For illustration purposes, I'm going to show you how I selected the funds for October 2016 for the Vanguard Capital Preservation, VCP, Strategy. Here is the PV link for my version of the VCP Strategy: bit.ly/2d4t7gQ

This is basically the strategy I presented here. The only difference between this version and the one reported in the SA article is the two-month Simple Moving Average, SMA, filter (instead of a 25-day SMA filter). This makes it easy to check if the fund passes or fails its filter. If the current month's price is greater than last month's adjusted price, then it passes.

Here is how I determined the selections were VCVSX and VWEHX by 2 pm EST (and executed the trades) on September 30, 2016. On EOM-1, I went to stockchart.com PerfCharts and determined the one-month returns based on EOM-1 data. I went from August 30 - September 29. This included the dividend distribution on August 31, but not the one on September 30. Here were the one-month returns:

VFITX = +0.47%

VCVSX = +0.45%

VFIIX = +0.36%

VWEHX = +0.27%

VWAHX = -0.39%.

So the numbers were pretty close except for VWAHX, but at that moment the two selections were VFITX and VCVSX. Both had positive returns, so they both passed their 2-month SMA filters.

I decided to wait and see what happened in the market on Friday (September 30) before making a final decision. I used IEF as a proxy for VFITX, CWB as a proxy for VCVSX, VMBS for VFIIX, HYS for VWEHX, and HYD for VWAHX.

I then went to stockcharts.com and found the one-month returns going from August 31 - September 29. The final one-month return will be the return from August 31 to September 29 plus the dividend distribution on September 30 plus the return on September 30. This is the way the one-month returns lined up:

VFITX: 0.43% + 0.13% (distribution) + September 30 return

VCVSX: 0.61% + 0.0% (no distribution) + September 30 return

VFIIX: 0.18% + 0.17% (distribution) + September 30 return

VWEHX: 0.0% + 0.45% (distribution) + September 30 return

VWAHX : -0.68% + 0.29% (distribution) + September 30 return.

For the distributions, I just used the distribution on August 31 (they don't change much month-to-month). I got the numbers from Schwab, but the information is available from many different sources.

When I checked the ETFs @ 1:30 pm EST on Friday, I saw these returns for September 30:

IEF = -0.23%

CWB = +0.61%

VMBS = 0.0%

HYS = +0.17%

HYD = -0.06%

This led to the final one-month returns I used:

1. VCVSX = +1.22%

2. VWEHX = +0.62%

3. VFIIX = +0.35%

4. VFITX = +0.33%

5. VWAHX = -0.45%.

This compares to the final ranking and one-month returns from PV at EOM:

1. VCVSX = +0.85%

2. VWEHX = +0.62%

3. VFIIX = +0.36%

4. VFITX = +0.29%

5. VWAHX = -0.48%.

So the ranking was correct, and the only fund I missed by a substantial amount was VCVSX. This was because CWB fell to +0.37% by the end of the day. But VCVSX was a clear winner, so no problem.

So my selections were VCVSX and VWEHX, the same as PV ended up making based on EOM data. This doesn't mean I won't miss a selection every once and awhile, but this methodology results in the correct selections most of the time.

This is a learning process, but it gets easier once you do it a few times. The selections for my strategies that use ETFs or longer time-periods are more easily determined.

]]>For illustration purposes, I'm going to show you how I selected the funds for October 2016 for the Vanguard Capital Preservation, VCP, Strategy. Here is the PV link for my version of the VCP Strategy: bit.ly/2d4t7gQ

This is basically the strategy I presented here. The only difference between this version and the one reported in the SA article is the two-month Simple Moving Average, SMA, filter (instead of a 25-day SMA filter). This makes it easy to check if the fund passes or fails its filter. If the current month's price is greater than last month's adjusted price, then it passes.

Here is how I determined the selections were VCVSX and VWEHX by 2 pm EST (and executed the trades) on September 30, 2016. On EOM-1, I went to stockchart.com PerfCharts and determined the one-month returns based on EOM-1 data. I went from August 30 - September 29. This included the dividend distribution on August 31, but not the one on September 30. Here were the one-month returns:

VFITX = +0.47%

VCVSX = +0.45%

VFIIX = +0.36%

VWEHX = +0.27%

VWAHX = -0.39%.

