One-Fund Portfolio With 22% CAGR Over 50+ Years, And Why You Should Avoid It

Summary

• A simulated version of UPRO delivers 22.6% CAGR, turning $1 into over $1,000,000 since 1950.
• The same fund also suffers 17-year downturns with 97% losses.
• UPRO can be a great part of a diversified portfolio, especially when balanced with uncorrelated assets.

Summary

A simulated 3x daily-leveraged S&P 500 fund, with the same fee structure as the ProShares UltraPro S&P 500 (NYSEARCA:UPRO) would have returned 22.6% CAGR since 1950. This would turn a single dollar in 1950 into more than $1,000,000 today.

However, the same simulated fund also endures downswings that last 17 years. The simulated fund would see a $685,000 portfolio dwindle down to only $22,200 - a loss of 97%.

Leveraged equity funds perform very strongly over the long term. However, they also have enormous swings that are far too large for a majority of investors.

Leveraged equity funds can be a part of a long-term portfolio, provided that the risks they present are balanced with other assets. For example, a risk-weighted portfolio (including but not limited to a risk-parity portfolio) may derive substantial additional returns from holding leveraged equity funds.

These funds are extremely risky, and should likely make up a relatively small part of a diversified portfolio. I will invest in leveraged funds after further research into portfolio allocations, but they are wildly inappropriate for investors with lower risk tolerance and shorter investment horizons.

My Objective

I am considering constructing a leveraged portfolio, likely to include at least a leveraged bond fund and a leveraged equity fund. This leveraged portfolio will not be my entire portfolio, but will hold daily leveraged funds long-term.

As part of this goal, I wish to back-test possible leveraged portfolios as far back as possible. Thus, I wish to simulate daily leveraged funds as far back as possible. In this article, I will simulate a leveraged 3x S&P 500 fund based on UPRO.

I have previously written about this portfolio several times. For those who missed my past articles:

• Simulated leveraged bond fund performance to 1962 (Summary: +18% CAGR for 3x bond fund, but with 62% maximum drawdown.)
• Performance of Leveraged Portfolios Since 2006 (Summary: Better returns than the S&P 500, and lower drawdowns, too.)
• Examination of Beta Slippage in Leveraged Funds (Summary: Holding 3x daily leveraged funds is okay for stocks and bonds, but I wouldn't touch 3x VIX.)

Currently Available Leveraged Funds

Many leveraged funds are available. In this article, I will focus on S&P 500-based funds. Some of the currently available leveraged ETFs include:

Fund (Symbol)	Lev	Index	Fees	AUM
ProShares UltraPro QQQ (TQQQ)	3x	NASDAQ	0.95%	$2,600 m
ProShares UltraPro S&P 500 (UPRO)	3x	S&P 500	0.95%	$1,300 m
Direxion Daily S&P 500 Bull 3X Shares (NYSEARCA:SPXL)	3x	S&P 500	1.06%	$900 m
ProShares UltraPro Dow30 (UDOW)	3x	DJIA	0.95%	$500 m
ProShares Ultra S&P 500 (SSO)	2x	S&P 500	0.90%	$2,400 m
ProShares Ultra QQQ (QLD)	2x	NASDAQ	0.95%	$1,600 m
ProShares Ultra Dow30 (DDM)	2x	DJIA	0.95%	$500 m

Click to enlarge

Leveraged mutual funds, such as ULPIX, are also available, but tend to have higher fees. I am unaware of advantages of using mutual funds over ETFs, given those higher fees. I recommend using ETFs with the lowest possible fees to achieve your desired leverage, which will often be a split between 3x daily leveraged ETFs and unleveraged ETFs.

I do not recommend investing in 2x leveraged funds. A portfolio split 50/50 of 3x leveraged funds and unleveraged funds on the same index accomplishes the goal of 2x daily leverage with lower fees than 2x funds. (In taxable accounts, this may increase taxes due to rebalancing.) They are included on this chart only for the sake of completeness.

Data Set

For this project, I have chosen to simulate a daily-leveraged S&P 500 rather than using the Nasdaq or the Dow Jones Industrial Average.

There are a few reasons for this choice. First, I plan to invest in an S&P 500 leveraged ETF, ultimately. I will invest in UPRO because it has lower fees than SPXL. Second, the S&P 500 has a longer history than the Nasdaq, and is more diversified. The former is especially important for backtesting purposes. Third, I don't like the lack of diversification in the Dow Jones Industrial Average, even though it also has a long history.

