Determining The Optimal Moving Average Length
- Date: 2007-04-30 - Word Count: 1617
Share This!
The moving average constitutes one of the simplest trading systems and is probably the most widely used tool for technical analysis. While its conceptual simplicity has attracted wide followers and perhaps indiscreet use, making a moving average (MA) system reliable and consistently profitable to any degree is an arduous exercise. The most critical task within this exercise is clearly the identification of the best moving average length to use. Over the years, I have heard many a technician, author, or trader extol the virtues of the 200-day MA, the 50-day MA, the 21-day and 13-day MA. The more exclusive writers seem to have distanced themselves from the plebeian choice of 50-day and 100-day moving average and chosen more esoteric numbers such as the 13-week MA, the 39-week MA. The more sophisticated software programmers working on technical analysis have tested a number of moving averages and have concluded that a certain moving average length is superior -- for example, 11 days beat 10. The key question is which moving average is the best choice, and why? In this article I describe an approach to finding this ideal moving average which I don't think has been published before. To understand the approach, it is essential to understand why moving averages work in the first place.
Let us do a simple exercise. Let us first draw a free chart of closing prices of a stock, with time on the x axis and prices on y axis. There are no restrictions on the shape except for the condition for any given time coordinate, there has to be only one price (i.e. you cannot have two closing prices for the stock for the same day).
Let us assume that this was the shape of the stock price movement. This price curve ("line chart") suggests that there was an opportunity to make money during the rise in the stock price from the low in March ("A") to the high in April ("B") by buying the stock and once again from "C" in April to "D" in May by short selling the stock. You probably wish you had made these trades. Probably those of us who are a bit more aggressive would also wish that we had made money by short selling at "B" and going long on the stock at the dip between "B" and "C". If only we had the prescient tool that forecasted this! Well the good news is we seem to have the right tool to achieve nearly that - the price itself!
In the chart below, I have just shifted the price plot by a few millimetres to the right on the chart and plotted that in light blue.
And there you have your trading system, that helps you to make money from very close to the peaks to very close to the troughs. The rule is whenever the red price plot cuts the blue price plot (i.e. the right shifted price plot) from below, you BUY and whenever the red price plot cuts the blue price plot from above, you SELL. Works brilliantly -- even our aggressive friends get more than their fill. They get to make money on the way down from close to "B" (the point of intersection of the two lines to be precise) to close to "1" and again from close to "1" to close to "C" and further from close to "C" to close to "2" down and from close to "2" to close to "3" up and so on. Our keen readers have probably noticed that there seems to be a confusion near point "4" if you traded the rule. The system will instruct you to sell and then buy back again, but with no significant price move. In this case it appears to be a marginal profit but there are several instances in which the net impact of this immediate reversal can be a loss (even in this case the trade around 4 could turn out to be a loss if you accounted for brokerage). These are called Whipsaws. Well, the system designer will tell you that the system does not work always but works most of the time. More specifically, the system designer claims this does not work in choppy or highly fluctuating markets but works well in trending markets. And in this case it has.
This system works on all curves and line charts that you plot, as long as you accept that it does not work in choppy markets. The following chart is an additional example with another stock. In this plot, we have highlighted the loss making ("L") and profit making ("P") trades based on the simple rule we used.
Try any plot, any shape, and this trading system works -- with the exception of highly fluctuating markets. But what about those choppy market scenarios? Let us work on them.
The best way to minimize losses is to shift the moving average further to the right. See the charts below.
With some additional right displacement we have managed to eliminate some of the losses on the right half of the chart. We have a clear trade - sell short at higher levels and buy to cover the short position at lower levels. However, on the left half, we still seem to have a wavy whipsaw. To eliminate that whipsaw as well, we have two options:
(i) We can smooth out the blue line, recognizing that some amount of the crisscross behaviour is due to the current blue line's fluctuations; OR
(ii) We smooth out the blue line while also shifting it further to the right.
Both of these charts are shown below.
