I don’t often write about “volatility” here at Mindfully Investing because mindful investors focus on long-term returns more than the routine ups and downs of the markets.  The standard deviation of return sequences is the most common measure of routine volatility for stocks, bonds, and other asset classes.  But as I explained in a previous post, standard deviation is actually a poor measure of the potential for a permanent loss, which is the risk that matters most to real-life investors.  A permanent loss is when your invested money is not available at the time you expected to spend it, such as when retirement begins.

Despite all that, I thought it was time to write more about volatility because 2020 was the second most volatile year for stocks in the last 50 years.  (Only the historic and brief crash of 1987 involved more stock volatility in a single year.)  Perhaps, you thought about selling your stocks in March 2020, when the S&P 500 was down nearly -35% as shown in this graph.

But if you resisted the urge to sell, you only had to wait four short months until all that “lost” money was back in your investing account like magic.

And investors in the S&P 500 who waited until the end of the year found that Santa had left 15% more money in their accounts as compared to the start of 2020!  That’s almost double the typical annualized return for stocks going back to 1887.  More than any other year since I started investing, 2020 has made it crystal clear that routine volatility does not equate to the risk of permanent loss.

And a brief review of a few common fallacies about volatility highlights some other reasons why volatility is a poor measure of risk.

Fallacy 1: More Volatility Means Higher Potential Returns

You may have noticed that asset classes with higher potential returns tend to be more volatile; they exhibit higher standard deviations.  I’ve previously pointed out the fairly consistent relationship between return and volatility when comparing the multi-decade histories of broad asset classes like stocks, bonds, and cash as shown in this graph.

But this long-term relationship amongst asset classes fails to describe the more routine interplay of volatility and returns within individual asset classes or individual portfolios.

Vanguard provides a good example in this graph of volatility as a sequence of returns plays out.

Volatility (purple dashed line) as measured by the standard deviation is the same for fictional Portfolios A and B at each point in time.  But Portfolio A has accumulated losses, while Portfolio B has accumulated gains.  Because volatility measures deviations in both positive and negative returns, volatility alone indicates very little about the potential for positive returns over time.

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I’ve posted before about sequence-of-return risk, or “sequence risk” for short.  Sequence risk is when several years of bad returns early in retirement cause a portfolio to run out of money too soon.  This risk applies specifically to retirement because retirees withdraw money from their portfolios regularly to fund living expenses.  This graph shows the huge impact that an early sequence of bad returns can have on portfolio value when annual inflation-adjusted withdrawals are made (blue line).

In contrast, when there are no withdrawals (orange line) the long-term impacts of a bad early sequence of returns can be relatively minimal due to math that’s explained more here.

To minimize sequence risk in my own retirement, I devised a rather elaborate “bucket investing” plan, where I withdraw from cash and bonds¹ early in retirement, giving stocks in my portfolio more time to grow and recover from any early declines.

But even back when I was devising my plan I knew it was potentially inconsistent with some research by Javier Estrada of the IESE Business School in Barcelona, Spain.  Estrada used 110 years of returns data from 19 countries and showed that a 100% stock portfolio has often performed as good or better than bucket-type approaches.  While that sounds promising for an all-stock retirement portfolio, I still thought it was prudent to guard against sequence risk in my own retirement.

So, I was intrigued when I saw a new research paper by Estrada that casts more light on sequence risk.  If you choose only one investing research article to read this year, Estrada’s paper on sequence risk is my top pick, particularly if you’re an investor nearing or in retirement.  Estrada explains his research in a way that is refreshingly understandable for the layperson.  But even so, I thought it would be worth summarizing some key points from his new paper and presenting a few of my related observations as a mindful investor.

What is Risk?

The standard measure of “risk” is the product of:

1. The probability or likelihood of a negative event occurring and
2. The magnitude of the negative event when it occurs.

In the world of risk assessment, a 90% chance of stubbing my toe in one sport, and a 1% chance of breaking my leg in another sport pose similar levels of risk.  One has a high probability of a minor negative event and the other has a low probability of a pretty serious negative event.  In this case, both sports seem pretty safe, but if one sport instead had a 90% chance of a broken leg, that would be too risky for me.

So, to determine the seriousness of sequence risk, we need to look at both its likelihood of occurring (probability) and how bad the outcome is when it occurs (magnitude).

How Likely Is Sequence Risk?

The blue line on the top graph looks super scary, but how likely is that sort of outcome?  Amazingly, back when I was devising my retirement plan, I couldn’t find a straightforward answer to that question.  For this reason, I performed my own calculations, which suggested my specific investing and withdrawal plan was unlikely to fail.

Helpfully, Estrada estimates the probabilities of portfolio failure due to sequence risk in several ways that are more widely applicable.  I won’t describe his methods in detail, but in general, Estrada uses S&P 500 annual return data going back to 1900 to estimate the probabilities that a bad sequence of early returns would cause an all-stock portfolio to fail (defined as running out of money in less than 30 years).