The index that later became the S&P 500 originated in 1923. Initially it tracked only a small number of stocks, but was expanded in 1926 to include 90 stocks. It did not expand to include 500 stocks until 1957, although data sets often include data from prior to this expansion.

For this project, I need daily total returns of the S&P 500, including all dividends for as far back as possible. I used the following data sources to approximate the daily total returns of the S&P 500 back to 1950:

• Yahoo Finance: S&P 500 Total Returns, 1988-01-04 to present
• Yahoo Finance: S&P 500 Closing Price (no dividends), 1950-01-03 to present
• Robert Shiller (Yale): S&P 500 monthly dividend yield, 1871 to present

I was unable to find daily prices for the S&P 500 prior to 1950, or to find total returns for the S&P 500 prior to 1988. If readers have this data, please leave a comment or send me a message on this site.

Despite that, it is trivial to approximate total returns using monthly dividend yields and daily closing prices. These figures will be approximations, but should be close to the total returns of the S&P 500 since 1950.

For the purpose of comparison, I have also compared returns with several leveraged and un-leveraged ETFs, with all data from Yahoo Finance as well.

Finding Daily Leveraged Returns

My primary comparison here is with UPRO, which is 3x leveraged daily and has annual fees of 0.95%. Therefore, returns will be based on those figures.

To approximate UPRO, I first get the daily total returns of the S&P 500, in percentage terms. I multiply this number by three, and subtract the management fee of UPRO (about 3.8 x 10^-5 or 0.0038%). This forms a first-pass at a simulated fund.

Results for this very closely approximate UPRO. Over the most recent 1,500 trading days, here is a scatter plot of daily results for UPRO and the first-pass simulated fund.

^{SOURCE: AUTHOR USING DATA FROM YAHOO FINANCE}

These results are very good: There is a very strong relationship between the simulated 3x fund daily returns and the actual price of UPRO.

The R² value for this first-pass simulation is 99.6%. This indicates that over 99% of the daily performance of UPRO can be explained by my calculated values for the simulated fund. The remainder of the differences may be due to the ETF trading slightly above or below its NAV, and other factors.

To improve results further, I used the data from the linear regression. This sets an intercept of -5.1 x 10^-5 and a coefficient of 0.9942. Note that the P-value of the intercept is 15.7%, indicating a one-in-six chance of the true intercept being zero or positive. Despite the relatively high P-value (below 5% would be optimal), I have chosen to use the intercept. My rationale is simple: A negative intercept will lower the simulated returns every day.

In this project, I prefer to err on the side of providing a conservative estimate of a simulated 3x daily-leveraged fund. Because I plan to invest in a later portfolio based in part on these results, I would strongly prefer to underestimate returns instead of overestimating returns. Therefore, I have decided to use the intercept for my simulated returns, despite the P-value being above 5%.

The simulated 3x daily-leveraged results below are the result of this linear regression.

Note: I am not a statistician. So, if any of the above is incorrect, please let me know in the comments below. I'd be especially interested if it's incorrect in a way that would alter my analysis and simulated fund estimate (as opposed to me simply explaining P-value incorrectly, for example).

Comparing Daily Leveraged Returns With Actual Results

^{SOURCE: AUTHOR USING DATA FROM YAHOO FINANCE}

Returns from the simulated fund very closely match those of UPRO. Over the life of UPRO (from 2009-06-25 to 2017-12-29), the simulated fund under-performs UPRO by 1.5% total, or less than 0.2% per year.

These returns are easily good enough for my purposes.

I also compared simulated results with other available funds. The results used here change the fees and leverage used above to match the underlying fund. These results show that other funds also closely match the actual performance of the S&P 500 and their stated management fees.

Fund (Symbol)	R2 to Sim. Equivalent	Lev	Fees	Inception*
Direxion Daily S&P 500 Bull 3X Shares (SPXL)	0.9896	3x	1.06%	2008-11-05
ProFunds UltraBull Investor Class (ULPIX)	0.9315	2x	1.42%	1997-11-28
Vanguard S&P 500 ETF (VOO)	0.9953	1x	0.09%	2010-09-09
SPDR S&P 500 ETF (SPY)	0.9600	1x	0.04%	1993-01-29

Click to enlarge

All data here is from Yahoo Finance. The inception used here is the beginning of Yahoo Finance's daily data, which often trails the "official" inception date of each fund by a few days.

Both the funds that have existed since the 1990s have lower R² values, although still over 90%. This could be due to factors including changing expense ratios over time, tracking errors of the underlying, differences between NAV and market prices for ETFs, or other issues. Since this was not the focus of my interest, I did not investigate further.

