While perusing the internet last weekend to research some ETF rotation strategies, I came across a site called Vector Grader (with which the author is not affiliated) that presented a strategy for rotating among a diverse collection of ETFs based on prior price performance. I have tested such systems on my blog and recently published an article providing analysis of these kinds of trading systems. The ETFs in the Vector Grader strategy, however, were far more diverse than the systems I had tested previously.

Successful rotation strategies on highly diverse ETF groups are difficult to devise because of the differences in the volatilities of the underlying ETFs. However, by applying a volatility compensation factor to these ETFs, I was able to develop a rotation strategy that backtested with successful results:

- Total returns of over 500% since January 1, 2007
- CAGR of over 26%
- Maximum drawdown of only 13.2%
- Sharpe ratio of 1.51
- Linearity of 8.1%
- Growth ratio of 3.11.

These last two values are custom metrics that this author has used to evaluate the backtests of trading systems.

## The basket of ETFs

The Vector Grader website proposes trading the following ETFs in a monthly rotation strategy:

IWM: iShares Russell 2000 ETF (small cap US equities)

IVV: iShares S&P 500 large cap US equities)

EFA: iShares MSCI EAFE Index (international equities)

ICF: iShares Cohen & Steers Realty Majors (real estate)

DBC: PowerShares DB Commodity (commodities)

VWO: Vanguard FTSE Emerging Markets (emerging markets)

IAU: iShares Gold Trust (gold)

TLT: iShares 20+ Treasury (long US bonds)

SHY: iShares 1-3 Year Treasury (short bonds)

For the testing described in this article, the dividend-adjusted price data for all of these ETFs was downloaded via Yahoo! Finance into an Excel spreadsheet. For ease, monthly prices were used.

## The Problem with diversity

The first thing the author investigated was the average annual standard deviation of prices for these ETFs. This value varied widely as shown in the table below:

IWM | IVV | EFA | ICF | DBC | VWO | IAU | TLT | SHY |

20.88% | 16.38% | 21.06% | 30.30% | 21.44% | 26.43% | 20.12% | 14.42% | 1.42% |

A rotation strategy for generating buy signals among these ETFs would have trouble accounting for the wide range of volatilities. What might seem like a large price swing for IVV or TLT might not be unusual for ICF or VWO. In other words, it is difficult to create a set of rules that applies to all the ETFs in the basket for generating reliable rotation signals.

## Volatility compensation to the rescue

The volatilities of the underlying ETFs can and should be compensated for. A simple algorithm was developed by the author. The average annual standard deviation of each ETF (ETF volatility) was calculated. The ETF volatilities were all averaged to give a total volatility. By dividing the total volatility by the ETF volatility of each ETF, a respective "volatility compensation factor" was calculated for each ETF.

For example, the volatility of IWM was determined to be 20.88% during the backtest period. The average of all the volatilities of all the ETFs (except SHY) was 21.38%. Thus, IWM's volatility compensation factor was 21.38 / 20.88 = 1.02. The factor for ICF was 0.71, reflecting its higher-than-average volatility, and the factor for TLT was 1.48, reflecting its lower-than-average volatility.

SHY was excluded from the compensation because it is meant to act as a cash stop and not part of the rotation.

## Using the volatility compensation factor in a rotation system

The author's ETF rotation systems have been based on buying the ETF having the best price performance over a certain period of time. The author's recent article discusses an 85-day lookback period. One of the author's blog posts discusses a three-month lookback period. In the proposed system of this article, the author calculated the 1-month, 3-month, and 6-month price performance, as well as a 6-month volatility, and weighted each of these to generate a total rank for each ETF. The author then applied a scenario analysis, discussed below, to determine how much each of these four factors should be weighted in calculating the total rank.

In calculating the performance values, the author relied on the natural logarithm of price performance. For instance, the 1-month price performance was the natural log of the ratio of this month's price to last month's price. The 3-month performance was the sum of the 1-month log performances for the prior three months. Similarly, the 6-month performance was the sum of the 1-month log performances over the prior 6 months. Lastly, the 6-month volatility was the standard deviation of the prior 6 months of 1-month log performance.

The volatility compensation factors come into play by adjusting the 1-month log performances. The author simply multiplied each 1-month log performance of each ETF by the respective volatility compensation factor. The result was that the volatility of the compensated 1-month log performances of all the ETFs was the same. For example, in December 2006, the 1-month log performance of VWO was -0.00937. The volatility compensation factor for VWO was 0.81 because of its higher volatility. The 1-month log performance was multiplied by this value to reduce it to -0.00758, effectively lowering the volatility to the average. When the 1-month log performances of all the ETFs are adjusted in this way, they all exhibit the exact same volatility.

Using the compensated data, now a suitable rotation strategy could be applied.

## Application of the system to the compensated data

The system determined the volatility-compensated 1-month, 3-month, and 6-month performance, as well as the 6-month volatility, of each ETF. Each of these parameters was ranked 1 through 9 using the Excel RANK function. These ranks were weighted and added to arrive at a final rank as follows:

Weight1 * 1-month performance rank + Weight2 * 3-month performance rank + Weight3 * 6-month performance rank + Weight4 * 6-month volatility rank = Total Rank.

