How To Beat The Market (Pt. 2): Two-Fund Portfolio Beats Market By 37% And Weathers Downturns Better

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Summary & Thesis

In this article, I compare the use of a risk-parity-weighted leveraged portfolio to a pure SPY portfolio. These portfolios use a leveraged index fund (SSO, ULPIX, FLGE, QLD, TQQQ, UPRO, SPXL) to gain leveraged exposure to equities. The risk from this leverage is offset using a bond fund (AGG, BND, IEF, TLT), and in one portfolio, also using a gold fund (GLD, IAU).

I compare the results between each portfolio from the Great Recession with today. The goal is to see how to use leverage while also being able to weather significant downswings.

Portfolio Total Return
(6/30/06 to 12/15/17)
CAGR Maximum
Draw-down
Sharpe
Ratio
Portfolio 1 (Bond ETF and leveraged equity ETF) 272% 12.1% 23.4%
(Mar-09)
0.96
Portfolio 2 (Same, but also
with a gold ETF)
213% 10.5% 19.5%
(Nov-08)
0.88
100% SPY Portfolio 164% 8.8% 55.2%
(Mar-09)
0.40

The leveraged portfolios showed excellent returns. Each portfolio outperformed the S&P 500 by a large margin, had much less significant draw-downs, and had a higher Sharpe ratio.

I am not yet leaping to invest in these portfolios, but risk parity-based weights show promise of achieving significantly better returns than other leveraged portfolios with reduced risk.

Background

As a note, I do not necessarily recommend the portfolios discussed herein to anyone. My interest here is for my own portfolio, and determining efficient allocations for the parts of my portfolio that I am not actively managing. The relevant portion of my portfolio I am considering investing in this manner is in a retirement account, so transaction fees apply but taxes are not a concern. Your investment goals are likely to vary from mine, of course.

This article is a continuation from what I wrote on Dec 14, 2017, "Using Leverage To Beat The Market." In that article, I discussed two leveraged portfolios and compared the performance of those portfolios with that of an un-leveraged portfolio consisting of only the S&P 500 (SPY, VOO).

In response to my prior article, I received several very insightful comments from those much more knowledgeable than I. I am thankful for all the comments and encourage people to opine below and help guide me on my path to better portfolio management.

Of specific interest was a comment from Varan, who noted:

Adding a leveraged equity ETF to an equity ETF is not the solution as it increases the drawdown.

A simple approach is to have a periodically rebalanced portfolio of the equity ETFs and some asset that is negatively correlated with the equities.

Here are some examples. (I have used ULPIX instead of SSO, but both are 2X SP500). The rebalanced portfolios, even though they contain a leveraged ETF have drawdowns which are lower that the drawdowns of the best of balanced funds."
- Varan, December 14, 2017

In his comment, Varan including a link to the following chart:

SOURCE: VARAN ON SEEKING ALPHA

These portfolios are attractive to me for at least two reasons.

First, Varan's risk parity portfolios have dramatically less draw-down than his two non-risk-parity portfolios. Draw-down is vitally important when considering leverage portfolios, since the primary risk from leverage is the risk of increased losses during poor economic times. Therefore, the remarkably good results during the 2007-09 crisis is promising.

Second, Varan's risk parity portfolios also significantly outperform the simpler portfolios of 100% SPY, and 75% SPY/25% ULPIX. I was intrigued, so I decided to dig in a little.

What is Risk Parity?

If you're already familiar with risk parity, feel free to skip this section. Alternatively, please read it and correct me in the comments where I make a mistake. I do not claim to be an expert on risk parity.

In short, risk parity seeks to find a portfolio in which each of the components of the portfolio contributes an equal amount to the risk of the portfolio. In theory, this reduces the risk of the portfolio while allowing for better performance.

For example, take a simple three-fund portfolio. Risk parity will seek to ensure that each of the three funds contributes 33% to the overall risk of the portfolio, by adjusting the weightings of the portfolio. Thus, safer funds will be owned in higher quantities than riskier funds.

Risk in this sense refers to the price variations of a given fund (daily, weekly, or monthly), as measured using a standard deviation. Risk parity also compensates for the correlation between the different funds.