Here are the key results based on all 91 overlapping 30-year periods since 1900:

• A 4% (inflation-adjusted) annual withdrawal rate would have failed only four times, a failure rate of 4.4%.
• With a reduced withdrawal rate of 3.5%, there were zero failures.

These findings are generally consistent with past “safe withdrawal rate” studies.  But Estrada goes further and finds:

• Among the four failed sequences of returns, there is only a 1% to 9% chance that they would cause portfolio failure again if the offending sequence occurred in a different order.

This means that the four historical failures were not caused by the general prevalence of poor returns in these periods, but instead by a relatively peculiar sequence of bad returns.

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Last February, I wrote a post called “Why Not Use Leverage?”, where I conducted forecast simulations for an Exchange Traded Fund (ETF) designed to produce 3 times the daily positive or negative return of the S&P 500.  These funds are called “leveraged ETFs” because they exaggerate the ups and downs of their more sedate benchmarks.

I estimated that one such fund (SPXL) had a 40% to 70% chance of underperforming a standard S&P 500 index fund over the next decade.  Therefore, I concluded that mindful investors can safely ignore leveraged ETFs.

But a reader, named Luke, commented about the “incredible performance” of a leveraged ETF portfolio being discussed and tested out on the Bogleheads forum.  Luke politely implied that my simple comparison of one leveraged ETF to the S&P 500 glossed over the merits of leveraged ETFs.

I was intrigued, so I read up on the whole project that was instigated by someone using the Bogleheads handle “Hedgefundie”.  And of course, thanks to Luke, I can’t resist posting a few thoughts about Hedgefundie’s leveraged portfolio idea.

What is Hedgefundie?

The portfolio itself is easy to describe.  It combines roughly equal allocations to a 3x S&P 500 ETF (UPRO) and a 3x long-term treasury bond ETF (TMF).  This portfolio seems to rely on the idea that government bonds have been relatively uncorrelated with stocks for the last two decades.  The hope is that when the 3x leveraged stock fund plummets, the 3x leveraged bond fund will sky-rocket as a counter-balance and vice versa.  I’ll call this idea the “Leveraged Mixed Portfolio”, with the “mix” referring to a relatively even balance of stocks and bonds, similar to the very common unleveraged 60/40 or 50/50 stock/bond portfolios.

Over 20 or 30 years, Hedgefundie is hoping to soundly beat the returns available from the S&P 500 as shown in this graph simulating the performance of the Leveraged Mixed Portfolio (blue line) going back to 1987.

 

In other words, the portfolio is intended to “beat the market”, a goal that the vast majority of investors consistently fail to achieve.

How Hedgefundie’s Leveraged Mixed Portfolio Might Perform

The perennial problem with assessing portfolios is that the future may turn out different than the past.  For example, the 30-year graph above resides entirely within the 37-year Great Bond Bull Market, when bond yields declined by more than a dozen percent.  Over this time, the total returns of long-term bonds actually outperformed stocks!

So, there is a lot of discussion on the Bogleheads forum about whether this leveraged portfolio will continue to outperform the S&P 500.  The advocates for the portfolio have presented a bounty of supporting data emphasizing these points:

• Going back to 1955, stocks and bonds have rarely crashed together.
• The portfolio can perform well even when stocks or bonds individually perform poorly.
• While the bond fund will suffer if interest rates start to rise, stocks can perform well when rates rise.
• Massive leaps in interest rates like those seen in the 1960s and 70s won’t happen again due to fundamental changes in Federal Reserve monetary policies.

But how realistic is this rosy view of the Leveraged Mixed Portfolio?

Chances of Portfolio Success

To answer that question, I took a closer look at the 64-year simulated historical dataset that Hedgefundie and some Boglehead helpers calculated for the Leveraged Mixed Portfolio going back to 1955¹.  Given the concerns about the interplay of interest rates and stock crashes for this portfolio, I picked out sequences of returns that occurred during times of:

• Rising and sinking interest rates, which impact bond returns as discussed more here.
• Rising and sinking price/earnings (P/E) ratios for stocks.

While long sequences of consistently negative stock or bond returns don’t exist in the dataset, rising interest rates and falling P/E ratios have historically signaled difficult headwinds for bond and stock investors, respectively.

This matrix shows the percentage of time over the last 64 years that bonds and stocks were subject to economic headwinds (rising interest rates and falling P/E ratios) or tailwinds (falling interest rates and rising P/E ratios).

	Stocks Tailwind	Stocks Headwind
Bonds Tailwind	43.8%	15.6%
Bonds Headwind	10.9%	29.7%

History shows that the individual annual returns of stock and bonds are positive in most years.  So, it’s perhaps a bit surprising that stocks and bonds have simultaneously benefited from economic tailwinds only about 44% of the time since 1955, as shown by the yellow cell in the matrix.  And they both suffered from simultaneous economic tailwinds about 30% of the time as shown by the green cell.

