## Summary

- A diverse basket of ETFs can be used in a rotation strategy if the strategy compensates for the variance in their volatilities.
- This article provides an 19-year backtest of a rotation among a broad group of 15 securities.
- The >16% CAGR with Sharpe ratio of 1.21 during the 19-year backtest provides additional evidence of the viability of the volatility-compensation concept described in Part I of this series.

In Part I of this series, I described a price-based approach for rotating among a diverse group of ETFs representing multiple asset classes. I have tested such systems on my blog and recently published an article providing an analysis of these kinds of asset rotation strategies. Because the volatility of the ETFs in a highly diversified portfolio can vary widely, a successful and robust rotation strategy based on price performance alone is difficult to implement. Part I of this series proposed a volatility compensation technique that normalized the volatilities of the underlying asset classes, providing a suitable basis for generating rotation signals.

The strategy presented in Part I provided high returns with low risk over the backtest period. However, the period of testing data for the nine ETFs was limited to late-2006 and resulted in a relatively short backtest time of only seven years. This left a question as to the robustness of volatility compensation over time. I suggested that a longer backtest using mutual funds to represent each asset class, would provide further evidence in support of a diverse, volatility-compensated ETF rotation system. The present article describes such a backtest.

## The funds selected for the backtest

In selecting funds for this article, I wanted the funds to represent as closely as possible the asset classes that had been represented by the ETFs in Part I of this series. I selected 15 mutual funds based on [i] the availability of price data at Yahoo! Finance "historical prices" to at least 1993 and [ii] how closely the fund represented an asset class as a whole, rather than the value of a unique active management strategy. The chosen funds are listed below with the year representing the earliest data I could acquire on Yahoo! Finance:

Fidelity US Growth FDGRX (1989)

Fidelity US Blue Chip FBGRX (1987)

Fidelity US Value Mid-Cap FDVLX (1989)

Fidelity Europe FIEUX (1986)

Fidelity Emerging Markets FEMKX (1993)

Fidelity Latin America FLATX (1993)

Fidelity Pacific FPBFX (1986)

Fidelity Overseas Large Blend FOSFX (1984)

Fidelity Japan Fund FJPNX (1992)

Vanguard Metals and Mining VGPMX (1987)

Vanguard Energy VGENX (1987)

Vanguard Long Treasury VUSTX (1989)

Vanguard Long Investment Grade Bond VWESX (1987)

Vanguard High-Yield Corporate Bond VWEHX (1989)

Vanguard Short Investment Grade Bond VFSTX (1987)

(Note: I was unable to find a real estate or REIT fund that had price data available before 1993.)

The backtest period begins on December 31, 1994 and runs through December 31, 2013, covering 19 years of performance. As shown in the table below, the volatilities of the underlying securities in this test (measured as annual standard deviation of daily price changes) varied significantly:

FDGRX | FBGRX | FDVLX | FIEUX | FEMKX | FLATX | FPBFX | FOSFX | FJPNX | VGPMX | VGENX | VUSTX | VWESX | VWEHX |

21.10% | 16.83% | 18.57% | 19.69% | 27.15% | 30.99% | 21.53% | 18.56% | 20.50% | 31.73% | 21.72% | 9.93% | 8.69% | 7.69% |

(calculated by me based on data from Yahoo! Finance historical prices, linked above for each fund)

The volatilities above reflect the annual volatilities over the entire 18-year backtest period. When the volatilities are calculated over a shorter span, e.g., 6 months, the differences are even greater.

For example, as of January 31, 1997, the 6-month volatilities of the underlying asset classes in this backtest were shown in the table below.

FDGRX | FBGRX | FDVLX | FIEUX | FEMKX | FLATX | FPBFX | FOSFX | FJPNX | VGPMX | VGENX | VUSTX | VWESX | VWEHX | VFSTX |

11.69% | 10.62% | 7.49% | 7.46% | 9.77% | 12.92% | 11.58% | 7.61% | 13.99% | 13.08% | 10.64% | 8.63% | 7.97% | 3.96% | 2.88% |

(calculated by me based on data from Yahoo! Finance historical prices, linked above for each fund)

## The volatility compensation factor

The differing volatilities of the underlying securities can and should be compensated for. A simple algorithm was developed by the author as described in Part I of this series. By way of summary, the volatility of each asset class was calculated. These volatilities were all averaged to give a total volatility. Dividing the total volatility by the volatility of each security provided a respective "volatility compensation factor" for each security.