So the numbers were pretty close except for VWAHX, but at that moment the two selections were VFITX and VCVSX. Both had positive returns, so they both passed their 2-month SMA filters.

I decided to wait and see what happened in the market on Friday (September 30) before making a final decision. I used IEF as a proxy for VFITX, CWB as a proxy for VCVSX, VMBS for VFIIX, HYS for VWEHX, and HYD for VWAHX.

I then went to stockcharts.com and found the one-month returns going from August 31 - September 29. The final one-month return will be the return from August 31 to September 29 plus the dividend distribution on September 30 plus the return on September 30. This is the way the one-month returns lined up:

VFITX: 0.43% + 0.13% (distribution) + September 30 return

VCVSX: 0.61% + 0.0% (no distribution) + September 30 return

VFIIX: 0.18% + 0.17% (distribution) + September 30 return

VWEHX: 0.0% + 0.45% (distribution) + September 30 return

VWAHX : -0.68% + 0.29% (distribution) + September 30 return.

For the distributions, I just used the distribution on August 31 (they don't change much month-to-month). I got the numbers from Schwab, but the information is available from many different sources.

When I checked the ETFs @ 1:30 pm EST on Friday, I saw these returns for September 30:

IEF = -0.23%

CWB = +0.61%

VMBS = 0.0%

HYS = +0.17%

HYD = -0.06%

This led to the final one-month returns I used:

1. VCVSX = +1.22%

2. VWEHX = +0.62%

3. VFIIX = +0.35%

4. VFITX = +0.33%

5. VWAHX = -0.45%.

This compares to the final ranking and one-month returns from PV at EOM:

1. VCVSX = +0.85%

2. VWEHX = +0.62%

3. VFIIX = +0.36%

4. VFITX = +0.29%

5. VWAHX = -0.48%.

So the ranking was correct, and the only fund I missed by a substantial amount was VCVSX. This was because CWB fell to +0.37% by the end of the day. But VCVSX was a clear winner, so no problem.

So my selections were VCVSX and VWEHX, the same as PV ended up making based on EOM data. This doesn't mean I won't miss a selection every once and awhile, but this methodology results in the correct selections most of the time.

This is a learning process, but it gets easier once you do it a few times. The selections for my strategies that use ETFs or longer time-periods are more easily determined.

]]>FCTFX = 1.77%

FMSFX = 1.88%

FAGIX = 0.58%.

So the top-ranked fund is FMSFX. FMSFX passes its 3-month SMA, so it is the selection.

For the Schwab version (whose universe is NHMAX, FAGIX and VFIIX), the winner is NHMAX. NHMAX had a 3-month total return of 2.89%.

I started investing in the Schwab version of this strategy at the start of the 4th quarter, 2015. The selection has been NHMAX for each quarter so far. Total return has been 5.5% over the last two quarters. The benchmark bond ETF (AGG) has returned 3.0% over this time, and the Vanguard Total Bond Fund (VBMFX) has returned 3.1%.

]]>FCTFX = 1.77%

FMSFX = 1.88%

FAGIX = 0.58%.

So the top-ranked fund is FMSFX. FMSFX passes its 3-month SMA, so it is the selection.

For the Schwab version (whose universe is NHMAX, FAGIX and VFIIX), the winner is NHMAX. NHMAX had a 3-month total return of 2.89%.

I started investing in the Schwab version of this strategy at the start of the 4th quarter, 2015. The selection has been NHMAX for each quarter so far. Total return has been 5.5% over the last two quarters. The benchmark bond ETF (AGG) has returned 3.0% over this time, and the Vanguard Total Bond Fund (VBMFX) has returned 3.1%.

]]>In this process, it has come to our attention that there are errors in the Yahoo data of some ETFs ands mutual funds that have regular dividend distributions. I have only looked at a few ETFs and mutual funds (the ones we are utilizing in some of the paired strategies), and I have already uncovered errors in three mutual funds and three ETFs.

