A self optimising moving average

Different markets and different timeframes will need different moving average periods. This article will show a way to construct a self optimising moving average, one which automatically adjusts its period to the charted market and timeframe.

Reading a simple moving average

I would like to start this new indicator with some thoughts about how to define how “good” a moving average is. Usually my (simplified) standard interpretation of a moving average is, that when it rises and the market trades above the average, I am in bullish mode and would expect the market to rise over the next  bars. This very simple interpretation of a moving average can be quantified, meaning that I can calculate a measure to judge if my assumption is any good. To do so, I just count the number of bars which have been rising and falling while (initial condition) the market has been above the average and the average has been rising. This will give me a number, and let’s say on 52% of the bars in history when the initial condition was met, the market rose on the day after. As the chance is better than 50%, I would conclude that the analysed average is a useful one.

Self optimising moving average

Instead of just analysing one specific moving average length one could calculate the metrics for all moving averages. The sample implementation (code at the end of the article) will calculate all moving averages within a given parameter range (eg. 5 bars to 200 bars), calculate the winning percentage (rising bars) on the next bar, and then pick the best performing period length.

self optimising moving average

self optimising moving average

The moving average on the chart above constantly changes its period to the period, which would have given the best indication in history. As the original criteria has been to maximise the percentage of up-moving bars when the market is above the average and the average is rising, the shown moving average will always be the one which will give you the highest probability of a rising bar (next bar) if the average is rising and the market is trading above it. These periods are shown in green. Otherwise, if the criteria is not met or the winning percentage is below 50 (=no average has a better than 50:50 prediction capability), the indicator is colour coded red.

Advantage of the perfect average

Beside plotting the best moving average, one could also plot the statistics of the best moving average. This would be the percentage of winning bars when the original criteria is met.

best average statistics

best average statistics

The chart above shows a comparison of 3 different timeframes. A daily, hourly and 5 minute chart. The indicator below shows the edge the best moving average would give when trying to predict rising bars. A level of 5 would mean that you got a 55% chance for a rising bar when selecting the best performing period for your moving average and the average is rising and the market trades above it.

Using the self adjusting average this way, you can easily see in which timeframes or markets a moving average prediction model would be useful. On the chart above you obviously do not want to use this simple indicator interpretation on a 5 minutes chart. If the indicator is colour coded in red, either the market is not trading above the best average, the best average is not rising, or it would give no edge when trying to predict the next bars move.

Stability of results

As the indicator is based on a statistic over a given period of time, we have to think about stability and outliners. To remove outliner results, the statistics are smoothed. Instead of taking the winning percentage for a given average length, also the 2 results to the left and right are taken into account. The indicator can also plot these smoothed results, so you can see the edge the average prediction would offer with different periods.

On the chart below, the magenta histogram on the right shows the historic edge (smoothed) over the tested periods for the averages. From length 7 to length 148 all results would have been positive (a better than 50:50 chance for a rising bar), the best result was obtained with a period of 31. Observe this with different lengths of history, and you will get a good guess if your market is the right one for this kind of analysis. If the edge is not above 50% with a lot of periods, then this prediction will hardly be useful.

best period average complete

best period average complete

Link to indicator source code

Find the indicator code over here. The code is written in Equilla, the scripting language of the Tradesignal software.

The indicator uses all available data on the chart to calculate the statistics. You can set the range of periods you want to analyse. If you would like to backtest the indicator (go long when green) then just add the line below at the end of the code (used as strategy)

best period average backtest code

best period average backtest code

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Z-Score Factor Portfolio Weighting

Technical Indicators can be used for timing and weighting strategies. Using momentum as an example, you could go long if the momentum turns positive, or you could dimension the weight of your position depending on the level of momentum. Applied on a portfolio of assets, this would be called factor investing. This article will show you a way to weight your portfolio using factors. Continue reading

Profit from large daily moves

Whenever the market shows an exceptional day ranges it is time to take bite. See how you can profit from large daily market moves.

Open-Close Range

When looking at any chart, you will surely notice that the large candles tend to close near the high or low. This is due to herding. Once the market is moving significantly, everyone hops on and the large move becomes even larger. This is true for daily, weekly and intraday candles.

The chart shows an indicator which plots the daily move. Every opening is set to zero and the absolute move of the day is drawn. Around these normalised candles a long term 2 standard deviation volatility band is drawn.  Right now the 2 standard deviation volatility for SPX is about +/- 46 points.

