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.

How did the simulated Leveraged Mixed Portfolio perform under each of these four economic conditions?  There’s actually quite a bit of this type of analysis on the Bogleheads forum, but most of it seems to focus on just one or two conditions.  I was yearning for a consistent side-by-side evaluation across all four conditions.

Hedgefundie’s uses a 55/45 balance of UPRO to TMF and quarterly rebalancing.  Luke mentioned that he used a 50/50 split, so I used that as my real-world example of an evenly balanced leveraged portfolio.  I checked my calculations against Hedgefundie et al.’s spreadsheet and came up with results that differed by a few dollars over 64 years.

This table shows the nominal Compound Annual Growth Rate (CAGR) of the 50/50 Leveraged Mixed Portfolio as compared to the S&P 500 in continuous timespans that generally match each of the four economic conditions.

Period (inclusive)	50% UPRO / 50% TMF (CAGR)	S&P 500 (CAGR)	Difference
1982-2000	25.5%	16.8%	8.78%
2001-2010	8.30%	1.31%	6.99%
1955-1961	19.0%	14.2%	4.80%
1962-1980	1.77%	7.32%	-5.54%

The recent period from 2011 to 2018 (the end of the simulated dataset) also fits with the stock and bond tailwinds condition (yellow), but I chose the period from 1982 to 2000 because it was longer.

So, the Leveraged Mixed Portfolio performed substantially better in three out of the four cases.  If the last 64 years of stock/bond history is generally predictive of the future, then we can expect something like a 30% chance that the Leveraged Mixed Portfolio could underperform the S&P 500 due to a “difficult sequence” of returns.  Or perhaps more accurately, there’s a roughly one-third chance that both the stock and bond portions of the Leveraged Mixed Portfolio could struggle simultaneously against economic headwinds.

Perhaps these odds seem promising to you.  But let’s dig a bit deeper.

Sequence of Events

As I noted above, this portfolio was proposed as a 20 to 30-year investing approach.  So, what happens when the “difficult sequence” occurs within a longer sequence of returns?  Specifically, what if the portfolio starts well (in one of the three conditions shown in red, blue, or yellow above) but then encounters the more difficult green condition?

Here are three graphs in nominal dollars showing an initial $10,000 investment, where each of the three non-difficult conditions (red, blue, or yellow) occurs first and is then followed by the difficult sequence (green).

Only the last scenario proves disastrous for the Leveraged Mixed Portfolio, but in all cases, the S&P 500 is either the winner or a pretty close second place.  So, almost any time a difficult sequence occurs, it has the capacity to erase most of the prior gains that the leveraged portfolio accumulated.

Monte Carlo Is Not The World

Obviously, the above graphs represent only three of many potential future sequences.  And some (perhaps many) possible sequences could turn out better than these three.  It’s also possible that the difficult sequence might never happen again.  Some of the evaluations at the Bogleheads forum try to address these issues through Monte Carlo simulations, which generate thousands of random sequences based on past returns.  (These particular simulations involved data going back to 1968, or 51 years.)

Although the results of these simulations aren’t showing up anymore on the relevant Bogleheads thread, I don’t really need to see the results to know that they probably look pretty good for the Leveraged Mixed Portfolio.  That’s because the leveraged portfolio had enough years with stellar returns (plus 50%) that they will often appear inside most randomly generated sequences.

But the problem with Monte Carlo simulations is that they can only draw upon history to predict the future.  In this case, they draw upon just 51 specific years of stock and bond returns.  The results of such a simulation must necessarily reside within the city limits of the Monte Carlo dataset.  The simulation can’t consider all the possible events that might happen in the much bigger world of the future.²

So, we have to ask one more question.  Is the next run of returns more likely to resemble or differ from past sequences?  I annually update a page of expected future returns for stocks and bonds based on the predictive models of various investing companies.  This table shows the historical nominal annualized returns as compared to the central tendency of annualized return predictions for the next 10 years.

Type	U.S. Stocks	10-Year Treasury Bonds
Historical	9.2% (back to 1871)	4.9% (back to 1928)
Expected Future (next 10 yr)	5%	1%

Most professional investors are expecting the next decade to differ substantially from past averages.³  If these predictions come true, what does it mean for the Leveraged Mixed Portfolio?  To answer that question, I applied the predictions to the next 10 years of investing for UPRO and TMF.

For stocks, I calculated 10-year CAGRs on a one-year rolling basis going back to 1955 for both UPRO and the S&P 500.  I plotted the CAGRs in this scatter plot, which also shows the best fit line with a very respectable r-squared value of 0.85.

If we use the best-fit equation and plug in the expected 10-year future return for the S&P 500 of 5.0%, the predicted result for UPRO is a:

• CAGR of -4.0% for the next 10 years.

Not so great.

For the bonds portion of the portfolio, the starting yield of a bond is the best predictor of a bond’s total annualized returns.  The current yield on the 30-year bond is 4.04%, which is a little better than the current 10-year bond yield of 3.93%.  But most expected return predictions focus on intermediate bonds or the 10-year bond specifically.

So, to get a prediction of a 10-year CAGR for TMF, I plotted the past one-year rolling 10-Year CAGRs for TMF against the starting 10-year bond yield for each period as shown in these two graphs.

Unsurprisingly, the relationship between the starting 10-year bond yield and the subsequent 10-Year CAGR for TMF is different when interest rates are rising versus declining.  That’s why I split the data into two plots.  But in both cases, the r-squared values are in a decent range of 0.58 to 0.62.  It’s possible that the plots would look a bit different if I had used the 30-year bond yield instead, which would more closely match the benchmark for TMF.  But the 30-year yield data are less consistent and more spotty as compared to the 10-year bond data.  Eyeballing the 30-year bond yields, I don’t think using them would alter these plots much.