Using the same example above as of January 31, 1997, the volatility compensation factors were:

FDGRX | FBGRX | FDVLX | FIEUX | FEMKX | FLATX | FPBFX | FOSFX | FJPNX | VGPMX | VGENX | VUSTX | VWESX | VWEHX | VFSTX | |

6-mo volatility | 11.69% | 10.62% | 7.49% | 7.46% | 9.77% | 12.92% | 11.58% | 7.61% | 13.99% | 13.08% | 10.64% | 8.63% | 7.97% | 3.96% | 2.88% |

Vol Comp | 0.84 | 0.92 | 1.31 | 1.32 | 1.00 | 0.76 | 0.85 | 1.29 | 0.70 | 0.75 | 0.92 | 1.14 | 1.23 | 2.48 | 3.41 |

(calculated by me based on data from Yahoo! Finance historical prices, linked above for each fund)

Like SHY in Part I, VFSTX was excluded from the compensation in the backtest.

The higher the volatility compensation factor, the lower the relatively volatility of that asset class relative to the others.

## Using the volatility compensation factor in an asset class rotation

The ETF rotation systems that I have investigated are based on buying the ETF having the best price performance over a certain period of time. One of my articles discusses an 85-day lookback period. One of my blog posts discusses a three-month lookback period. In the proposed system of this article, I 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 asset class.

In calculating the performance values, I 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. I multiplied each 1-month log performance of each asset class by the respective volatility compensation factor for that asset class. The result was a "compensated 1-month log performance" for each of the asset classes in the test basket. Using the compensated data, now a suitable rotation strategy could be applied and tested.

## Application of the rotation 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 asset class. Each of these parameters was ranked 1 through 15 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 two top-ranked asset classes were purchased and held for one month. At the end of the month, the values were recalculated and a new signal given.

In Part I of this series, I applied a scenario analysis to determine how much each of these four factors should be weighted in calculating the total rank. The result of this analysis was a weighting of 1, 1, 1, and -1 for the 1-month, 3-month, and 6-month performance and 6-month volatility, respectively. These values were also used in the 19-year backtest discussed here.

## Results of the 19-year backtest

From December 31, 1994 to December 31, 2013, the system as described outperformed the S&P500 index, as shown in the graphic below, generated by the author:

*System performance vs.* SPY *during backtest period:*

The table below shows the relevant metrics of the system versus the S&P 500 and the Fidelity growth and value US equity funds:

SYSTEM | SPY | FDGRX | FBGRX | |

TOTAL | 18.06 | 5.45 | 8.12 | 4.95 |

CAGR | 16.45% | 9.33% | 11.65% | 8.79% |

Stdev | 13.57% | 16.77% | 24.02% | 18.64% |

Sharpe | 1.21 | 0.56 | 0.49 | 0.47 |

Max DD | 24.46% | 50.78% | 68.24% | 55.26% |

Linearity | 16.65% | 21.45% | 24.84% | 49.96% |

Growth R | 0.99 | 0.44 | 0.47 | 0.18 |

(calculated by me based on data from Yahoo! Finance historical prices, linked above for each fund)

The volatility compensated system outperformed these funds in both risk and return.

As discussed in Part I, linearity and growth ratio ("Growth R") are custom parameters that I use to measure how closely the system's returns align with an ideal exponential growth curve. A lower linearity means the systems is closer to the curve. The table above shows that the system trades far more like a fixed compounded investment than the S&P 500. The graph below, generated by the author, shows the logarithm of the system's performance compared to an ideal growth curve:

*Log of system performance vs. ideal growth curve during backtest period:*

The performance of the system versus all 15 of the underlying asset classes is shown in the graph below, generated by the author.

*System performance vs. asset classes in the portfolio:*

Finally, the chart below shows the percentage of months in which the system invested in each asset class. Because more than one asset is invested in each period, these percentages add up to more than 100%.

*Percentage of time in position, by asset class:*

*(click to enlarge)*

You can see that the system is almost always invested in a bond fund of one form or another, providing a hedge against the equity stake and reducing volatility.

## Conclusion

A diverse basket of asset classes 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 results from Part I of this series have been corroborated by the long 19-year backtest and diverse group of asset classes discussed in this article.

**Disclosure: **I am long EDV. 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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