRs exceed 3.5%, SPXL returns exceeded the S&P 500 returns.  A 3.5% S&P 500 return represents the 40th percentile of the simulated future returns distribution.  That is, the simulation indicates that if you bought SPXL today, you have a 40% chance of underperforming the S&P 500 over the next 10 years.

However, my 40% failure estimate assumes that future markets will stay aligned with the price change distribution observed between 1964 and 2018.  It also assumes that SPXL will continue to generate leveraged price changes similar to its historical performance over the last 10 years.  Either one or both of these assumptions could turn out wrong.  So, let’s look at each assumption in a little more detail.

Past and Future S&P 500 Returns – As I noted above, from 1964 to 2018 the annualized return from S&P 500 price changes was 6.8%, and it was 10.1% with dividends reinvested (total return).  However, almost no one is predicting those types of returns for the next 10 years as summarized in my article on Future Expected Returns.  The central tendency across many different predictions is about 4 to 6% total return for the S&P 500.  Right now, the dividend yield on the S&P 500 is 1.7%.  As a rough estimate, we can subtract out about 2% for compounded dividends to arrive at a future expected price change return of just 2% to 4% for the S&P 500.

So, the most-predicted outcome for the next 10 years of S&P 500 annualized price returns is 3%, and the point at which SPXL would start to outperform the S&P 500 is at about 3.5%.  By this measure, if you bought SPXL today, you’d have a roughly 50% to 60% chance of underperforming the S&P 500 over the next 10 years.   Of course, I’ve often pointed out that predictions of future returns are highly uncertain, and therefore, so is this estimate.

Past and Future SPXL Returns – The S&P 500’s past may not predict it’s future, and the same is true of SPXL.  An examination of the SPXL price changes since 2009 shows a meaningful scatter in SPXL’s daily performance.  You can find many examples of SPXL generating a 2x change one day and a 4x change a few days or weeks later.  And some of the deviations are even greater.  For today’s post, it doesn’t matter why these deviations occur, although it seems likely that the complex financial instruments used in these ETFs must be a substantial part of the cause.

So, what if these complex instruments start to work a little differently in the next 10 years?  One way to at least partially answer that question is to consider what would happen if SPXL started to drift toward a perfect 3x relationship instead of the historic averages of 3.44x up and 2.89x down.  Here’s a graph showing the price growth of $100 invested in SPXL since it’s inception (orange dotted line) as compared to a theoretically perfect 3x ETF (gray line).  And for general comparisons, I added the simulated SPXL (blue line) as applied to the past 10 years of data and S&P 500 itself (green line).  The graph shows price returns only (no dividends included).

The final values for the growth of the initial $100 investment are:

• SPXL – $2704
• Simulated SPXL – $2704
• Perfect 3x ETF – $783
• S&P 500 – $359

Over the last 10 years, a perfectly performing 3x ETF would still have been a great investment, but it’s less than a third of the price return from the actual SPXL over this period.  So, what if we simulate the future of that perfect 3x ETF performance?

As you might have expected, this shifts the CAGR relationship between the S&P 500 and the 3x leveraged ETF substantially in a negative direction.  In this case, the annualized price return of the S&P 500 has to be greater than about 11.5% before the 3x ETF would make more money than an S&P 500 index fund.  The distribution of simulation results indicates that, if you bought a perfectly performing 3x ETF today, there’s a 71% chance you will underperform the S&P 500 in the next 10 years.  And it’s worth noting that there’s a 57% chance you will lose some or most of your initial investment in a perfect 3x ETF.

Of course, this all assumes that SPXL’s average price changes move toward a perfect 3x multiple.  There’s no way to tell whether that’s more or less likely than SPXL price changes departing further from the target multiple.  Or SPXL performance could become more variable and erratic.  But the perfect 3x scenario illustrates one plausible outcome, particularly if the markets in the next 10 years don’t resemble anything like the raging bull market of the last 10 years.

