John Ehlers' MAMA and FRAMA indicators

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John Ehlers' MAMA and FRAMA indicators

Last comment by - January 2022

John Ehlers' MAMA and FRAMA indicators

John Ehlers' MAMA and FRAMA moving averages use advanced math to incorporate cyclical patterns in the market, reducing false trading signals.

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John Ehlers' MAMA and FRAMA indicators

JP B | December 2015

Here is the MAMA and F(R)AMA moving averages by John Ehlers.

Most technical analysis is quite simple but John Ehlers takes it one step further and incorporates fractals and sine waves into his analysis. The mathematics in his technical analysis indicators is really some of the most advanced that you can find. He releases most of his findings publicly on his website here. Some of his papers are really a must-read for those who want to take their technical analysis to the next level.

I wanted to backtest some of his strategies so I've converted his EasyLanguage code into C#.

In this share, I present to you the MAMA and FRAMA moving averages. These moving averages follow the logic of most moving averages, except for the fact that they take the cyclical pattern of the market into account. Therefore, false trading signals (when there is no trend) are less likely to occur. If anything, these averages are quite interesting to study. You can find the original MAMA paper here, and the original FRAMA paper here.

With moving averages, there is always a common problem: they work very well when the market is trending. When the market is neutral, however, they fail. John Ehlers decided to tackle this problem and decompose the market into a cyclical regime and a trending regime using an Empirical Mode Decomposition. The intuition behind this decomposition is that when the market is cyclical, you could use his Sine Wave Indicator. When the market is trending, you could use a moving average-based indicator, like the MAMA and FRAMA moving averages. Note that you can play with the parameters to change the sensitivity of the indicators.

I hope you like it. Happy coding.

Author

JP B

December 2015

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9 people upvoted this

Jared Broad INVESTOR

QuantConnect | December 2015

Wow pretty epic series of posts @JPB! Thank you for sharing! If you're interested please submit the Sine wave to github as an indicator and we'll build it into the LEAN Engine :)

The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by QuantConnect. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. QuantConnect makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances. All investments involve risk, including loss of principal. You should consult with an investment professional before making any investment decisions.

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JP B INVESTOR

December 2015

@Jared Broad Thank you :) I would enjoy seeing it being added to LEAN, but I'm not that familiar with github and the format for submitting new indicators. Is there some sort of guideline/ example I can follow?

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1 person upvoted this

Jared Broad INVESTOR

QuantConnect | December 2015

No worries! Its great seeing high quality posts like this, showcasing a powerful indicator. We wrote a contributor guide here which steps you through working with github, and here's an example of the moving average indicator. There was also this quick tutorial on how to create an indicator (https://lean.quantconnect.com/docs#topic14.html)

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Eugeny Kaminsky INVESTOR

December 2015

Really cool software. Do you test on Forex symbols ? Where is better results ? Which symbols is most profitable for trading?

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Jared Broad INVESTOR

QuantConnect | December 2015

I had the same thought @Eugeny - FX symbols are more cyclical so potentially this indicator would work better. I wonder if the flat period in 2001 could be avoided by using History to warm up the indicators first.

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Eugeny Kaminsky INVESTOR

December 2015

I try use another MAMA & FAMA indicators for manual trading on metatrader platform. And they working not very well. Test on EUR/USD. Can you place here rules for opening and closing position ? May be I can translate this software for metatrader platform.

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Timothy Comisky INVESTOR

January 2016

JP, Very intrigued! Have you done any comparisons between MAMA & FRAMA vs fast EMA & Slow EMA yourself? Would love some screenshots if you have them. I am also very curious as to how well these work with forex given the nature of forex. Look forward to messing around with it! - Having this built into QC would be sweet! Eugeny, The signals woud still be the same- buy when Mama crosses up through FRAMA and sell/short when MAMA crosses down through FRAMA. Have you tried adjusting the M & F and or the time frame?

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JP B INVESTOR

January 2016

@Timothy Comisky I'm afraid such comparisons are not completely objective due to the differences between the MAMA & FRAMA framework and the normal EMA strategy. This because any design decisions will largely impact the strategies' outcomes. What you could do, however, is try to find the most profitable (general) setup for both frameworks and then test them over the same period for the same symbol. This could yield a decent comparison.

