Performance of Moving Average Crossover Indicator on US Stocks

[Henry - Guiix 10]

A moving average crossover is a simple variation of the moving average indicator. It is also a trend following indicator (not to mention one of the most famous). It does not predict price but it shows price trends. This indicator uses two (or more) moving averages, a slower moving average and a faster moving average. The faster moving average is a short term moving average. It may be 5, 10 or 25 day period while the slower moving average is medium or long term moving average. This moving average involves 50, 100 or 200 day period. A short term moving average is "faster" because it only considers prices over short period of time and is thus more reactive to daily price changes. On the other hand, a long term moving average is deemed "slower" as it encapsulates prices over a longer period and is more lethargic. However, it tends to smoothen out price noises which are often reflected in short term moving averages.

 

A moving average, as a line by itself, is often overlaid in price charts to indicate price trends. A crossover occurs when a faster moving average (i.e. a shorter period moving average) crosses a slower moving average (i.e. a longer period moving average). In other words, this is when the shorter period moving average line crosses a longer period moving average line. This meeting point is important as it gives us an idea of the optimum time to either enter (buy) or exit (sell) the market. In this article, we'll go into a semi-thorough analysis of the buy signal only.

 

The image below gives us a picture of how a buy signal is triggered. A buy signal is triggered when the shorter moving average (red line) rises above the longer moving average (orange line).

 

 

Figure 1 shows how moving average crossover works as a buy indicator.

 

So why is it advantageous to consider two moving averages instead of one? The common dilemma of investors is in trying to make a moving average responsive to changes in trend while not allowing it to be so sensitive that it causes a trader to prematurely enter or exit a position. This is addressed by using the moving average crossover technical indicator. This indicator stands in the middle ground. It combines the shorter period moving average's price sensitivity and the longer period moving average's sense of reality, thus giving the investor a fairly accurate appreciation of price trends.

 

The table 1 shows moving average crossover indicators grouped according to the number of days the crossover is sustained. Each indicator is given the following parameters: c=short term close price, moving average short period, w=weighted moving average, c=long term close price, moving average long period, w=weighted moving average, days crossover is sustained; couched inside the parenthesis.

 

This article will explore the reliability of the moving average crossover indicator using the results of a backtested simulation. The test used close prices of 7072 US stocks from 4th January 1982 to 31st December 2007. Prices are in US Dollars (USD). The test reviews six (6) statistics: Profit Per Year, Simulated Portfolio Gain (in US Dollars), Median Signals Per Year, Median Profit %, Success Ratio and Maximum Drawdown Loss. Sell signal is placed at 15 % stop loss (after a 15% fall from any stock price).

 

Profitability

 

See attached worksheet

 

The purpose of any good study is to determine which indicator could make a good profit. We did this by using three (3) statistics: Profit per Year, Simulated Portfolio Gain and Median Signals per Year.

 

The Profit per Year column shows the average profit of simulated stock investment per year. This simply shows the return to investor of the money used to purchase the stock at the time of entry (simulation starting at $100k and investing 1% cash-at-hand for every buy). The next column shows the Simulated Portfolio Gain of each entire backtest over all stocks at the end of the historic data period. These two statistics measure the return of money or growth of investment as shown by increase in price of stock. In other words, these statistics tell us which technical indicator has historically yielded the highest possible profit for our investment. We are therefore interested with the indicator with the highest profit or portfolio gain.

 

The third column Median Signals per Year is quite different from the two statistics. It does not give us direct measure of profit but gives us an idea as to how often we get buy signals triggered. If the value is too low, we wouldn't be able to trade, as there'd be nothing to buy. If on the other hand, the value is too high, it could also be hard to manage, as it would be impossible to buy them all as an individual. Here we are interested with the indicator having an average to high value.

 

In terms of obtaining profit, two indicators (in green highlight) performed ahead of the pack (movx(c,5,w,c,50,w,1) and movx(c,10,w,c,50,w,1). These two are highly profitable technical indicators. Both indicators show an average of 12% Profit per Year compared to the others showing only 8-11% [1]. Also, we can see that both indicators are reactive. They triggered the buy signal 7000-8000 times a year. This means that stock trading is possible and manageable. This is even recommended for short-term trading as both indicators could easily alert the investor of an uptrend.

 

However, we have also identified three indicators (highlighted in rose) which did not perform well in terms of profitability movx(c,10,w,c,100,w,3), movx(c,10,w,c,150,w,3) and movx(c,25,w,c,200,w,5)) [2]. These indicators, while having an average yearly profit, have one of the lowest, if not the lowest portfolio gains among all. We are of course not interested in indicators which do not yield a high portfolio gain for the investment.

 

On a deeper note, it seems that group 1 in Table 1 is the group with highly profitable indicators compared to other groups. This group provides the highest gain, yearly profit and above average median signals per year compared to the last two groups. The best indicators for each of the statistic belong to such group. Thus, if we are looking for a profitable indicator, we should always look at the indicator with the shorter moving average (group 1 in Table 1).

 

It may be best to show you the increase in portfolio one may expect from highly profitable indicators we have recommended so far. The image shows portfolio growth simulated using indicator movx(c,10,w,c,50,w,1) (one of the best performing indicator in terms of profitability) with 15% stop loss as buy signal for US stocks from 1983 to 2007. You can see that in a matter of 24 years, the stock value went from 94k USD to 700k USD or almost 7 times its initial value. This is a reasonable return for the investment.

 

 

Risk Management

 

See attached worksheet

Table 2 shows moving average crossover indicators' performance in terms of risk management statistics

 

It is of such importance for an investor to consider risk in arriving at a financial decision. Investment entails gain or loss depending on the reliability of one's technique and experience. This section will help the investor ascertain which indicators provide the most and least win-to-loss ratio as well as the "worst case scenario" in terms of possible losses. A correct appreciation therefore of indicator performance could save an investor from undertaking ventures which may not return profit as much as expected.