Right Displaced Blue Line
Right Displaced and Smoothed Blue Line
As we can see from the charts above, all that we need to develop a successful trading system is a signal line that has a shape similar to the price curve and is shifted to the right. A moving average serves exactly that purpose.
By their very nature, moving averages smooth out interim fluctuations. Also by plotting the moving average of the preceding n trading days on the nth day, we are automatically shifting the moving average to the right. (Mathematically, the accurate day to plot the moving average would be around the n/2th day.) If the explanation so far is clear, then it is very easy to see that the choice of moving average for maximum profitability depends upon the extent of deviation from the main trend the stock witnesses from time to time. The figure below shows the deviation that I am referring to.
A simple visual optimization of the moving average so as to prevent the deviations from turning into whipsaws will produce the best possible moving average for the stock. For the more mathematical minded readers, the ideal moving average length would depend upon the average daily equivalent of the size of the deviation. The average day equivalent is calculated as:
Average size of deviation (measured over, say, last 10 identified deviations)
=
Average price move in the stock (calculated over, say, last 250 trading days)
The ideal moving average length would be two to two and a half times the average day equivalent of the deviation.
Some of the examples of this optimization are presented in charts below. An 18-day MA applies ideally to Advanced Micro Devices (AMD) stock, while a 42-day MA suits AMB Properties (AMB).
In both of these cases, the moving average has been drawn to avoid as many whipsaws as possible and keep the trader with the trend. But whipsaws are simply unavoidable during periods of sideways movement. During such periods one will see a continuous series of whipsaws. One way to avoid this would be act on the moving average signal only after the second confirmation, i.e. act only after the price line has completed a pull back to the moving average after a price crossover (shown in figure above).
So does this mean that we would be able to identify the ideal moving average length only after the event? Yes. Optimization can be done only with some history of price action. But it still does have forecasting value. Unlike methods that rely on cycles or lengths of past trends to compute the moving average length, our method uses the deviation size (which is a measure of variance from the main trend) to determine the moving average data. The size of this deviation tends to remain broadly constant for any given stock for a considerable period of time and depends upon the nature of the stock (i.e. a cyclical stock would in general have a deviation size as a larger fraction of the trend size as compared to a trending technology stock). Given this, every stock will probably require a broad optimization effort once in a while.
The next question that commonly arises is this: Does every stock have one single optimum moving average length? Clearly, no. We have illustrated the principle of a moving average and why it works on a daily chart purely as a default case. The same arguments can be applied to an hourly chart or a one-second intraday chart to optimise the moving average length for shorter term trading but it is my experience that moving average is not the most reliable intraday trading tool. I would use an optimized moving average on the daily chart for stock that I intend to hold for a three month horizon at the very least. I usually don't get perturbed with every little violation of MA line but would be very concerned if the line was emphatically broken, i.e. with a gap or on high volume and would be cautious if the MA line was flattening. Moving Averages can be terrific tools if you understood why they work and do not treat them as a holy grail or a trading system.
Let us do a simple exercise. Let us first draw a free chart of closing prices of a stock, with time on the x axis and prices on y axis. There are no restrictions on the shape except for the condition for any given time coordinate, there has to be only one price (i.e. you cannot have two closing prices for the stock for the same day).
Let us assume that this was the shape of the stock price movement. This price curve ("line chart") suggests that there was an opportunity to make money during the rise in the stock price from the low in March ("A") to the high in April ("B") by buying the stock and once again from "C" in April to "D" in May by short selling the stock. You probably wish you had made these trades. Probably those of us who are a bit more aggressive would also wish that we had made money by short selling at "B" and going long on the stock at the dip between "B" and "C". If only we had the prescient tool that forecasted this! Well the good news is we seem to have the right tool to achieve nearly that - the price itself!
In the chart below, I have just shifted the price plot by a few millimetres to the right on the chart and plotted that in light blue.
