The Adaptive Moving Average (AMA) modifies the amount of smoothing it applies to data in an attempt to adjust to the changing needs of a dynamic market. It makes these adjustments based on the readings from a Volatility Index (VI). Any measure of volatility or trend strength can be used, however in this article we will focus on how the AMA performs using the Standard Deviation Ratio (SDR).
The SDR-AMA requires five user selected inputs: SD1, SD2, a High – Low smoothing period range for the AMA and a power that Alpha is raised to. With five variables there are thousands of possible combinations so we had to make some educated assumptions based on our previous tests to narrow the choices down.
First of all we have seen that nearly all of the performance characteristics exhibited by a VI have rung true in tests on both a VMA and an AMA. When we tested the SDR in a VMA we found that it was best if SD1 was around half of SD2. We also selected SD lengths that corresponded with the approximate number of trading days in standard calendar periods: 10 days = two weeks, 20 days = 1 month, 40 days = 2 months, 80 days = ⅓ year, 126 days = ½ year and there are 252 trading days in an average year:
SD1/SD2 = 10/20, 40/80, 80/126, 126/252
Second we have seen that a moving average range produces the best results when it can move to as little as 4 periods or less, therefore we will test:
AMA Actual Fast Moving Average (FN) = 1, 4
With the slow moving average we have consistently seen 300 produce the best results while changing this setting hasn’t usually made a big impact. However we still ran tests through several settings:
AMA Actual Slow Moving Average (SN) = 100, 150, 200, 250, 300
For the Alpha Power we also tested several variables:
Alpha Power (P) = 0.5, 0.75, 1, 1.5, 2, 2.5
We tested trades going Long, using Daily data, taking End Of Day (EOD) signals~ analyzing several combinations of the above settings.
Now each time the Alpha Power was adjusted the SC and FC had to be modified to account for the change but the actual FN and SN stayed the same.
For instance a SC – FC range of 1 – 24 with alpha ^ 2 has an actual FN – SN range of about 1 – 300 due to the effect of squaring alpha. Here is a table that shows the SC – FC ranges used so that the FN – SN ranges stayed constant regardless of ‘P’:
If that doesn’t make a lot of sense then please read our explanation of the Adaptive Moving Average. A total of 240 different averages were tested and each one was run through 300 years of data across 16 different global indexes (details here).
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Standard Deviation Ratio Adaptive Moving Average – Test Array
Above we have charted the annualized returns achieved from each SDR with Alpha raised to different powers along the X axis. The chart on the left shows the results when the FN = 1 and SN = 300 while on the right FN = 4 and SN = 300. Clearly extending the FC to 4 had a positive effect and the best returns were achieved with a SDR of 126/252 where Alpha was raised to the power of 2.
Best Standard Deviation Ratio Adaptive Moving Average
Included on the above chart is the performance of the 126 Day FRAMA, EOD 4, 300 Long becuase so far this has been the best performing Moving Average. The 126 Day SDR-AMA, EOD 2, 24 Long ^ 2 performed OK but could not best the FRAMA and has a much shorter average trade duration; just 8 days compared to 14 for the FRAMA. For these reasons the FRAMA remains our preferred moving average and the SDR-AMA does not warrant further testing. But lets take a quick look under the hood:
126 Day SDR-AMA, EOD 2, 24 ^ 2 – Smoothing Period Distribution
The smoothing distribution of the 126 Day SDR-AMA, EOD 2, 24 ^ 2 is much more localised around the 4 – 20 range than the FRAMA which explains the shorter trade duration. The FRAMA on the other hand allows the average to move much slower at times, presumably when the trend is weak.
126 Day SDR-AMA 2, 24 ^ 2 – Alpha Comparison
To get an idea of the readings that created these results we charted a section of the alpha for the 126 Day SDR-AMA 2, 24 ^ 2 and compared it to the best performing FRAMA and the best SDR-VMA to see if there were any similarities that would reveal what makes a good volatility index:.
Remember higher alpha readings result in a faster average. The SDR-AMA and the SDR-VMA are clearly both much faster than the FRAMA. However the SDR-AMA does slightly outperform the SDR-VMA and notice that the SDR-AMA’s Alpha moves through a greater range from high to low. This greater ‘adaptability’ is likely to have been a key factor in its better performance.
Excel Spreadsheet
Want to use this indicator? Get a free Excel spreadsheet at the flowing link under Downloads – Technical Indicators: Adaptive Moving Average (AMA). It will automatically adjust to your choice of many different VIs including the Standard Deviation Ratio used in this article.
For more in this series see – Technical Indicator Fight for Supremacy
- ~ An entry signal to go long for each average tested was generated with a close above that average and an exit signal was generated on each close below that moving average. No interest was earned while in cash and no allowance has been made for transaction costs or slippage. Trades were tested using End Of Day (EOD) signals on Daily data. Eg. Daily data with EOD signals would require the Daily price to close above a Daily Moving Average to open a long and to close below that Average to close the position.
- We used the average annualized return of the 16 markets during the testing period. The data used for these tests is included in the results spreadsheet and more details about our methodology can be found here.