Here are the errors I have uncovered so far:

1. HYMB: Dividend of $0.2324 on 11/1/2012 is not included in Yahoo data;

2. HYS: Dividend of $0.4300 on 10/31/2012 is not included in Yahoo data;

3. AMHIX: Dividend of $0.056 on 4/30/2009 is not included in Yahoo data, dividend of $0.057 on 6/30/2004 is not included in Yahoo data, and dividend of $0.065 on 10/31/2002 is not included in Yahoo data;

4. TLT: Dividend of $0.2696 on 11/1/2012 is not included in Yahoo data;

5. FAHDX: Dividends on 4/30/2010, 1/30/2004, 11/31/2002 and 7/31/2002 of $0.03727, $0.05195, $0.04775, and $0.04933 respectively are not included in the Yahoo data.

6. VUSTX: Dividend on 4/30/2010 of $0.0396 is not included in Yahoo data.

I'm sure these errors are not just isolated events in Yahoo data. My guess is that there are dividend errors in many, if not most, of the ETFs and mutual funds that have regular dividend distributions.

I thought I would bring this information to the attention of those who use Yahoo adjusted price data on a regular basis. Perhaps someone knows how to get Yahoo to correct these dividend errors.

]]>In this process, it has come to our attention that there are errors in the Yahoo data of some ETFs ands mutual funds that have regular dividend distributions. I have only looked at a few ETFs and mutual funds (the ones we are utilizing in some of the paired strategies), and I have already uncovered errors in three mutual funds and three ETFs.

Here are the errors I have uncovered so far:

1. HYMB: Dividend of $0.2324 on 11/1/2012 is not included in Yahoo data;

2. HYS: Dividend of $0.4300 on 10/31/2012 is not included in Yahoo data;

3. AMHIX: Dividend of $0.056 on 4/30/2009 is not included in Yahoo data, dividend of $0.057 on 6/30/2004 is not included in Yahoo data, and dividend of $0.065 on 10/31/2002 is not included in Yahoo data;

4. TLT: Dividend of $0.2696 on 11/1/2012 is not included in Yahoo data;

5. FAHDX: Dividends on 4/30/2010, 1/30/2004, 11/31/2002 and 7/31/2002 of $0.03727, $0.05195, $0.04775, and $0.04933 respectively are not included in the Yahoo data.

6. VUSTX: Dividend on 4/30/2010 of $0.0396 is not included in Yahoo data.

I'm sure these errors are not just isolated events in Yahoo data. My guess is that there are dividend errors in many, if not most, of the ETFs and mutual funds that have regular dividend distributions.

I thought I would bring this information to the attention of those who use Yahoo adjusted price data on a regular basis. Perhaps someone knows how to get Yahoo to correct these dividend errors.

]]>In TAA strategies, a ranking of ETFs (or mutual funds if you are using mutual funds as proxies) is determined by relative growth over a specified period. For illustrative purposes, let's say we use a 2-month growth period. So the ETF that has the highest percentage growth in a 2-month period would be selected in the TAA strategy. Rather than use actual price data, we use adjusted price data that includes the effects of dividends. The growth is thus based on total return over the 2-month period.

When we backtest to earlier years, we continue to use adjusted price data to determine the ranking of the ETFs. Thus, if the backtesting goes back to January, 2000, we would determine the top-ranked ETF (or mutual fund) by calculating the 2-month growth percentage of each ETF, and selecting the one with the highest growth. Pretty simple.

But there is an accuracy issue that creeps into the data (Yahoo data) if the adjusted price close data becomes much less that the close price data. And the inaccuracy becomes very significant as the adjusted price gets to less than $5.00. The ETF that would have been selected in 2000 (at that time) based on relative 2-month growth may not be the ETF that our backtesting selects. And therein lies the problem with using Yahoo adjusted price data.

The reason this problem occurs is because the Yahoo adjusted price data is rounded off to $0.01. $0.01 is not that important when the price of the ETF/mutual fund is $50.00 (only 0.02%). But $0.01 is very significant when the price (i.e. the adjusted price) is $1.00 (1.0%). When we are calculating relative growth between ETFs in a 2-month period, 1% can greatly affect the selection process.