And there you have your trading system, that helps you to make money from very close to the peaks to very close to the troughs. The rule is whenever the red price plot cuts the blue price plot (i.e. the right shifted price plot) from below, you BUY and whenever the red price plot cuts the blue price plot from above, you SELL. Works brilliantly -- even our aggressive friends get more than their fill. They get to make money on the way down from close to "B" (the point of intersection of the two lines to be precise) to close to "1" and again from close to "1" to close to "C" and further from close to "C" to close to "2" down and from close to "2" to close to "3" up and so on. Our keen readers have probably noticed that there seems to be a confusion near point "4" if you traded the rule. The system will instruct you to sell and then buy back again, but with no significant price move. In this case it appears to be a marginal profit but there are several instances in which the net impact of this immediate reversal can be a loss (even in this case the trade around 4 could turn out to be a loss if you accounted for brokerage). These are called Whipsaws. Well, the system designer will tell you that the system does not work always but works most of the time. More specifically, the system designer claims this does not work in choppy or highly fluctuating markets but works well in trending markets. And in this case it has.
This system works on all curves and line charts that you plot, as long as you accept that it does not work in choppy markets. The following chart is an additional example with another stock. In this plot, we have highlighted the loss making ("L") and profit making ("P") trades based on the simple rule we used.
Try any plot, any shape, and this trading system works -- with the exception of highly fluctuating markets. But what about those choppy market scenarios? Let us work on them.
The best way to minimize losses is to shift the moving average further to the right. See the charts below.
With some additional right displacement we have managed to eliminate some of the losses on the right half of the chart. We have a clear trade - sell short at higher levels and buy to cover the short position at lower levels. However, on the left half, we still seem to have a wavy whipsaw. To eliminate that whipsaw as well, we have two options:
(i) We can smooth out the blue line, recognizing that some amount of the crisscross behaviour is due to the current blue line's fluctuations; OR
(ii) We smooth out the blue line while also shifting it further to the right.
Both of these charts are shown below.
Right Displaced Blue Line
Right Displaced and Smoothed Blue Line
As we can see from the charts above, all that we need to develop a successful trading system is a signal line that has a shape similar to the price curve and is shifted to the right. A moving average serves exactly that purpose.
By their very nature, moving averages smooth out interim fluctuations. Also by plotting the moving average of the preceding n trading days on the nth day, we are automatically shifting the moving average to the right. (Mathematically, the accurate day to plot the moving average would be around the n/2th day.) If the explanation so far is clear, then it is very easy to see that the choice of moving average for maximum profitability depends upon the extent of deviation from the main trend the stock witnesses from time to time. The figure below shows the deviation that I am referring to.
A simple visual optimization of the moving average so as to prevent the deviations from turning into whipsaws will produce the best possible moving average for the stock. For the more mathematical minded readers, the ideal moving average length would depend upon the average daily equivalent of the size of the deviation. The average day equivalent is calculated as:
Average size of deviation (measured over, say, last 10 identified deviations)
=
Average price move in the stock (calculated over, say, last 250 trading days)
The ideal moving average length would be two to two and a half times the average day equivalent of the deviation.
Some of the examples of this optimization are presented in charts below. An 18-day MA applies ideally to Advanced Micro Devices (AMD) stock, while a 42-day MA suits AMB Properties (AMB).
In both of these cases, the moving average has been drawn to avoid as many whipsaws as possible and keep the trader with the trend. But whipsaws are simply unavoidable during periods of sideways movement. During such periods one will see a continuous series of whipsaws. One way to avoid this would be act on the moving average signal only after the second confirmation, i.e. act only after the price line has completed a pull back to the moving average after a price crossover (shown in figure above).
So does this mean that we would be able to identify the ideal moving average length only after the event? Yes. Optimization can be done only with some history of price action. But it still does have forecasting value. Unlike methods that rely on cycles or lengths of past trends to compute the moving average length, our method uses the deviation size (which is a measure of variance from the main trend) to determine the moving average data. The size of this deviation tends to remain broadly constant for any given stock for a considerable period of time and depends upon the nature of the stock (i.e. a cyclical stock would in general have a deviation size as a larger fraction of the trend size as compared to a trending technology stock). Given this, every stock will probably require a broad optimization effort once in a while.