Take a bite before the market closes

As you can see this +/-46 point barrier above/below the opening of the day is a wonderful entry point. If you enter long 46 points above the opening and go short 46 points below the opening nearly all entries would have lead to a profitable trade. To get an even higher probability of success you can volume as a confirmation. Large moves must also show high volume. The exit is done at the end of the session. This analysis does not give any indication for the next days move. So be fast, take your bite and go home with a small profit and no overnight position.

No free lunch

On the chart it looks easy, but be careful. As an example the last bar shown on the chart first crossed the band to the downside, reversed and crossed above the upper band. So you will need to use a trailing stop to lock in profits and avoid to take the full -46 to +46 points trade as a loss!

 

 

 

 

How to detect unwanted curve fitting during backtest

Whenever you develop an algorithmic trading strategy, unwanted curve fitting is one of the most dangerous hazards. It will lead to substantial losses in real time trading. This article will show you some ways to detect if the performance of your algorithmic trading strategy is based on curve fitting.

Curve fitting – what is it?

Every algorithmic trading strategy will have some parameters. There is no way around it. You will have to decide what length your indicators have, you will have to specify a specific amount for your stop loss or profit target. Beside the actual rules of your strategy the chosen parameters will usually significantly influence the back-test performance of your strategy. And with any parameter you add the danger of curve fitting rises significantly. Continue reading

The Edge of Technical Indicators

Classical technical indicators like RSI and Stochastic are commonly used to build algorithmic trading strategies.  But do these indicators really give you an edge in your market? Are they able to define the times when you want to be invested? This article will show you a way to quantify and compare the edge of technical indicators. Knowing the edge of the indicator makes it an easy task to select the right indicator for your market.

The edge of an indicator

Any technical indicator, let it be RSI, moving averages or jobless claims, has got a primary goal. It should signal if it is a wise idea to be invested or not. If this indicator signal has any value, on the next day the market should have a higher return than it has on average. Otherwise  the usage of no indicator and a buy and hold investing approach would be the best solution.

The edge of an indicator in investing consists of two legs.

  1. the quality of the signal
  2. the number of occurrences

Continue reading

S&P500 – when to be invested

The stock market shows some astonishingly stable date based patterns. Using a performance heat map of the S&P500 index, these patterns are easily found.

Date based performance

The chart below shows the profit factor of a long only strategy investing in the S&P500. Green is good, red is bad. The strategy is strictly date based. It always buys and sells on specific days of the month. Continue reading

Noisy Data strategy testing

Adding some random noise to historic market data can be a great way to test the stability of your trading strategy. A stable strategy will show similar profits with noisy and original data. If the noise has a great impact on your results, the strategy might be over fitted to the actual historic data.

Synthetic market data?

Generating completely synthetic market data to test algorithmic trading strategies is a dangerous endeavour.  You easily lose significant properties like classic chart patterns or the trend properties of your market. Continue reading

Dollar Cost Averaging Investment Strategy – success based on luck?

This article is about the dollar cost averaging investment strategy and the influence of luck in it.

The Dollar Cost Averaging Investment Strategy

To invest parts of your income into financial markets has been a profitable approach, especially in times when bond yields are low. One approach to do so is the dollar cost averaging investment strategy. Continue reading

Overnight vs Daytime Performance & Volatility

Analysing the market performance of the day session vs. the overnight movement reveals some interesting facts.

Daytime vs. Overnight Performance

The chart below gives a visual impression on where the performance of the SPY ETF is coming from.

The grey line represents a simple buy and hold approach. The green line shows the performance if you would have held SPY only during daytime, closing out in the evening and re-opening the position in the morning. Continue reading

Technical vs. Quantitative Analysis

“The stock market is never obvious. It is designed to fool most of the people, most of the time” Jesse Livermore

Technical Analysis

Technical analysis is a form of market analysis based on historic price patterns. The basic assumption of technical analysis is, that human behaviour does not change over time, and thus similar historic market behaviour will lead to similar future behaviour. Technical analysis is a predictive form of analysis, a technical analyst will try to estimate what the market might most probably do over the next period of time. Continue reading

An Algorithmic Stock Picking Portfolio

In this article I will discuss a simple algorithmic stock picking approach based on momentum and volatility. The goal will be to generate excess returns versus a capital weighted stock basket.

Alpha and Beta

Investing in assets with low volatility and high return is on a lot of peoples wish list. Portfolios which archive this goal will have a high Sharpe ratio and in the end get the investors money. By reverse engineering this criteria, one can find promising stocks to invest in and out perform a given capital weighted index.

