# Error-Adjusted Momentum

In the last post I introduced a method to normalize returns using the VIX to improve upon a standard momentum or trend-following strategy. There are many possible extensions of this idea, and I would encourage readers to look at one of the comments in the previous post which may inspire some new ideas. The motivation for this method was to provide an alternative approach that is more broadly applicable to other assets than a VIX-based strategy (which is more appropriate for equities). This method uses the standard error of the mean to adjust returns instead of using the VIX, which is a proxy for market noise. The logic is that returns should be weighted more when predictability is high, and conversely weighted less when predictability is low. In this case, the error-adjusted moving average will hopefully be more robust to market noise than a standard moving average. To calculate the standard error, I used the 10-day average return to generate a forecast, and then took the 10-day mean absolute error of the forecast. To normalize returns, I divide each return by this standard error estimate prior to taking a 200-day average of the re-scaled returns. The rules for the ER-MOM strategy are the same as in the last post (although poorly articulated):

Go LONG when the Error-Adjusted Momentum is > 0, Go to CASH if the Error-Adjusted Momentum is < 0

Here is how this strategy compares to both the VIX-adjusted strategy and the other two baseline strategies:

The error-adjusted momentum strategy has the best returns and risk-adjusted returns- edging out the previous method that used the VIX. In either case, both adjusted momentum strategies performed better than their standard counterparts. One concept to note is that the benefit or edge of the adjusted momentum strategies tends to be more significant at longer trend-following lookbacks. This makes sense because there are likely to be a wider range of variance regimes throughout a long stretch of time than over a shorter lookback. Adjusting for these different variance regimes gives a clearer picture of the long-term trend. Using the historical standard deviation is also a viable alternative to either using the standard error or the VIX, and there are a lot of other ways to measure variability/noise that can be used as well.

Nice post! I just tried to use only night returns instead of daily ones in standard error momentum formula to forecast the nights: the equity curve end at 6,61 just a bit below Vix momentum one. 4332 total occurences, 57,59 % winnings with a 1,29 profit factor. I think much happens during nights as usual, anyway you built a solid filter. This is my blog http://nightlypatterns.wordpress.com

Hi Marco, thank you. That is a very interesting finding and I will have to look into that and also your blog.

best

david

I’m only a beginner compared to you and others but things keep working and I manage to keep my equity curve steady. I’m looking for any possible advice. Have a look at my research area too. I need different ideas on some difficult money management tasks. If you can help me adding to your blogroll, I would be grateful too. Thank you for replying!

Best

Marco

Nice series on adjusted momentum. Regarding the ER-MOM, are you using “standard” statistical analysis – ie – are you taking the most recent past 10 days average, calculating the Standard Error on that, and applying that SE to divide the log return on the most recent day? The use of the word “forecast” is throwing me off – there is no look-forward bias I assume…

I’m looking forward to coding and running this. It seems counter-intuitive. I would think that as volatility is increasing and the daily returns are turning negative, that reducing the negative value using the volatility divisor would keep one in the market longer than one wants to be whilst all heck is breaking loose.

Thanks!

Good point! I think you may want to divide the price by the SE and not the returns.

hi Cm, thank you, no look forward bias because you are using the mean absolute error of the 10-day average return as the forecast ie abs(10-day avg return- next day return) and then finding the 10-day average of those values starting with the most recent error being yesterday’s 10-day average return versus today’s return.

the error function de-emphasizes returns when noise is high since it is in the divisor and emphasizes them when noise is low (predictability is high).

hope that helps

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david

Hi david, interesting post. I’m a little lost on the method. Why do you do the standard error on the mean but not on the last ten close instead?

hi Armand thank you. not sure what you mean?

ROC dominates ER-MOM on ES futures that only exist since 1997, I also added commissions and slippage

Hi David,

Same as Antonio, a clear explanation would be extremely useful.

Tried to make an XL with it but results are really not in line with your table.

Could you spend 5 minutes making a google doc / xl file ?

I think it would make the post far more useful.

Thanks for the hard work !

One more question, I was trying to use this corrected momentum to compare 2 stocks and select the most performing one.

Do you think it’s a valid idea ? (results are not that good in my test 😉 )

Tx for ideas !

Unfortunately, returns are not that great when you backtest these strategies from the sixties. ER-MOM underperforms buy-and-hold and only MA200 outperforms b&h slightly. MA2000 does reduce vol significantly.

hi David, that is not surprising- especially since pre 1980 the market had a pronounced follow through effect which would favor using close/ average versus looking at velocity that is standardized by error (and hence lagging). however, if you look at the concept and also various derivatives you will be able to see how this can be extended into something more useful.

best

david

Hi David,

Would you (or anyone else reading this) know how well this works with shorter/longer time-periods? Is 200 days the sweet spot or was it just an arbitrary number you chose?