The top ranked ETF was purchased and held for one month. At the end of the month, the values were recalculated and a new signal given. Out of 90 months, the signal stayed the same 44 times. Nine times there was a tie for the top ETF; in those cases, equal dollar shares of both ETFs were purchased.

## Scenario analysis: the results

The weights to be given to each of the four performance parameters (1-month, 3-month, 6-month performance and 6-month volatility) created a 4-dimensional problem in optimization. Rather than attempt to optimize the system to the maximum returns, the author sought to try several, simple scenarios and see what emerged. The author looked for three things: [i] high returns, [ii] low risk, and [iii] principled performance across parameters. If only one small set of weights provided a good system, then it would be doubtful that the system would continue to do so in the future. If, however, the system performed well over a large variety of weights, then it would increase the likelihood that the system would continue to perform in the future.

Below are the results of the scenarios from multiple different weights:

Scenario testing of the author's rotation strategy | ||||||||

Weights | Results | |||||||

1-month | 3-month | 6-month | volatility | CAGR | Max DD | Sharpe | Linearity | Growth R |

1 | 1 | 1 | -1 | 26.11% | 13.18% | 1.51 | 8.38% | 3.11 |

1 | 1 | 1 | 0 | 24.37% | 17.06% | 1.20 | 15.76% | 1.55 |

0 | 1 | 0 | 0 | 21.95% | 16.96% | 1.15 | 9.50% | 2.31 |

0 | 1 | 1 | -1 | 18.62% | 11.36% | 1.13 | 6.86% | 2.71 |

1 | 0 | 0 | 0 | 18.40% | 21.50% | 0.96 | 7.98% | 2.30 |

1 | 1 | 0 | 0 | 17.36% | 14.02% | 0.97 | 10.52% | 1.65 |

-1 | 1 | 1 | 0 | 15.39% | 36.54% | 0.77 | 12.18% | 1.26 |

-1 | 1 | 1 | -1 | 12.29% | 24.89% | 0.73 | 6.62% | 1.85 |

0 | 0 | 1 | 0 | 9.97% | 23.66% | 0.50 | 11.60% | 0.86 |

0 | 0 | 1 | -1 | 9.72% | 19.20% | 0.70 | 6.68% | 1.45 |

0 | 0 | 0 | -1 | 2.40% | 1.20% | 1.65 | 2.00% | 1.18 |

0 | 0 | 0 | 1 | -4.90% | 63.80% | -0.22 | 26.50% | -0.19 |

Using volatility as a positive factor gave severely negative results. Using volatility as a negative factor improved results but only slightly. Using any two of the 1-month, 3-month, and 6-month performances as positive factors gave high returns with low drawdown and Sharpe ratios generally over 1.0.

At the optimal values of 1, 1, 1, -1 for the four weights, the signals were more heavily weighted to IVV but otherwise generally evenly distributed among the positions, as shown below:

MONTHS (and %) IN POSITION | ||||||||

IWM | IVV | EFA | ICF | DBC | VWO | IAU | TLT | SHY |

6 | 21 | 8 | 14 | 9 | 12 | 8 | 13 | 8 |

6.06% | 21.21% | 8.08% | 14.14% | 9.09% | 12.12% | 8.08% | 13.13% | 8.08% |

Below is the equity curve based on the author's analysis of the system's performance versus the other ETFs:

A numerical comparison of the CAGR and maximum drawdown (monthly) of the system and the underlying ETFs is below:

System | IWM | IVV | EFA | ICF | DBC | VWO | IAU | TLT | SHY | |

Total | 5.07 | 1.73 | 1.54 | 1.16 | 1.10 | 1.06 | 1.37 | 1.94 | 1.63 | 1.20 |

CAGR | 26.12% | 8.13% | 6.40% | 2.17% | 1.38% | 0.86% | 4.65% | 9.91% | 7.21% | 2.60% |

Max DD | 13.18% | 52.72% | 51.57% | 58.17% | 73.61% | 56.65% | 61.70% | 34.46% | 21.80% | 1.21% |

Note that the system's drawdown was even less than the TLT long bond ETF.

Below is the system's performance based on the author's analysis depicted on a log scale compared to an ideal growth curve.

The system hugs the ideal curve tightly, showing consistent returns year over year. The author's custom parameters of "linearity" and "growth ratio" attempt to quantify how far the system's equity curve deviates from a perfect exponential (compounded) growth curve. The 8.38% linearity is the root mean square of the difference between these two curves and is remarkably low compared to other systems that this author has tested. The growth ratio is the CAGR divided by the linearity. This is over 3, which is also remarkably high.

## Conclusion

A diverse basket of ETFs can be used in a rotation strategy if the strategy compensates for the variance in their volatilities. The strategy discussed above provided high returns with low risk over the backtest period. The data for these ETFs was limited to late-2006 and resulted in a relatively short backtest time of only seven years. This leaves some question as to the robustness of this system over time. The author may investigate whether similar mutual funds exist having data into the 1990s for further testing of a diverse, volatility-compensated ETF rotation system.

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