We received a lot of constructive feedback after introducing the “Universal Investment Strategy” (UIS). Therefore here now the leveraged version employing the ETF SPXL & TMF. The strategy can be traded shorting the ETF SPXS and TMV, which we will analyze in future.

3x leveraged Universal Investment Strategy with SPXL & TMF

  • Aggressive leveraged version of our previously published Universal Investment Strategy
  • Variable SPXL / TMF allocations dynamically adapted to the market conditions.
  • 45% annual return with a Sharpe Ratio of 1.3 since 2002.

We’re received a lot of constructive feedback after our recent article introducing the “Universal Investment Strategy” (UIS). Many bloggers have contributed to validate the strategy with their own backtests. Among them Ilya Kipnis from QuantStrat Trader, and Michael Kaplan from Systematic Investor. In its January 2015 meeting, Al Zmyslowski and the CI-MI group of the AAII Silicon Valley chapter discussed the Strategy in detail. They were kind enough to post the videos (Part I, II and III).

Due to its simplicity and low correlation to the S&P 500, there is a continued interest in the UIS version that uses 3x leveraged ETFs: ETF SPXL (Direxion Daily S&P 500 index Bull 3X Shares ETF) and TMF (Direxion Daily 30-Year Treasury Bull 3x Shares ETF). Following the suggested nickname by Al from AAII SV we call this version “Hell on fire”. This alludes to the high risk/return profile of the strategy. We will show ways to blend this strategy in a well-balanced and risk-optimized portfolio to overcome the generally negative perception towards leveraged ETF.

The interested reader might ask, why a separate article for this? Why not simply use the signals of the non-leveraged strategy, but execute with the leveraged ETF? Or just use margin? We will come back to this question after introducing some methodology used in our extended backtest.

Synthetic time series for extending backtest of SPXL and TMF

Due to the limited history of both funds ETFs (SPXL & TMF) we decided to extend the time series to include the 2008-2009 timeframe.

The approach we took was to determine a multiplication factor to the daily returns of SPY (TLT) which would minimize the sum of squared differences of the leveraged and non-leveraged versions. Applying the resulting factor of 2.84 for the SPXL ETF (3.04 for TMF ETF) visually confirms the good fit.

But why not apply the UIS signals to trading the 3x leveraged ETF? The answer lies in the effective leverage both ETF offer versus the base version.

SPXL results with factor of 2.84 and falls short of the 3.0 leverage target. TMF delivers a 0.28 higher leverage, and with a factor of 3.04 more than delivers the targeted leverage. We show that using the synthetic 3x leveraged time series in the algorithm results in better performing trading signals.

 leveraged spxl spxs investment tmf tmv etf portfolio

leveraged version spxl spxs investment tmf tmv etf portfolio

For the backtest we use the same ‘modified Sharpe Ratio’ algorithm as introduced in the original UIS. Normally the Sharpe Ratio is calculated by Sharpe = rd/sd with rd = mean daily return and sd = standard deviation of daily returns. We don’t use the risk free rate, as we only use the Sharpe ratio for ranking the funds ETFs.

Our algorithm uses a modified Sharpe formula: Sharpe = rd/(sd^f) with f=volatility factor. The f factor allows us to change the importance of volatility.

We analyze the performance of three different backtests and present the charts from our “QuantTrader” software:

1) Formerly ‘plain’ UIS with the SPY and TLT ETF for Jan 2002 – Mar 2015

spxl etf leveraged performance rotation

2) The 3x leveraged UIS since inception in 2009 to Mar 2015

leveraged return using spxs tmv etf portfolio

3) The 3x leveraged UIS from 2002 to Mar 2015

leveraged spxl and spxs with hedge

4) Same as 3), using lookback and f factor as in 2).

This to confirm the parameter stability of our extended backtest, discussed later.

leveraged spxs and spxl etf strategy

5) – 10) The plain and leveraged versions since inception and extended to 2002.

The performance statistics of the backtests and their underlying ETF in comparison:

  CAGR % Volatility % Sharpe Max DrawDown %
1. UIS SPY/TLT 2002 – 2015 13.57 10.10 1.34 -17.13
2. UIS SPXL/TMF 2009 – 2015 53.27 25.26 2.11 -19.28
3. Synth. UIS SPXL / TMF 2002 – 2015 (selected for publication) 44.78 33.59 1.33 -43.95
4 Synth. UIS SPXL / TMF 2002 – 2015
(same parameter as 2)
35.72 32.65 1.09 -48.97
5 SPY 2002 – 2015 8.92 19.36 0.461 -55.19
6 TLT 2002 – 2015 7.81 13.84 0.56 -26.58
7 SPXL Jul 2009 – 2015 44.17 47.69 0.93 -53.82
8 TMF Jul 2009 – 2015 20.04 45.88 0.44 -53.33
9 Synth. SPXL 2002 – 2015 15.93 56.81 0.28 -94.18
10 Synth. TMF 2002 – 2015 16.39 42.15 0.39 -66.39

Note the Maximum DrawDown of -94% (-66.39%) in the synthetic SPXL (TMF) from Oct 2008 to March 2009. In practical terms, $100 invested in SPXL would have decreased to $6. We estimate only few people on this planet would have gone through this roller-coaster without de-leveraging. Thus with the retrospective knowledge that the world did not ‘go bust’, losing a major part of their account.

