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Muhammed Ali was known for floating like a butterfly and stinging like a bee. We all want to have the best of both worlds. This article proposes a trading system that provides returns like the S&P with the risk of a long bond fund. Results and analysis of 10-year and 23-year backtests are also provided. The system can easily be understood and implemented using unspecialized tools and without the need for complex mathematical calculations.

The results:

  • Over 15.5% CAGR from January 1, 2004 to December 31, 2013
  • Maximum drawdown of 17%
  • Sharpe ratio of 1.08
  • Growth ratio of 1.33 (this custom metric is explained below)
  • Trades only two ETFs: SPY and TLT

A Simplified Approach

A web search of rotation strategies inevitably returns countless ways of trading between US stocks and US long treasuries in light of various market conditions. Many of these systems require sophisticated charting and analysis of the underlyings in order to determine the appropriate trigger. The data used by many of these systems is not readily available on popular websites like Google Finance and the like. Further, the signals relied on by these systems (e.g., ADX, RSI, Bollinger Bands) can be difficult to understand and calculate without some mathematical expertise.

This article presents a simple approach that can be implemented in Excel or a hand calculator with minimal effort or sophistication.

The Basis Of The Proposed System: Trending.

People follow other people. This fact is terribly true in trading, and is the basis of the trading system presented: follow the money.

The system determines the x-day price performance of the S&P500 (via SPY) and US long bonds (via TLT). An investment is made in the ETF having the highest prior x-day performance.

The x-day performance is calculated daily by dividing the current close by the close x days ago. These calculations can be performed in Excel, on a napkin at the bar, or in one's head. The data is available at almost all of the popular investment websites.

Although the x-day performance is calculated each day, trades are rarely signaled daily. Only 89 trades were made in the 10-year backtest period.

A 10-Year Backtest

The 85-day lookback provided maximal returns over the past 10 years, and was used for the results below. From January 1, 2004 to December 31, 2013, the results of the system versus SPY and TLT are:

 SYSTEMS&PTLT
    
Total4.302.521.86
CAGR15.69%9.69%6.38%
Stdev14.58%20.34%14.19%
Sharpe1.080.480.45
Max DD17.06%55.19%26.59%
CAGR/MDD0.920.180.24
Linearity11.83%16.85%7.46%
Growth1.330.580.86

The total returns of 430% over 10 years corresponds to about 15.7% compounded annual growth rate (OTCPK:CAGR). This trounces the 9.69% and 6.38% returns from SPY and TLT alone.[1]

While performance is improved versus buying and holding SPY, it can be seen that the risk aligns more closely with the TLT bond fund. The "Stdev" metric above reflects the average annual standard deviation of returns, a generally accepted measure of volatility. The average annual volatility of the system is quite close to the TLT bond fund volatility and less than the SPY's volatility.

The Sharpe ratio is the CAGR divided by the average annual standard deviation of returns. It is an indicator of the relative trade-off of risk and reward. In other words, the higher the Sharpe ratio, the less risk you are exposed to for each percentage point of returns. By providing returns that meet or exceed the stock market while also providing a lower volatility, you can see that the Sharpe ratio for the proposed trading system is significantly improved when compared to SPY or TLT.

Perhaps most striking is the maximum drawdown of the system, which is only 17%, compared to 55% (!) for the S&P and 27% for the long bond (due, among other things, to interest rate risks). The reduced drawdown comes at no cost to performance, as the ratio of CAGR to maximum drawdown shows. The system's returns were nearly four times less risky than the TLT long bond ETF.

Lastly, we see custom parameters that are named "linearity" and "Growth." These attempt to measure how much a trading system deviates from an ideal growth curve R = exp(k * t) where R is returns, k is a growth constant, and t is time. For this, one fits a linear regression to the natural log of the system's returns. One then calculates the root-mean-square of the differences between the system's logarithm returns and the regression line. The result is labeled "linearity." A lower linearity means less deviation from an ideal growth curve. Thus, the linearity is a measure of volatility, but it differs from "stdev" in that it measures volatility from a growth curve rather than from a constant. The label Growth" in the table refers to the Growth ratio, which is the CAGR divided by the linearity.