If we plug the current 10-year bond yield of 0.85% into these two equations, the predicted results for TMF are:

• CAGR of -13.2% for the next 10 years, if rates are generally rising
• CAGR of +4.3% for the next 10 years, if rates are generally declining.

On Bogleheads many people once argued that interest rates simply won’t rise substantially in the foreseeable future because of modern Federal Reserve monetary policies. This turned out to be incredibly flawed, of coures. Even back in 2020, it was hard to imagine how rates could decline much more given that the Federal Funds rate was already sitting firmly at zero.  I suppose one could have made a case for the possibility of negative-yielding 10-year bonds in the U.S., but to me, that never seemed likelier than rates rising rapidly, which they ended up doing.

Expected 10-Year Return for the Leveraged Mixed Portfolio

Given the uncertainty about future interest rate regimes, I calculated the future expected 10-year CAGR for the 50/50 Leveraged Mixed Portfolio two ways, one using rising rates and the other using declining rates.  I used sequences from the simulated dataset that best matched predicted CAGRs for UPRO and TMF above.  The closest match for UPRO was a sequence from 1970 to 1979 that produced a CAGR of -4.7%, which is a little lower than -4%.  The closest matches for TMF were sequences from 1972 to 1981 with a -14.5% CAGR and from 1979 to 1988 with a 4.0% CAGR.  These two are a fair approximation of the -13.3% value for rising interest rate TMF case and the +4.3% value for declining interest rate case.  I used annual rebalancing in both cases.  This table shows the CAGR results and final value for $10,000 invested in the Leveraged Mixed Portfolio and the S&P 500 after 10 years.

Portfolio / Measure	Rising Interest Rates	Declining Interest Rates
Leveraged Mix Portfolio / CAGR	-3.4%	6.7%
S&P 500 / CAGR	5.0%	5.0%
Leveraged Mix Portfolio / Final $	$7,111	$19,174
S&P 500 / Final $	$16,289	$16,289

So, if you were to have bet that interest rates were going to decline from near-zero (or perhaps suddenly rise in a year or two followed by a slow decline for 10 years after) in 2020, then the Leveraged Mixed Portfolio would have won you an extra 1.7% annualized return as compared to investing in the S&P 500.  As I noted before, rising interest rates seemed much more likely, which would have produced an annualized return of -8.4% less than the S&P 500. In fact roughly 3 years later after this post was initially published, UPRO has outperformed SPY significantly due to the recent rise of the market overall, but with gut-wrenching volatility the entire time. And there’s still plenty of time for UPRO to lag behind the overall SPY’s performance, in case of further drawdown.

Conclusions

I’ve argued that mindful investors shouldn’t worry much about relatively unlikely outcomes.  For example, if you invest in an S&P 500 index fund for more than 10 years, history suggests that your chances of losing money are less than about 10%.

In contrast, the simulated history of the Leveraged Mixed Portfolio suggests that the chances of underperforming the S&P 500 for many years (the difficult sequence) are somewhere around one in three.  And the difficult sequence will significantly erode just about any progress the portfolio may have made up to that point.

Even worse, if we consider where the markets may be headed next, high current P/E ratios and rock bottom interest rates suggest that both stock and bond returns will be struggling against strong headwinds for the next decade or so.  Of course, predictions of future returns are highly uncertain, and the next decade of stock and bond returns may prove these prognosticators wrong.  But make no mistake, the Leveraged Mixed Portfolio is a gamble either way.  If you prefer to focus on history, you have a pretty beefy one-third chance of underperforming the S&P 500.  If you focus instead on future predictions, the chances of failure could be a bit higher.

Given all this, it may not surprise you that Hedgefundie describes him or herself as highly “risk-tolerant”.  Even so, Hedgefundie has devoted only about 15% of his/her investable assets to this portfolio.  So, despite all the evidence presented in the Bogleheads forum supporting the Leveraged Mixed Portfolio, even its biggest advocates realize that this portfolio involves substantial risks of poor outcomes.

That caution is prudent because investors rarely experience the “average” outcome.  We can talk about the future in probabilities, but as time plays out, we’ll experience only a single good, bad, or mediocre result.  And the Leveraged Mixed Portfolio has the ability to hand out both really good and really bad results.  There are no do-overs in investing.  You can’t spin the wheel over and over again to average out your outcome.

I also have to say that seeing this all discussed on a forum called “Bogleheads” is pretty startling.  Jack Bogle was a steadfast advocate for super-simple stock/bond index investing.  He had a strong distaste for unnecessary complexity, including relatively well-established ideas like factors and even exposures to foreign markets.  So, I think Bogle would be spinning in his grave if he knew things like the Leveraged Mixed Portfolio were being seriously discussed in a forum bearing his name.  Rest in peace Jack.

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1 – You might reasonably ask whether “simulated” data are reliable predictors of future or even past theoretical performance.  I frequently conduct these kinds of simulations myself, and in short, I don’t see anything obviously wrong with Hedgefundie’s approach.  So, I used the simulated data.

2 – Don’t get me wrong.  I conduct Monte Carlo type simulations fairly often, including in my last post on leverage.  It’s just that we always need to consider both “inside the sample” and “outside the sample” situations.  The future never turns out exactly like the past.   I’m sure I’m also guilty of failing to look outside the Monte Carlo city limits on some occasions.  But in this case, I think it’s a particularly helpful additional perspective.

3 – You may have noticed that the bond prediction here is for the 10-year bond, while the Leveraged Mixed Portfolio uses long-term bonds.  I’ll resolve this discrepancy in a moment.