For example, if a three-fund portfolio included both the S&P 500 and the NASDAQ, as well as a gold fund, the first two funds would be highly correlated. That is, they would tend to rise and fall similarly each day, whereas daily performance of the bond fund would differ substantially. Accordingly, a risk parity portfolio would adjust for this correlation by reducing the weights of the first two funds.

Thus, a risk-parity portfolio adjusts for the risk of the funds within it, and the correlation of those risks, to allow each security in the portfolio to contribute an equal amount of risk.

If you would like a more mathematically rigorous definition and formula for risk parity, here are some Efficient Algorithms for Computing Risk Parity Portfolio Weights. As a warning, it involves somewhat heavy levels of statistics and linear algebra.

Risk parity is only useful if it results in better portfolio performance. Therefore, I wanted to back-test risk parity portfolios against other portfolios.

Constructing Leveraged Portfolios

The main point of this article is to look at leveraged risk-parity portfolios and to compare their risk profiles with those of other leveraged portfolios. To do this, I will construct a few portfolios, and compare how they have fared since at least before the beginning of the 2007-09 crisis.

My focus here is on leveraged portfolios. Therefore, it is vitally important to see how those portfolios fare during draw-downs. Nearly any leveraged portfolio will outperform an un-leveraged portfolio during a bull market, but those gains may come at the cost of taking on an undue amount of risk during bear markets. Making twice as much money when the market rises 40% is great, but not if it means you'll go broke if the market drops 40%.

Chart^SPX data by YCharts

Therefore, I have chosen funds which were created prior to the beginning of 2007. This excludes 3x leveraged funds, since the earliest of those was the Direxion Daily S&P 500 Bull 3X Shares (SPXL), but it was not introduced until November 5, 2008.

Portfolio 1 ("P1"): Portfolio 1 is a combination of two ETFs. These holdings will be weighted and re-balanced every six months using risk-parity-based weights.

  1. iShares 20+ Year Treasury Bond ETF (TLT): Government bonds are used to hedge risk from a leveraged stock ETF. I chose TLT because it is the largest long-term government bond fund. Other choices here could include intermediate-term treasuries (IEF, IEI).

    The expense ratio of TLT is 0.15%. While this is not high, Vanguard's government bond funds (VGLT, VGIT) have lower expense ratios at 0.07%. If I were to invest in this portfolio, I would invest in the lower-fee Vanguard funds rather than the iShares fund. However, the Vanguard funds have inception dates in 2009, which is insufficient for my back-testing.
  2. ProShares Ultra S&P 500 (SSO): My leveraged fund of choice here is SSO, with an inception date in 2006 and an expense ratio of 0.90%. This ETF is 2x leveraged. In an actual portfolio, I would consider using 3x leveraged ETFs as well, but they have inception dates too late to observe their responses during the 2007-09 crisis.

Portfolio 2 ("P2"): Portfolio includes the same two funds as Portfolio 1, but adds another fund to further reduce risk. I have chosen to use gold because its performance is uncorrelated with either stocks and bonds, which is desirable in this setting.

  1. iShares Gold Trust (IAU): Gold has long been known as a hedge against risk, so it seemed an appropriate choice to hedge against the risks involved in a leveraged portfolio. This fund was founded in 2005.

    IAU also offers a lower expense ratio than the larger GLD (0.25% versus 0.40%), and so it is the fund I would use in my own portfolio.

Portfolio 3 ("SPY"): The third portfolio is just 100% SPY. Adding leverage to this portfolio will only worsen the performance during the 2007-09 crisis. Details on the performance of those portfolios can be found in my previous article. Note that in an actual portfolio, I would use VOO over SPY, due to lower expense ratio. The difference would be very minimal, however.

All portfolios were tested back to June 30, 2006. Performance of the relevant funds is shown below.

ChartSPY Total Return Price data by YCharts

I have also included maximum draw-downs, to show the effect of the 2007-09 crisis on these various investments. Note that the chart shows the bottom of the S&P 500 specifically, but is not the lowest point for IAU or TLT. As shown, SSO dropped nearly 85% from its peak, while SPY dropped over 55%.