As time moves away from the present and the effects of dividends are included in Yahoo adjusted prices, the adjusted prices drop and backtesting will have fidelity issues. Many mutual funds have adjusted prices near $1.00 and close prices near $10.00 before 2000. I will give one example of this inaccuracy based on real data. If I look at PREMX before 2000, I find the close price increases from $10.45 to $10.55 over a time period. This is a growth of 0.957%. The Yahoo adjusted price data increases from $1.92 to $1.93 over this same time period. This is a growth of 0.521%. Maybe PREMX would have been selected in the TAA strategy with a growth of 0.957%, and maybe it would not be selected with a growth of 0.521%.

To avoid this error, the adjusted price data needs to carry more significant digits. Instead of $1.92, the adjusted price needs to be something like $1.922. __Relative growth based on adjusted price close data needs to duplicate relative growth based on price close data to maintain backtesting fidelity.__ My guess is that some datasets may be of higher fidelity, but they are not free (or may not be available to the public). And I would also guess that just because you pay for the use of adjusted price data, does not mean you will always get higher fidelity data.

In TAA strategies, a ranking of ETFs (or mutual funds if you are using mutual funds as proxies) is determined by relative growth over a specified period. For illustrative purposes, let's say we use a 2-month growth period. So the ETF that has the highest percentage growth in a 2-month period would be selected in the TAA strategy. Rather than use actual price data, we use adjusted price data that includes the effects of dividends. The growth is thus based on total return over the 2-month period.

When we backtest to earlier years, we continue to use adjusted price data to determine the ranking of the ETFs. Thus, if the backtesting goes back to January, 2000, we would determine the top-ranked ETF (or mutual fund) by calculating the 2-month growth percentage of each ETF, and selecting the one with the highest growth. Pretty simple.

But there is an accuracy issue that creeps into the data (Yahoo data) if the adjusted price close data becomes much less that the close price data. And the inaccuracy becomes very significant as the adjusted price gets to less than $5.00. The ETF that would have been selected in 2000 (at that time) based on relative 2-month growth may not be the ETF that our backtesting selects. And therein lies the problem with using Yahoo adjusted price data.

The reason this problem occurs is because the Yahoo adjusted price data is rounded off to $0.01. $0.01 is not that important when the price of the ETF/mutual fund is $50.00 (only 0.02%). But $0.01 is very significant when the price (i.e. the adjusted price) is $1.00 (1.0%). When we are calculating relative growth between ETFs in a 2-month period, 1% can greatly affect the selection process.

As time moves away from the present and the effects of dividends are included in Yahoo adjusted prices, the adjusted prices drop and backtesting will have fidelity issues. Many mutual funds have adjusted prices near $1.00 and close prices near $10.00 before 2000. I will give one example of this inaccuracy based on real data. If I look at PREMX before 2000, I find the close price increases from $10.45 to $10.55 over a time period. This is a growth of 0.957%. The Yahoo adjusted price data increases from $1.92 to $1.93 over this same time period. This is a growth of 0.521%. Maybe PREMX would have been selected in the TAA strategy with a growth of 0.957%, and maybe it would not be selected with a growth of 0.521%.

To avoid this error, the adjusted price data needs to carry more significant digits. Instead of $1.92, the adjusted price needs to be something like $1.922. __Relative growth based on adjusted price close data needs to duplicate relative growth based on price close data to maintain backtesting fidelity.__ My guess is that some datasets may be of higher fidelity, but they are not free (or may not be available to the public). And I would also guess that just because you pay for the use of adjusted price data, does not mean you will always get higher fidelity data.

The data for the mutual funds actually go back to 1996, so theoretically we should be able to backtest to at least 1997. These mutual funds are proxies for nine ETFs, so the strategy can be traded with mutual funds or ETFs. And the ETFs have almost perfect correlation with the mutual funds from 2011-present.

More information on the QTS can be found here and in the figure below. The CAGR=28.8%, and the maximum drawdown is 19.1%. There are only seven losing quarters in this timeframe. The QTS produces positive returns every year (minimum annual gain of 17.7% in 2004), and beats the S&P 500 Index every year except 2013 (25.6% versus 32.3%).