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My view of “market timing” is a bit different than most people’s.  While market timing is often poorly defined, to start today’s post, I’ll define it as buying and selling assets over time based on anything from strict rules to vague feelings.

Most stuff you’ll see about market timing falls into one of two camps.  The first camp maintains that market timing is entirely possible, and many of those campers are more than willing to sell you a “great system” for timing the market¹.  The second camp maintains that successful market timing is nearly impossible with any regularity.  These campers will tell you that investing is all about “time in the market, not timing the market”.

Mindfully Investing camps elsewhere, based on a critical distinction between “short-term” and “long-term” timing.  Short-term timing involves buying and selling on timescales ranging from daily to annually.  Long-term timing is about making one or two key decisions over many years of investing.  My view is that short-term timing is mathematically impossible, and long-term timing is entirely feasible if it’s executed carefully.

Although it’s rarely stated, most of the time people address this topic they are talking about short-term timing, where routine market gyrations and economic indicators are used to jump in and out of markets, funds, individual stocks, or other assets.  But my main concern in past posts, and today’s post, is the much less discussed topic of long-term timing.

One Type of Long-Term Timing

Specifically, in Article 8.3 of Mindfully Investing I’ve advocated that “older” investors who are nearing retirement or recently retired should hold a predefined amount of cash, usually 20% or less of a portfolio, to invest in the event of a market crash.²  This procedure is intended to manage so-called sequence-of-return risk, where portfolio losses early in retirement can severely reduce the number of years your portfolio lasts.  That’s because most retirees are routinely divesting small amounts to fund retirement expenses and don’t have any new income to replace those investments.  You can learn more about sequence-of-return risk from this post.

Basically, this type of long-term timing boils down to a once-in-a-lifetime decision.  Under this procedure, there is only one event (a large market crash) that would trigger using the cash reserve to buy additional stocks, and only if the crash occurs in the first several years after retirement, for reasons I describe more in Article 8.4 of Mindfully Investing.

For this procedure to work, we also need a definition of a large market crash.  Based on the magnitude and length of past market crashes, I came up with a rule that a 35% or greater decline in the S&P 500 triggers investing cash reserves in stocks.  History has shown that when the stock market (S&P 500) has declined by less than 35%, it usually started to recover in less than 2 years.  In contrast, more severe declines took 5 to 15 years to fully recover.  Because the future is unpredictable, the 35% threshold is admittedly, somewhat of a simplification.

I use this long-term timing procedure to manage the sequence-of-return-risk in my own investing plan.  And it turns out that the market decline earlier this year required me to put this theory into practice.  So, I thought I’d review my real-life example of implementing long-term timing and describe how it’s working out so far.

My Own Plan

I fully retired in 2017.  At that time, I set up our investment portfolio as follows:

• 80% low-cost stock index funds (diversified by geography and sector, and to a lesser extent by size).
• 20% cash held in a high-yield online savings account.

This does not include our home, which is paid off, as an investment.  This also does not include two rental properties we owned at the time, because the plan was to sell the rentals (which we did) and plow the proceeds into stocks and cash at the same 80/20 ratio.

Since late 2017 we’ve been funding our retirement by slowly depleting the cash account.  All the stocks have been left untouched to grow and all dividends have been reinvested in the same stock funds.  The cash account now stands at about 14% of the total portfolio, which again, is roughly consistent with the original drawdown plan.  So, earlier this year when the stock market started to tank, we had a bit more than 14% of our total nest egg that I could have used to buy stocks.

The Face-Off with Reality

Consistent with mindful investing principles, I don’t pay a lot of attention to daily stock market gyrations.  By the same token, I try not to expressly avoid market news either, because mindfulness is about being aware without being reactive.

I’m not sure exactly when, but I woke up one morning in March this year and thought to myself, “Hey, this coronavirus thing is really starting to make the stock market tumble.”  So, I looked at some S&P 500 stock charts and realized that the market had gone down by nearly 30% from its February 19th peak.  Alarm bells went off in my head.  I knew my threshold to start buying stocks (a lot of stocks) was 35%, so I needed to start paying more attention.

The first thing I did was review my plan.  Frankly, I couldn’t remember whether I was supposed to measure the 35% starting from the calendar year or the market’s last peak.  I also wasn’t sure whether my rule was based solely on the S&P 500 or some other indices as well.  This is where having a written investing plan is invaluable.  All I had to do was review my past articles (particularly the ones I linked to above) to recall that my threshold was based solely on the S&P 500’s decline from the last market peak.

I won’t lie.  There was some doubt in my mind whether I should actually stick to this “silly rule” or rely more on my intuition about the specifics of this crash.  But then I paused and remembered, the whole point about having a plan is that you have to stick to it.  The rules you’ve adopted may be over-simplified or even relatively arbitrary.  But if you don’t stick to those rules, you’re essentially making it up as you go along, which leaves you prey to a litany of behavioral biases and potentially counterproductive emotional reactions.

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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.