Alpha and beta are measures to describe an assets performance relative to its index. Both are used in the CAPM – capital asset pricing model.

Alpha is a measure for an assets excess return compared to an index. Continue reading

Bollingerband: The search for volatility

Usually it makes no sense to fight against normal distribution. But there are setups which have got a high probability of unexpected behaviour.  Volatility can be the key to future market movements.

Bollinger bands width percentile

Bollinger Bands are a great tool to describe market volatility. And my favourite tool to measure the width of Bollinger Bands is Bollinger percentile.

Like the IV percentile indicator my Bollinger percentile indicator is a probabilistic indicator. It gives the probability of Bollinger Bands having a narrower upper band – lower band range than currently given. Continue reading

Scanning for Support and Resistance Probabilities

I have been in search for a signal I could use for a short vertical spread or naked short option strategy. So my main concern has been to find a level, which will most probably not be penetrated over the next few bars.

This is what I came up with.

Algorithmic RSI Support and Resistance Levels

We are all familiar with oscillators like the RSI indicator. It gives an idea if the market is oversold or overbought. Continue reading

A graphical approach to indicator testing

A graphical approach to indicator testing

The first step in algorithmic strategy design usually is to find some indicators which give you an edge and tell you something about tomorrow’s market behaviour. You could use a lot of statistics to describe this edge, but I like to take a graphical approach in indicator testing first, and only later on worry about the maths and statistics.

Scatter Charts

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Using Autocorrelation for phase detection

Autocorrelation is the correlation of the market with a delayed copy of itself. Usually calculated for a one day time-shift, it is a valuable indicator of the trendiness of the market.

If today is up and tomorrow is also up this would constitute a positive autocorrelation. If tomorrows market move is always in the opposite of today’s direction, the autocorrelation would be negative.

Autocorrelation and trendiness of markets

If autocorrelation is high it just means that yesterdays market direction is basically today’s market direction. And if the market has got the same direction every day we can call it a trend. The opposite would be true in a sideway market. Without an existing trend today’s direction will most probably not be tomorrows direction, thus we can speak about a sideway market.

Autocorrelation in German Power

But best to have a look at a chart. It shows a backward adjusted daily time series of German Power.

The indicator shows the close to close autocorrelation coefficient, calculated over 250 days. You will notice that it is always fluctuating around the zero line, never reaching +1 or -1, but let`s see if we can design a profitable trading strategy even with this little bit of autocorrelation.

The direction of autocorrelation

Waiting for an autocorrelation of +1 would be useless. There will never be the perfect trend in real world data. My working hypothesis is, that a rising autocorrelation means that the market is getting trendy, thus a rising autocorrelation would be the perfect environment for a trend following strategy. But first we have to define the direction of the autocorrelation:

To define the direction of the autocorrelation I am using my digital stochastic indicator, calculated over half of the period I calculated the autocorrelation. Digital stochastic has the big advantage that it is a quite smooth indicator without a lot of lag, thus making it easy to define its direction. The definition of a trending environment would just be: Trending market if digital stochastic is above it`s yesterdays value.

Putting autocorrelation phase detection to a test

The most simple trend following strategy I can think about is a moving average crossover strategy. It never works in reality, simply as markets are not trending all the time. But combined with the autocorrelation phase detection, it might have an edge.

Wooha! That`s pretty cool for such a simple strategy. It is trading (long/short) if the market is trending, but does nothing if the market is in a sideway phase. Exactly what I like when using a trend following strategy.

To compare it with the original moving average crossover strategy, the one without the autocorrelation phase detection, you will see the advantage of the autocorrelation phase filter immediately: The equity line is way more volatile than the filtered one and you got lots of drawdowns when the market is sideways.

Stability of parameters

German power has been a quite trendy market over the last years, that`s why even the unfiltered version of this simple trend following strategy shows a positive result, but let`s have a test on the period of the moving average.

Therefore I calculated the return on account of both strategies, the unfiltered and the autocorrelation filtered, for moving average lengths from 3 to 75 days.

Return on account (ROA) =100 if your max drawdown is as big as your return.

The left chart shows the autocorrelation filtered ROA, the right side the straight ahead moving average crossover strategy. You don`t have to be a genius to see the advantage of the autocorrelation filter. Whatever length of moving average you select, you will get a positive result. This stability of parameters can not be seen with the unfiltered strategy.

Autocorrelation conclusion:

Trend following strategies are easy to trade, but only make sense when the market is trending. As shown with the tests above, autocorrelation seems to be a nice way to find out if the market is in the right phase to apply a trend following strategy.