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JP B INVESTOR

January 2016

As a side note: Note that MAMA and FRAMA attack the neutrality problem in a different way. Much like the SMA and EMA attack the smoothing problem in a different way. In the algorithm posted above, I combined MAMA and FRAMA. However, you can also duplicate the indicators themselves with different parameters and make a strategy out of that. Much like a SMA(20) and SMA(50) cross-over strategy. So you can create strategies purely based on MAMA or purely based on FRAMA or a combination of the two. Happy coding ;)

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JP B INVESTOR

January 2016

Don't forget to check out my demonstration too!

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1 person upvoted this

James Smith INVESTOR

March 2016

I've made some minor adaptations of this algorithm and have got some very interesting results. I can't admit to understanding a great deal about the theory behind this, but regardless, the behavior of it is fascinating and quite unlike anything else. Presumably this has something to do with the signal filters: the win/loss rate is noticeably superior to other moving averages. Thanks for sharing this.

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JP B INVESTOR

March 2016

@James Smith Glad to hear that. There are some small bugs in this version of the algorithm. You can find the updated version at the top of this discussion. The first algorithm in that thread has been corrected for the bugs. With regards to the behaviour: it remains quite complex indeed. Mostly because optimising with respect to cycle lengths is not so intuitive.

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James Smith INVESTOR

March 2016

Yes, I'm glad I'm not the only one to notice such a high quality contribution. I had to tweak some parameters on the original version before putting it into production, so will look forward to further improvements as a result of the fixes. I've also started backtesting an adaptation of your Sine Wave indicator. Will give you an idea of the results if you're interested.

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JP B INVESTOR

March 2016

@James Smith Thank you for the compliment. Sure, I'm always interested in backtesting results! My backtesting results with the Sine Wave indicator were quite positive only for periods in which stocks actually exhibit cycles. By construction, the Sine Wave indicator doesn't work well in trends. For trends, the MAMA/FRAMA indicators are very useful. Most difficult part is combining the two: trading the Sine Wave indicator in neutral times and the MAMA/FRAMA indicators in trends. Question remains when to switch between the two. The Empirical Mode Decomposition is supposed to help with this but I wasn't able to get it to work properly.

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.ekz. INVESTOR

ThePrinters.io | January 2022

This is quite interesting --anyone out there want to take a stab at converting these to Python, as standalone indicators?

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.ekz. INVESTOR

ThePrinters.io | January 2022

Looks like FRAMA already exists. Will start there…

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HughStryker INVESTOR

August 2020

Thanks for the update!

I'm happy that Jovad included an options straddle, as I was planning to replace VXX in the Dragon portfolio with a rolling straddle on SPY to serve as the long vol component. As I haven't used options in QC before, Jovad's algo is very useful as a starting point.

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Sairaj Patil INVESTOR

August 2020

This is amazing Derek Melchin

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Jovad Uribe INVESTOR

August 2020

Hi everyone,

This week Derek built a strategy he heard on episode #10 of the Better System Trader podcast. The guest, Perry Kaufman, explained the strategy idea came from George Douglas Taylor in the '50s, but Derek reversed the strategy rules. The strategy trades IWM and QQQ, and the backtest can be viewed here. It generates a 0.845 Sharpe ratio and a drawdown of 2.7% when backtested over the last several years.

Adding this strategy to the InternFund algorithm increases the diversification as we do not currently trade IWM or QQQ. Although the historical Sharpe ratio decreases slightly from 1.931 to 1.902, the compounding annual return increases from 6.845% to 7.019%, and the max drawdown decreases from 3.8% to 3.3%. With this new deployment, our backtest has a max drawdown of just $1,379. This deployment (with an increased max drawdown limit) is attached below.

Shile also built a Risk Parity strategy inspired by this article. During his research, he noticed that the drawdown was a whopping 43.4%, outlined in this backtest. To reduce this drawdown, the effects of risk parity were increased by shorting TBT, a -2x 20+ Years ETF, which gives us a positively leveraged position. Then, the dip of SPXL was bought, then sold using the Risk Management inspired by this Strategy Library Addition. See the results of the strategy here.