Simulated Returns For Past 68 Years

For these returns, I generally used the best data available. That is, I used simulated returns only when actual returns were not available. This is consistent with my overall goal of replicating actual achievable performance as closely as possible. Using simulated data when real data is available would be counterproductive.

I have also included simulated returns from a hypothetical S&P 500 ETF. Those returns are just for comparison, although I will also use them in the future to de-leverage the 3x leveraged funds as desired in back-testing leveraged portfolios (for example, a 50/50 split to achieve 2x leverage).

I used the following data for the leveraged fund:

• 2009-06-26 to present: Daily price movement of UPRO.
• 2008-10-01 to 2009-06-25: Daily price movement of SPXL.
• 1950-01-03 to 2008-09-30: Daily price movement of the simulated fund.

For the comparison unleveraged fund, I used the following data:

• 1993-02-01 to present: Daily price movement of IVV (0.04% fees).
• 1988-01-05 to 1993-01-29: Daily price movement of SPY (0.09% fees).
• 1950-01-03 to 1988-01-04: Daily price movement of a simulated un-leveraged fund (0.04% fees).

Since 1950-01-03	Simulated S&P 500 Fund (S&P 500, 0.04% Fee)	Simulated 3x Fund (3x S&P 500, 0.95% Fee)
Total Return	856x	1,054,268x
CAGR	10.4%	22.6%
Best Year	50% (1955)	219% (1955)
Worst Year	-37% (2009)	-85% (2009)
Max Draw-down	55% (2009-03-09)	97% (2009-03-09)
Longest Draw-down	2,406 days (2000-03-24 to 2006-10-25)	6,174 days (2000-03-24 to 2017-02-17)
Annual Excess Return	6.2%	18.4%
Annual Volatility	14.2%	42.8%
Sharpe Ratio	0.44	0.43

Click to enlarge

Total Return of the simulated 3x fund was very strong. A CAGR of 22.6% over a 68 years sample is tremendous.

However, a 97% draw-down is terrible. Few investors would be able to stomach such a draw-down. I am also sure that some contributors and commentators on this site believe we're on the cusp of a crash or correction. People who hold bearish views on the market are numerous. In the case of such a downturn, results for UPRO will be terrible. Then again, if you believe we're on the cusp of a downturn, you were never going to invest in a leveraged long fund anyhow.

Note that I have changed how I calculate Sharpe ratios since my article on leveraged bonds. Here, the annual excess return is simply the CAGR minus the CAGR of my chosen risk-free rate, over the entire duration of the sample (since 1950). The risk-free rate I am using is the three-month T-bill, with monthly data from the St. Louis Fed. Annual volatility here is monthly volatility, which is then annualized. The Sharpe ratio is merely the excess returns over the volatility.

^{SOURCE: AUTHOR BASED ON DATA FROM YAHOO FINANCE AND ROBERT SHILLER}

An investment of a single dollar into a hypothetical S&P 500 fund in January 1950 would be worth $857 today. But if that investment was made into a hypothetical 3x leveraged S&P 500 fund, that dollar would be worth over one million dollars.

However, the 3x leveraged fund owner would also endure a 17-year downturn. During that time, the investor would also see his $685,000 on March 24, 2000 turn into $22,200 on March 9, 2009. Best of luck stomaching a 97% downturn, which did not recover for two economic cycles.

Conclusion And Further Work

I do not recommend long-term investments in UPRO or SPXL, except in the context of a well-designed portfolio. While 22.6% CAGR is very attractive, 17-year, 97% downturns are going to ruin most investors; few will manage to endure those downturns without altering their strategy.

However, in the context of a diversified portfolio, a leveraged equity fund can provide extremely good returns. These funds can be combined with un-leveraged funds to achieve desired leverage ratios, based on each investor's risk tolerances and investment timelines.

I expect that I will invest in a leveraged equity fund (likely UPRO) in the future. This will be chronicled in future articles, once I have completed additional simulations and backtests. I expect to invest using an approach that incorporates some degree of risk-weighting, to balance leveraged equity funds, leverage bond funds, and potentially other assets as well, such as gold or various market-neutral investing approaches.

In the future, I will look at leveraged gold funds and perhaps other leveraged asset classes, such as commodities. I will also construct and back-test portfolios based on those simulated funds. I will test portfolios with leverage ratios ranging from 1x to 3x, and observe the changes in performance, including maximum draw-downs and Sharpe ratios. Eventually, I will invest a portion of my portfolio using such an approach, provided that I find a portfolio with risk/return characteristics that I find desirable.

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