Conclusions

To summarize, if you bought SPXL or a similar 3x ETF today, I estimate the following percent chances that the leveraged ETF would underperform the S&P 500 in the next 10 years:

• 40% – if future markets and SPXL performance mimic past performance
• 50% to 60% – if the future stock market has lower returns than historical averages
• 70% – if SPXL moves closer to a perfect 3x price-change performance.

Given that I only simulated one of many leveraged ETFs, other leveraged funds may have better or worse chances than these estimates.  And given all the other uncertainties with predicting future market and ETF performance, I’d say it’s entirely plausible that the chances of failure with 3x leveraged ETFs could be even greater than 70%.

In my view, these probabilities are the opposite of what a mindful investor would like to see before taking the plunge into leveraged ETFs.  I’d like to see the chances of failure below 20%, or even 10% before I’d consider using leveraged ETFs.  That’s because the downside risks of leveraged ETFs are huge.  Some of the “failures” in my simulation trials underperformed the S&P 500 by one or two percent annualized.  But many trials failed catastrophically.  For example, 20% of the simulated SPLX trials produced annualized returns of negative 10% to 36%!  And 30% of the perfect 3x ETF trials produced annualized returns of negative 20% to 45%!

This graph shows an example of one of my catastrophic trials.  The simulated S&P 500 investment (blue line) only lost about 10% over 10 years, but the simulated 3x ETF (orange dotted line) lost 90% of its initial value.

With all the uncertainties around predicting the future, I’d say its generally a coin-flip chance that investing in leveraged ETFs will leave you completely broke.  So, it’s safe for the mindful investor to completely ignore the existence of leveraged ETFs.

Methods Postscript

To test a leveraged ETF against future market conditions we need a way to simulate both the future performance of the markets and the leveraged ETF.  My steps for simulating the market (future random market generator) were:

1. From a QVM Group blog post, I obtained distribution statistics on the daily price changes of the S&P 500 from 1964 to 2018.
2. I sorted these data into 20 bins each representing 5% of the distribution and set the daily percent change to the mid-point of historical price changes within each bin.
3. I randomly selected one of the 20 bins (one of 20 historical price changes) to represent each day over a 15 year period.
4. I ran hundreds of 15-year trials and compared the results to the actual annualized returns of the S&P 500 from 1964 to 2018.
5. The first iteration of my random future market generator yielded an average (across many trials) annualized price return (not including dividends) that was somewhat below the actual annualized price return since 1964, which was 6.8%.
6. I calibrated my random future market generator to better match 6.8% annualized by shifting the distribution of price changes upward by 0.115%.  This resulted in an average annualized return across many trials of between 6.1% and 7.6%, which brackets the calibration target of 6.8%.

Armed with a decent future market generator, my steps for simulating the future performance of SPXL were:

1. From Yahoo Finance, I obtained the daily price changes of SPXL since it started.
2. I compared the SPXL daily price changes to those of the S&P 500 and found that the average multiple for up days of SPXL was 3.44 and the average for down days was 2.89.
3. I constructed a simple model to mimic the price deviations of SPXL.  The best-fitting model I could devise used the multiple of 3.02 for up days and a multiple of 2.89 for down days.  Using an up-multiple any higher than 3.02 tended to make the SPXL simulation grow too fast as compared to actual SPXL data for the last 10 years.
4. The price changes generated by the random future market generator were used to calculate SPXL price changes for the same days using the up and down multiples from Step 3.  I ran a hundred 10-year trials to assess the future performance of the simulated SPXL as compared to the simulated S&P 500.

Perhaps you’re surprised that a 3x ETF doesn’t generate a perfect 3x price movement, but you shouldn’t be.  Larry Swedroe has also pointed out that the daily price changes of leveraged ETFs are not a perfect reflection of the 2 or 3 multiple in their names.  As I noted above, this makes sense if you start to think about the complex derivatives that drive these ETFs.  It’s probably impossible to design a leveraged ETF that will give a perfect multiple of a benchmark every day regardless of what the financial markets are doing.

This cross plot shows that my SPXL simulation fits the actual historical SPXL price change data quite well.