You can find further discussion of these parameters on my blog.

The linearity of the proposed trading system lies squarely in the middle of the linearity of the S&P and long bond ETFs. While the bond ETF provides better linearity, the returns are proportionally much lower, as reflected in TLT's inferior Sharpe* ratio when compared to the proposed trading system.

The Equity Curves

The performance of the system versus the SPY and TLT ETFs is plotted below:

Returns of the proposed system, SPY, and TLT since January 1, 2004 (author's analysis)

(click to enlarge)

The enormous drawdown of the S&P is stark. Also, despite what many may think, even the long bond ETF shows clear volatility. The system, in blue, steadily climbs with relatively little variation.

The performance of the system plotted on a log scale is shown below in comparison to the ideal growth regression curve:

Returns of the proposed system and ideal growth curve on a log scale (author's analysis)

(click to enlarge)

One thing to notice is how consistently the system sticks to the growth curve over time, which is what linearity attempts to measure.

Lastly, below is the 252-day (~1 year) periodic performance versus the S&P.

YearThe SystemSPY
12.81%10.22%
28.50%7.18%
310.09%13.89%
49.91%1.59%
518.33%-32.71%
622.31%25.22%
719.44%13.94%
840.25%2.68%
92.67%16.84%
1026.16%26.16%

When the S&P rose, it occasionally beat the system by a few percentage points. When the S&P tanked, however, the system stayed steady. Notice that there were no down years using the proposed system since January 1, 2004. Again, the 17% maximum drawdown over 10 years reflects the remarkable risk control of the proposed system.

A 23-Year Backtest

In order to test the system further back in time, I chose to try it against similar mutual funds: FDVLX (for stocks) and VUSTX (for long bonds). Using the same 85-day lookback period, the results from January 1, 1990 are remarkably similar to the ETF-traded system:

 SYSTEMFDVLXVUSTX
    
Total27.2113.975.41
CAGR15.45%12.15%7.61%
Stdev12.73%18.99%10.49%
Sharpe1.210.640.73
Max DD15.49%66.90%18.43%
CAGR/MDD1.000.180.41
Linearity15.17%23.01%6.40%
Growth1.020.531.19

Despite the various market conditions over the past 23 years, the log returns are quite straight as shown below:

Returns of the fund-based system and ideal growth curve on a log scale (author's analysis)

(click to enlarge)

The system returns appear generally time invariant.

An Investigation Of Robustness Across Lockback Parameters

The 10-year ETF backtest provided maximal returns when the lookback was set to 85. This article also provides results for different values of the lookback parameter ranging from 65 to 99 days:

 6570758085909599
Total3.103.253.283.204.303.672.973.23
CAGR11.98%12.49%12.63%12.34%15.69%13.89%11.49%12.43%
Stdev14.56%14.45%14.59%14.66%14.58%14.58%14.63%14.59%
Sharpe0.820.860.870.841.080.950.790.85
Max DD19.05%17.06%18.43%23.71%17.06%17.06%19.66%17.43%
CAGR/MDD62.90%73.24%68.52%52.04%91.99%81.42%58.46%71.35%
Linearity15.14%13.81%13.20%9.80%11.83%14.44%13.39%8.81%
Growth0.790.900.961.261.330.960.861.41

Returns and Sharpe are maximal with a lookback period of 85 days, but all values beat the SPY ETF's return (9.69% CAGR) and Sharpe (0.48). The Growth ratio was maximal at a 99-day lookback, where the system most closely followed the ideal growth curve as shown by the low linearity of less than 9%.

My Conclusion

Although the returns and volatility exhibit minor variation across different lookback time periods, the results uniformly exceed the S&P returns and Sharpe ratio. It was also seen that the results exhibited generally constant exponential growth over a 23-year backtest period. In light of this analysis, we find it highly probable going forward that risk reduction can be achieved without compromising returns through a simple rotation between stocks and bonds based on prior price performance as described above.

[1] The analysis herein is based on dividend-adjusted prices obtained from Yahoo! Finance.

Source: Return Like A Stock, Risk Like A Bond: 15.5% CAGR With 17% Drawdown