I decided to try and extend the timeframe of the backtesting. That is the focus of this article. It turns out that stockcharts.com has data on the mutual funds back to January, 1999, and I could run the calculations by hand. I know hand calculations are taboo in this technology age, but I'm not against using them when push comes to shove. So I carefully went through the timeframe of June 30, 1999 - December 31, 2003. I started on June 30, 1999 because I needed rankings of 5-month (i.e. 105 day) returns.

I tried to mimic the calculation used by ETFreplay for the QTS. From stockcharts.com, I obtained 5-month returns and 20-day returns for each mutual fund at the end of each quarter, and ranked the mutual funds in each category. I then found the top-ranked mutual fund by multiplying the weighting (0.5) by the ranking of the mutual fund in each category, and adding the two components together. This is the process that ETFreplay utilizes. The mutual fund with the lowest number was selected as the top-ranked mutual fund in that quarter.

I didn't calculate the 3-month moving average of the top-ranked ETF each quarter, but it appeared that the top-ranked mutual fund would pass the filter test in all quarters.

Anyway, here are the quarterly results:

July-Sept 1999 PREMX Growth = +4.98%

Oct-Dec 1999 PREMX Growth = +19.22%

**1999 (partial) = +25.5%; SPY = +8.0%;** **Difference = 17.5%**

Jan-Mar 2000 VEIEX Growth = -2.40%

Apr-June 2000 PREMX Growth = +2.94%

July-Sept 2000 PREMX Growth = +6.47%

Oct-Dec 2000 VFIIX Growth = +3.71%

**2000 = +11.1%; SPY = -9.8%;** **Difference = 20.9%**

Jan-Mar 2001 PREMX Growth = +4.62%

Apr-June 2001 VFIIX Growth = +1.23%

July-Sept 2001 VGSIX Growth = -2.48%

Oct-Dec 2001 PREMX Growth = +7.44%

**2001 = +11.1%; SPY = -12.1%;** **Difference = 23.2%**

Jan-Mar 2002 VEIEX Growth = +10.39%

Apr-June 2002 VGSIX Growth =+4.80%

July-Sept 2002 VGSIX Growth = -8.45%

Oct-Dec 2002 VFICX Growth = +1.59%

**2002 = +7.6%; SPY = -21.5%;** **Difference = 29.1%**

Jan-Mar 2003 PREMX Growth = +5.85%

Apr-June 2003 PREMX Growth = +13.76%

July-Sept 2003 NAESX Growth = +8.65%

Oct-Dec 2003 VEIEX Growth=+18.85%

**2003 = +55.5%; SPY = +28.2%;** **Difference = 27.3%**

It can be observed that out of 18 quarters in this backtesting, there were only three negative quarters. It should be noted that 2000-2002 were bear equity markets, so the annual growth by the strategy in those years is excellent (considering SPY dropped about 50% in those years).

Please note that the return in 2003 is more than what ETFreplay calculated in 2003 (55.5% versus 44.3%). The reason there is a difference is because NAESX was selected in my calculations while PREMX was selected in the ETFreplay calculation in the third quarter. I have searched for what caused the difference, and at this time, I am not able to resolve why there are different selections. When I go to ETFreplay and look at the 5-month (105 day) and 20 day returns, it seems NAESX should have been selected in this quarter. But it was not; rather PREMX was selected.

In conclusion, if I did not make any mistakes, I have successfully backtested the QTS to mid-1999, and the results look very good. This should give us more confidence in the capability of the QTS.

There is an additional benefit of this exercise. There is always a valid concern in tactical asset allocation strategies that data bias is present. Sometimes the expression "data mining" is used to express this idea. In this particular TAA strategy, the model was developed using data from 2003-present. By extending the backtesting to mid-1999 and calculating good results, I am, in a way, showing that perhaps this strategy is not the result of "data mining."

Please realize you use this information at your own risk. I am only sharing this information for your consideration.

]]>The data for the mutual funds actually go back to 1996, so theoretically we should be able to backtest to at least 1997. These mutual funds are proxies for nine ETFs, so the strategy can be traded with mutual funds or ETFs. And the ETFs have almost perfect correlation with the mutual funds from 2011-present.