Previously, Ernest mentioned that our 60:40 strategy would exceed a 100% allocation ratio. We added an update to this strategy ensuring that it does not exceed this ratio. The line we updated is:

quantity = self.CalculateOrderQuantity(ticker, weight * self.SF_AR / sum(self.weight_by_ticker.values()))

Tamim Fund pointed out that our Fibonacci Option Straddle was primarily purchasing Apple. We converted the strategy to the algorithm framework and added a dynamic universe selection model to remove look-ahead bias. To further clarify the strategy's logic, if the market sentiment of a stock is down, the bid price for the call option will decrease and fall below the retracement level, causing a sell. If market sentiment is up, then the bid price may cross above the retracement, causing a buy. Many TA traders use this strategy, but their execution may take some time. The strategy attempts to enter the same position but quicker. I have attached the backtest here. As we cannot implement this in the InternFund, we will not continue with it.

As for the InternFund's performance, here is a screenshot of our latest track record.

This week our strategy lost 0.099276% of its value while SPY gained ~1.8%. Although this is a small setback, we aim to improve our algorithms alpha of 0.067.

Our backtest produces a whopping Treynor ratio of 2.298. It is no surprise that this ratio is high because the current risk-free rate (10YR Treasury Rate) is at a low 0.69%, and our beta of 0.031 is also low. However, this is one indication that our algorithm is a worthwhile investment.

Thanks for tuning in for this week's update. Constructive criticism and feedback help us build better strategies for the fund. Stay tuned for more updates!

Cheers,

Jovad Uribe

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3 people upvoted this

Shile Wen INVESTOR

UW CFRM | August 2020

Hi Everyone!

We are planning on continuing the InternFund past summer!

This week, we are allocating 5% of our portfolio to Taylor Robertson’s post on using Leveraged ETFs. This led to a .4% decrease in drawdown as well as a 1.7% increase in the CAGR. Furthermore, our strategy is now very close to a Sharpe of 2.0, sitting at 1.98. After that, we increased the ratios of our existing strategies to take advantage of the cheap leverage offered by IB, and the new deployment algorithm is attached below.In addition, I also implemented a very simple seasonal strategy described in this article, and the results can be seen here. The high drawdown of 11.4% did not justify the returns of only 4.356%, so this strategy will not be making it into our InternFund algorithm.

Derek implemented an ETF rotation strategy that was sourced from RotationInvest. During each monthly rebalance, it calculates the trailing 3-month Sharpe ratio of SPY, EFA, and GLD. For the top-ranking ETF, it'll invest in it only if it's trading above its 150-day simple moving average. Otherwise, it allocates 100% of the portfolio to a bond ETF (TLT).
When backtested since 2015, this strategy generates a 1.218 Sharpe ratio and an annual standard deviation of 0.118. By comparison, the S&P 500 produces a 0.712 Sharpe ratio and 0.185 annual standard deviation over the same period. See the backtest results here. We will add this strategy to the deployment algorithm next week.

Furthermore, Jovad implemented the Golden Butterfly Portfolio from this article in this backtest. After a few alterations, he achieved a relatively low drawdown at 4.4% and a CAGR of 3.9%, and the updated backtest can be found here. Unfortunately, when added to our algorithm, the drawdown increases while the CAGR decreases (backtest), so it will not be making it into our live deployment.Our updated track record can be seen here:

And we are only $1 away from a new equity high!

Best Regards,
Shile Wen

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HughStryker INVESTOR

August 2020

Thanks for the update, Shile. What the InternFund is doing is very cool and I'm learning a lot.

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Derek Melchin INVESTOR

QuantConnect | August 2020

Week 7: A Little Turbulence

Hi everyone,

The InternFund had a sharp increase in volatility this week. However, we are still within our allowed max drawdown of $1000. Here's an image of our live track record over the last 7 weeks.

This week, we built a few more strategies with the hope of adding more to the InternFund algorithm.