The next question that commonly arises is this: Does every stock have one single optimum moving average length? Clearly, no. We have illustrated the principle of a moving average and why it works on a daily chart purely as a default case. The same arguments can be applied to an hourly chart or a one-second intraday chart to optimise the moving average length for shorter term trading but it is my experience that moving average is not the most reliable intraday trading tool. I would use an optimized moving average on the daily chart for stock that I intend to hold for a three month horizon at the very least. I usually don't get perturbed with every little violation of MA line but would be very concerned if the line was emphatically broken, i.e. with a gap or on high volume and would be cautious if the MA line was flattening. Moving Averages can be terrific tools if you understood why they work and do not treat them as a holy grail or a trading system.
Related Tags: stock, trading system, palma research, stock price movement, price curve, minimize losses, cyclical stock
The author is the managing director of Palma Research, an independent global equity research firm, serving institutional and individual clients worldwide. Palma Research uses a comprehensive approach to research combining fundamental trends and technical analysis. Palma Research has one of the largest teams of technical analysis in the world and currently covers over 250 stocks every day. Palma's research can be accessed at www.palmaresearch.com. Your Article Search Directory : Find in Articles
Recent articles in this category:
- The Secrets to Getting Low Down Payment Car Insurance
Upon purchase of a new car, there is almost always a requirement to buy an auto insurance policy as - The Wisdom Behind Auto Insurance Comparison Quotes
No one in his right mind would not go for a good deal. In fact, everyone is out on their feet and ru - The Benefits of Auto Insurance Comparisons Florida
Insurance can be expensive. This is something everyone knows about especially in the sunny state of - Auto Insurance Florida: The No-Fault Policy
There are different kinds of car insurance offered by a wide range of providers today. Different sta - Finding the Cheapest Auto Insurance Companies
Everyone is asking and searching for the cheapest auto insurance companies available today. Consider - How do You Compare Private Health Insurance Cover in Australia?
Deciding what is the best and most affordable private health insurance cover can be easy if you take - How Payment Protection Insurance Was Mis-Sold
For over six years the issue of Payment Protection Insurance (PPI) and how it was mis-sold to custom - Finding Quotes For Auto Insurance Online
One of the many concerns when you are shopping for auto insurance is being able to get access to quo - How You Can Find the Best Auto Insurance Online
When it comes to renewing your car insurance you are going to quickly discover that there are a numb - Guidelines For Searching For Auto Insurance Online
The internet can be a great source of discounts and values related to auto insurance. However, many
Most viewed articles in this category:
- Trading Forex With Pivot Points
Forex Pivot Point Trading are used today by Forex Traders and are calculated on the previous days mo - Where To Search For Free Grants
Where do you look for free grants? The search must be thorough or it could be an exercise in futilit - The Connection Between High Blood Pressure and Salt
We are a society of Salt Addicts. It cannot be denied. When you look at the things we do and the pla - Tips For Avoiding HYIP Scams
Before knowing about HYIP Scams, refer to the functioning of HYIP or "High Yield Investment Programs - Getting Credit After Bankruptcy
Consumers do not have to live sans credit following a bankruptcy. By following certain steps consume - Tips For Choosing A Credit Card
Are you looking for that perfect credit card? If so, you may be confused about what exactly to look - Cheap Car Insurance For Teens Online
Many elements determine a car insurance policy. Car insurance companies look at the person's age, hi - What Exactly Is Free Grant Money?
You can apply for free grant money from various government agencies. But where exactly does this mon - Small Business Owners Marketing and Customer Service
Marketing can be time-consuming, but it doesn't have to be hugely expensive now, thanks to the Inter - Apply Online For A Credit Card - How To Choose A Card?
The best type of credit card for you will be dependant on how you intend to use the credit card. Are