More information on the QTS can be found here and in the figure below. The CAGR=28.8%, and the maximum drawdown is 19.1%. There are only seven losing quarters in this timeframe. The QTS produces positive returns every year (minimum annual gain of 17.7% in 2004), and beats the S&P 500 Index every year except 2013 (25.6% versus 32.3%).

I decided to try and extend the timeframe of the backtesting. That is the focus of this article. It turns out that stockcharts.com has data on the mutual funds back to January, 1999, and I could run the calculations by hand. I know hand calculations are taboo in this technology age, but I'm not against using them when push comes to shove. So I carefully went through the timeframe of June 30, 1999 - December 31, 2003. I started on June 30, 1999 because I needed rankings of 5-month (i.e. 105 day) returns.

I tried to mimic the calculation used by ETFreplay for the QTS. From stockcharts.com, I obtained 5-month returns and 20-day returns for each mutual fund at the end of each quarter, and ranked the mutual funds in each category. I then found the top-ranked mutual fund by multiplying the weighting (0.5) by the ranking of the mutual fund in each category, and adding the two components together. This is the process that ETFreplay utilizes. The mutual fund with the lowest number was selected as the top-ranked mutual fund in that quarter.

I didn't calculate the 3-month moving average of the top-ranked ETF each quarter, but it appeared that the top-ranked mutual fund would pass the filter test in all quarters.

Anyway, here are the quarterly results:

July-Sept 1999 PREMX Growth = +4.98%

Oct-Dec 1999 PREMX Growth = +19.22%

**1999 (partial) = +25.5%; SPY = +8.0%;** **Difference = 17.5%**

Jan-Mar 2000 VEIEX Growth = -2.40%

Apr-June 2000 PREMX Growth = +2.94%

July-Sept 2000 PREMX Growth = +6.47%

Oct-Dec 2000 VFIIX Growth = +3.71%

**2000 = +11.1%; SPY = -9.8%;** **Difference = 20.9%**

Jan-Mar 2001 PREMX Growth = +4.62%

Apr-June 2001 VFIIX Growth = +1.23%

July-Sept 2001 VGSIX Growth = -2.48%

Oct-Dec 2001 PREMX Growth = +7.44%

**2001 = +11.1%; SPY = -12.1%;** **Difference = 23.2%**

Jan-Mar 2002 VEIEX Growth = +10.39%

Apr-June 2002 VGSIX Growth =+4.80%

July-Sept 2002 VGSIX Growth = -8.45%

Oct-Dec 2002 VFICX Growth = +1.59%

**2002 = +7.6%; SPY = -21.5%;** **Difference = 29.1%**

Jan-Mar 2003 PREMX Growth = +5.85%

Apr-June 2003 PREMX Growth = +13.76%

July-Sept 2003 NAESX Growth = +8.65%

Oct-Dec 2003 VEIEX Growth=+18.85%

**2003 = +55.5%; SPY = +28.2%;** **Difference = 27.3%**

It can be observed that out of 18 quarters in this backtesting, there were only three negative quarters. It should be noted that 2000-2002 were bear equity markets, so the annual growth by the strategy in those years is excellent (considering SPY dropped about 50% in those years).

Please note that the return in 2003 is more than what ETFreplay calculated in 2003 (55.5% versus 44.3%). The reason there is a difference is because NAESX was selected in my calculations while PREMX was selected in the ETFreplay calculation in the third quarter. I have searched for what caused the difference, and at this time, I am not able to resolve why there are different selections. When I go to ETFreplay and look at the 5-month (105 day) and 20 day returns, it seems NAESX should have been selected in this quarter. But it was not; rather PREMX was selected.

In conclusion, if I did not make any mistakes, I have successfully backtested the QTS to mid-1999, and the results look very good. This should give us more confidence in the capability of the QTS.

There is an additional benefit of this exercise. There is always a valid concern in tactical asset allocation strategies that data bias is present. Sometimes the expression "data mining" is used to express this idea. In this particular TAA strategy, the model was developed using data from 2003-present. By extending the backtesting to mid-1999 and calculating good results, I am, in a way, showing that perhaps this strategy is not the result of "data mining."

Please realize you use this information at your own risk. I am only sharing this information for your consideration.

]]>