Shile worked on a trend following strategy that measured the strength of the trend using an Ordinary Least Squares (OLS) model. When the past 50 days of close data have an r2 > .7, and the (current price - the average of the absolute values of the residuals) is at least the predicted value from the OLS model, we hold SPY, else, we liquidate our position. This model only had a Sharpe of .475 with a large drawdown of 34.2%, so this strategy will not be making it into the InternFund. The backtest can be found here.

I built a strategy that was inspired by Scott Andrews (aka "The Gap Guy"). Each market open, it fits a linear regression model using overnight gaps as the independent variable and the open-to-close returns as the dependent variable. It trains the model using the previous 10 weeks of data, using only weekdays that match the current trading day. After the model is trained, it predicts the direction of the current day's intraday return given the overnight gap and places its trade. The strategy achieves a 0.488 Sharpe ratio when backtested since 2015. See the backtest for reference. Since this strategy underperforms our benchmark, we didn't integrate it into the InternFund algorithm.

I also built a strategy I sourced from InvestiQuant that takes advantage of the long-bias in traders after a bull market breakout. Whenever the SPY has a multi-month breakout during a bull market rally but then gaps down into the next open, the strategy longs from the open until 15 minutes before the close. Backtesting the strategy since 2015 generates a 0.991 Sharpe ratio, outperforming the buy-and-hold Sharpe ratio of 0.742. See the backtest results here. After integrating this strategy into the InternFund algorithm, the Sharpe ratio of the algorithm backtest increases from 2.103 to 2.161. See the attached backtest for a copy of our latest deployment (with an extended drawdown limit).

In regards to the ETF rotation strategy we published last week, there was actually a bug in it. Line 71 should have read

if data[top_symbol].Price >= sma:

instead of

if data[symbol].Price >= sma:

After fixing this, the strategy underperforms the SPY, so we did not add it to our live deployment.

Thanks for tuning in for our weekly update!

Best,
Derek Melchin

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Mark Reeve INVESTOR

August 2020

Hi guys,

I am wondering is it possible to combine several strategies like this using the algorithm framework?

Is there a reason you chose to avoid using the Algorithm Framework, other than simplicity?

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1 person upvoted this

Shile Wen INVESTOR

UW CFRM | September 2020

Hi Mark,

It would be possible to combine these strategies using the Algorithmic Framework, however, we chose to stick with the classic algorithm because it is easier to account for multiple strategies.

From my experience, an algorithm developed using the Algorithmic Framework is best suited to a single signal type, however, our algorithm is a Frankenstein’s monster of various strategies that aren’t related. If we were to divide up our algorithm strategies into separate projects, then it would totally be viable for us to use the Algorithmic Framework on the strategies individually.

Best,
Shile Wen

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3 people upvoted this

Samuel Schoening INVESTOR

September 2020

You guys have helped me a lot so I just wanted to reach out and make sure you know that the orders for VXX may not be executing as you go back in history. This is because the price was over 30,000 in 2010 due to countless splits. Same goes for UVXY. The data is not adjusted so the order will not fill. That is why I just trade with 1 or 100 billion dollars in my backtests lol. With that said, this is very compelling research and do please keep up the good work!

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1 person upvoted this

Josh M INVESTOR

October 2020

It has been a few months -- any live trading update from the intern team?

Cool project and great work!

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Zicai Feng INVESTOR

May 2021

hey interns, your self.max_dd is a fixed amount, should change it to a ratio as a % of the portfolio value. Because as your portfolio gets bigger due to profitable trades, a fixed amount that was set during a smaller AUM will just terminate your strategy randomly. I am sure Jared would understand and let you risk a fixed % of AUM rather than a fixed dollar amount with a fluctuating n growing AUM

Keep up the good work and build those RenTech libraries!

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Derek Melchin INVESTOR

QuantConnect | June 2021

Hi Zicai,

Thank you. We will adjust the drawdown limit if the InternFund is launched again this summer.

Best,
Derek Melchin

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Zicai Feng INVESTOR

June 2021

Hope it gets launched again :). Btw, similarly, your stop loss limit in your tesla example is a fixed amount. Similar reason to above, it should be a % number not a fixed $ amount as tesla price is all over the place depending on the price of dogecoins

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