ChartSPY Total Return Price data by YChartsMethodology

The following methodology is used for each relevant portfolio within the sample.

  1. Each portfolio begins with $1,000 on June 30, 2006.
  2. All portfolios with multiple holdings are re-balanced every six months, on July 1 and January 1 of every year.
  3. Dividends are always reinvested into the same equity. This is equivalent to using a dividend reinvestment plan, and is what I would use in my real portfolio, primarily to minimize trading fees. But for trading fees, it would be better to put dividends into whichever holding was short of its target percentage, but I expect the impact would be extremely minimal.
  4. All risk parity weightings are based solely on data from prior to the date of that weighting, and use the past five years of data. All weightings are based on daily price data (rather than weekly or monthly).

    That is, these are weightings that I could have calculated on the day of that weighting, rather than weightings based on future data. The latter would not accurately reflect possible real-world portfolios.
  5. I do not account for partial shares. Using only $1,000 would often result in a relatively significant amount of money being un-invested due to the inability to purchase partial shares during re-balancing. I do not account for this, and the model assumed all that money has been invested. This is more realistic in a large portfolio than a small portfolio.
  6. I do not account for any trading fees or taxes. This is unrealistic, but given re-balancing only every six months, there will be a small number of trades (six/year for a three-fund portfolio). I anticipate investing in a non-taxable account, such that taxes are not relevant.
  7. Sharpe ratios herein are calculated annually. These ratios are based on the values of the 10-Year Treasury Constant Maturity Rate.

    I use internally consistent methodology for my Sharpe ratios, but my methodology is unlikely to match that used elsewhere. Therefore, they are best used in comparison with each other, but not to externally sourced Sharpe ratios. I do not personally put much faith in Sharpe ratios. They are provided only for the convenience of readers who would like to see them.

Results & Analysis

SOURCE: AUTHOR BASED ON DATA FROM ALPHA VANTAGE

As shown, the risk parity portfolios significantly outperformed the pure SPY portfolio. Both risk parity portfolios offered much better performance than SPY during the 2007-09 crisis especially. Both risk-parity portfolios stayed above $1,000 during the entire crisis.

Here are a few statistics from these portfolios:

Portfolio Total Return
(6/30/06 to 12/15/17)
CAGR Maximum
Draw-down
Sharpe
Ratio
1: TLT and SSO 272% 12.1% 23.4%
(March 2009)
0.96
2: TLT, SSO, and IAU 213% 10.5% 19.5%
(November 2008)
0.88
3: SPY 164% 8.8% 55.2%
(March 2009)
0.40

It is easy to spot which portfolio offers the worst performance. The 100% SPY portfolio gained the least of the three portfolios, in total return and CAGR. It also suffered the highest draw-down during the crisis. Further, its Sharpe ratio was also the lowest.

The choice between Portfolios 1 and 2 may come down, in part, to taste.

ChartGold Price in US Dollars data by YCharts

Returns: Portfolio 1 offers the highest returns over the sample. However, its returns were lower than P2 from 2007 to 2013. P1 only passed P2 when the price of gold dropped in 2013. Gold prices have no recovered since then. As a result, P1 has been able to outperform P2, since P1 does not have gold in its portfolio.

It is unclear which portfolio will offer better returns in the future. I suspect that P1 will offer better performance in bull markets, while P2 offers better returns in bear markets. This is because P2 has less exposure to the stock market, and more exposure to gold.

Maximum Draw-downs: Both P1 and P2 dramatically outperformed SPY during the downturn. P2 offered better performance, however.

P2 recovered its maximum draw-down in mid-November 2008, at 19.5% off its peak. However, be the end of December 2008, P2 had regained all its previous losses. During the rest of the downturn, P2 was usually less than 10% off its peak levels.

P1 fared slightly worse during the 2007-09 crisis. For a majority of 2009 (from January until August), P1 was down double-digits from its peak, recorded its worst draw-down in March 2009. Although it performed a bit worse by this metric than P2, the two-fund P1 still performed very well during the crisis.