That said, it is also clear that any leveraged strategy with fixed (not adaptive) allocation ratios, would not survive a 2008 crash. It is just an absolute necessity to reduce the allocation if you go through a longer market correction. Unfortunately these 3x leveraged ETFs have all been issued after the 2008 crash. Since then we had a continuous bull market which makes any post-2009 backtest look really attractive.

Performance Analysis of the leveraged version

There is a notable different behavior of the strategy before and after the financial crisis in 2008/09, which is visible in the chart. Only after the 2008 correction investors seem to really see Treasuries as a save haven asset which goes up when the stock market goes down. Since 2008 the average correlation between the stock market and Treasuries was about -0.5. Before 2008 it was only around 0.

Due to more stable performance over the whole 2002 – 2015 period, we select Option 3) for inclusion in our overall portfolio of strategies. All further analysis refers therefor to this option.

Parameter stability in the extended 2002 – 2015 period

Our algorithm optimizes for the ‘modified Sharpe Ratio’, so we plot this instead of the regular Sharpe Ratio, together with the Annual Return (CAGR) and volatility with the horizontal axis representing our f factor, and the vertical axis the lookback period.

leveraged quantitative analysis spxl spxs Heatmap

You can see that both the annual return and volatility are very stable across the parameter range. Values go from 39%-45% annual return, and 32%-34% annualized volatility – even our heat-map plot goes aggressively from ‘very green’ to ‘very red’ in these close ranges.

Portfolio options for calming the ‘Fire in Hell’

As we stated in the beginning, this SPXL / TMF “Hell on fire” strategy might look excessively aggressive to many private investors due to the 3 times leverage resulting in relatively high volatility. So why do we present this here? Well, we see this strategy as a very good complement even to conservative or moderately growth seeking portfolios.

Here are two examples of how this strategy might be blended with other Strategies. We combine ‘Hell on fire” with two other strategies we had previously introduced in SeekingAlpha: The “Sleep Well Bond Rotation” and the “Maximum Yield Rotation” Strategies.

The first Portfolio of Strategies (“Custom Portfolio”) seeks maximum annual return with a maximum Volatility of 20%, so suited for investors looking for rather aggressive growth:

leveraged investment portfolio with spxl and spxs

By allocating 23% to the 3x UIS, this portfolio delivered a very aggressive 45% annual return, but backed up by a dream Sharpe Ratio of 2.2.

The second Portfolio option (“Custom Portfolio 1”) also seeks maximum Annual Return, but this time with a maximum Volatility of 13%. This is better suited for investors who seek moderate growth or require a low volatility portfolio with stable returns due to having reached the retirement age:

leveraged investment portfolio spxl spxs

In this portfolio we observe that by just allocating 5% to the 3x UIS, we achieved a very good 23% annual return, with an even higher Sharpe Ratio of 2.3.

Custom Investment Portfolio employing the SPXL / TMF model

Plotting the custom portfolios together with the different strategies on a Risk / Return chart:

leveraged spxl and spxs Portfolio Markowitz

These blends of strategies deliver dramatically better results. Even compared with what would possible using any combination of some common market proxies we included in the plot chart.

Yet the same ‘power of diversification’ like in conventional asset allocation still applies. Using a blend of a Bond Rotation Strategy, an Equity Rotation Strategy, and as additional diversifier some inverse volatility and treasuries we achieve results which again drastically outperform each individual strategy performance. Using this blend of strategies also enables us to configure virtually all possible portfolios targets through our Portfolio Analyzer and Builder. Either by constraining volatility, classically optimizing for Sharpe Ratio or setting minimum or maximum weights by asset class.

Inverse leveraged using TMV and SPXS ETF

Part II of this article will look at the same model, but executed with the inverse -3x leveraged SPXS and TMV funds ETFs. By shorting SPXS and TMV we benefit from harvesting the daily roll losses of the funds ETFs even after absorbing the daily borrowing cost, that is we we expect to further enhance the total return.

SPXL can be replaced by either the 2x SSO ETF or 3x UPRO depending on the availability of the ETF in your plan and your personal risk appetite. Shorting the TMV and SPXS ETF can be done by inverting the long signals.