Sharpe Ratios: The general idea of a Sharpe ratio is that a portfolio should be compensated for the risk it contains. For example, if your portfolio takes on a great deal of risk, it should be compensated for that risk through higher returns. A Sharpe ratio represents how much a portfolio gained (compared with the risk-free rate) for each unit of risk.

A higher ratio is better, since it indicates that risks are being rewarded with higher gains. By this metric, P1 and P2 were similar at 0.96 and 0.88, with P1 having a slight edge. Both portfolios had much higher Sharpe ratios than SPY.

Note: These Sharpe ratios are not comparable with those found elsewhere. Calculating a Sharpe ratio requires many choices, including the risk-free rate used, the frequency of sampling (daily, weekly, monthly, annually, etc.), and the duration of the sample (here, from June 30, 2006 to present). Thus, don't compare these values with values found elsewhere, as it will not be an apples-to-apples comparison.

Current Portfolios And Future Work

Here are the current portfolio weights, if these portfolios were to be weighted today. This is not the weight used in the portfolios modeled above, since they last re-balanced on July 1, 2017. As a result, weights were slightly different.

Weightings As Of Dec. 16 TLT SSO IAU SPY
1: TLT and SSO 65.4% 34.6%
2: TLT, SSO, and IAU 44.3% 23.4% 32.2%
3: SPY 100%

I do not necessarily recommend (or not recommend) that anyone invest in any of these portfolios. Future results may not look at all like past results.

In the future, I would like to look at a few different things, before I'd consider using a portfolio like this for the passive portion of my portfolio. These include:

  1. The addition of more investments into the portfolio. I expect that my passive portfolio will include at least two equities ETFs (one Canadian and one American or global). I may also wish to include other asset classes, such as REITs, or sector ETFs such as Vanguard Consumer Staples (VDC). I am interested to see how the addition of more asset classes might reduce risk, although at the cost of having to make more trades when re-balancing.
  2. Reviewing how a risk-parity portfolio performs with and without leveraged ETFs. I am not sold on the use of leveraged ETFs, due to beta-slippage and to higher fees than non-leveraged ETFs. In a retirement account, those long-term effects may be detrimental to returns compared with non-leveraged ETFs, especially if the market move sideways or declines over a longer timeline.
  3. Investigating longer timelines. This may not be possible using actual ETFs, since data is limited by when those funds were founded. However, similar work may also be possible using the underlying indices. It may be instructive to see how model portfolios would have performed in the more distant past.

    On the other hand, the further back data goes, the less relevant it will be to today's market and to future markets. For example, the risk and return of bonds in the next ten years is more likely to parallel the last ten or twenty years than the distant past.
  4. The effects of longer and shorter look-back windows when determining standard deviation and correlation of securities in a portfolio. This is used for weights in the portfolio. The portfolios above use five years.

    The idea here is that the correlation and risk in different asset classes will change over time as the economy changes. Thus, using windows that do not include potentially outdated data can be beneficial. However, using a window that is too short may exclude relevant data. This is a trade-off, like those made when choosing shorter-term or longer-term betas (although I tend to use a bottom-up beta).

Conclusion

In this back-test, risk parity portfolios performed extremely well against the S&P 500 (SPY). The risk parity portfolios offered both higher returns and lower risk (as measured by maximum draw-downs) than a pure SPY portfolio. The risk parity performance during 2007-09 was especially impressive to me.

If I was to invest in one of these portfolios today, I would choose Portfolio 1. While it suffered worse draw-downs, it also offered better performance over the life of the sample.

This choice is also because I do not hold especially positive views about gold as an investment. I personally do not expect gold to match the performance of bonds or the stock market in the future. Others will hold contrary views, of course.

However, I do not plan to invest in any of these portfolios today. My timeline for re-allocating parts of my portfolio is at least a month away. During that time, I anticipate looking at other investments for a portfolio and at other ways to balance portfolios to achieve desirable returns with reduced risk.

Please leave a comment below if you have questions, criticism, or any other feedback or suggestions. Please also follow me if you're like to receive updates on my portfolio and my strategies for obtaining good results while reducing downside risk.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.



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