 

If we are looking at risks, we should be interested first in measuring the likelihood of gain versus the likelihood of loss. This is shown by statistic Success Ratio (first column in Table 3). Technically, success here is where the stock price at the 15% stop loss sell point was above the buy price, and loss when the stop loss sell point was below the buy price. After determining the indicator which could provide more gain than loss, we also need to look at largest loss we can expect if we take the investment. This is maximum drawdown loss. It is simply the value of the portfolio after the largest string of losses assuming the investor acts according to the signals triggered. In other words, we need the indicator with a high success ratio because it is likely to gain which means safe investment for us. On the other hand, we are interested in the indicator with the lowest drawdown loss.

 

For easy reference, the least risky indicators are in green (movx(c,25,w,c,200,w,1), movx(c,25,w,c,200,w,3,0) and movx(c,25,w,c,200,w,5)), while the risky indicators are in red. The least risky indicators gave us the one of the highest success ratios and the lowest drawdown losses. By using these indicators, you can expect a more steady return of profit compared to all other indicators in the list. The risky indicators, on the other hand, are those which gave lower success ratios and highest drawdown losses. These risky indicators could result to quite unstable return and high losses.

 

Also, you will immediately notice how high the drawdown loss values are. Massive drawdowns like these suggest a risky market over a long historic period when investments are likely to lose a large portion of investment at some stage. This means that, using a moving average crossover alone is probably unwise. Some knowledge of market conditions would be quite helpful here. The image below shows yearly returns of US stocks from year 1983 to 2007 using indicator movx(c,10,w,c,50,w,1) with 15% stop loss as buy signal. The red line indicates the point where there is neither profit nor loss. Notice how the green line falls below the horizontal red line as much as it rises above it? This connotes that the stocks almost always have no returns as much as they profit. This suggests that there is just as much potential for wins as for losses during that period.

 

 

Recommendations

 

The moving average crossover is one of the most well-known technical analysis tools. It gives us an appreciation of the price direction of a stock. Knowing how and when to utilize an indicator such as the moving average crossover and what specific indicator to use fit for a particular trading purpose can delineate the line between potential gain or loss.

 

This article, I hope, goes into some of the statistics of real-world performance of the moving average crossover. We have come to know which indicators suit what aspect and which indicators will not be much of a help. Thus to summarise we'll rate indicators according to overall performance. Table 3 below shows us which indicators are best for short-term, medium-term or long-term trading highlighted in green.

 

From these simulations, I'd recommend indicator movx(c,10,w,c,50,w,1) for short-term trading. It performed ahead of the pack when it comes to profit and portfolio gain yet maintained an average success ratio and relatively high median signals per year value. It suits short term trading because it triggers buy signal more often and earlier. It reacts easily to price fluctuations. One downside is its high drawdown loss value but this only makes sense because the indicator only covers a very short period of time when there is yet no strong trend forming.

 

On the other hand, two indicators proved useful to medium-term trading (movx(c,25,w,c,100,w,3) and movx(c,25,w,c,100,w,5)). These two performed remarkably in profitability statistics but still show one of the highest success ratios and one of the lowest drawdown loss values. As for long-term trading, one indicator seem to outperform the other long-term indicators in terms of both profit and risk (movx(c,25,w,c,150,w,5)). This indicator gave one of the lowest drawdown values we seek for in terms of long-term trading. Also, it has 42.94% win-to-loss ratio; one of the highest likelihood of gain compared to other indicators in the list. Overall, these four indicators topped the others.

 

See attached worksheet

MA Crossover.xls

[RickW00716 10]

A moving average crossover is a simple variation of the moving average indicator. It is also a trend following indicator (not to mention one of the most famous). It does not predict price but it shows price trends. This indicator uses two (or more) moving averages, a slower moving average and a faster moving average. The faster moving average is a short term moving average. It may be 5, 10 or 25 day period while the slower moving average is medium or long term moving average. This moving average involves 50, 100 or 200 day period. A short term moving average is "faster" because it only considers prices over short period of time and is thus more reactive to daily price changes. On the other hand, a long term moving average is deemed "slower" as it encapsulates prices over a longer period and is more lethargic. However, it tends to smoothen out price noises which are often reflected in short term moving averages.

 

A moving average, as a line by itself, is often overlaid in price charts to indicate price trends. A crossover occurs when a faster moving average (i.e. a shorter period moving average) crosses a slower moving average (i.e. a longer period moving average). In other words, this is when the shorter period moving average line crosses a longer period moving average line. This meeting point is important as it gives us an idea of the optimum time to either enter (buy) or exit (sell) the market. In this article, we'll go into a semi-thorough analysis of the buy signal only.

 

The image below gives us a picture of how a buy signal is triggered. A buy signal is triggered when the shorter moving average (red line) rises above the longer moving average (orange line).

 

 

Figure 1 shows how moving average crossover works as a buy indicator.

 

So why is it advantageous to consider two moving averages instead of one? The common dilemma of investors is in trying to make a moving average responsive to changes in trend while not allowing it to be so sensitive that it causes a trader to prematurely enter or exit a position. This is addressed by using the moving average crossover technical indicator. This indicator stands in the middle ground. It combines the shorter period moving average's price sensitivity and the longer period moving average's sense of reality, thus giving the investor a fairly accurate appreciation of price trends.

 

The table 1 shows moving average crossover indicators grouped according to the number of days the crossover is sustained. Each indicator is given the following parameters: c=short term close price, moving average short period, w=weighted moving average, c=long term close price, moving average long period, w=weighted moving average, days crossover is sustained; couched inside the parenthesis.

 

This article will explore the reliability of the moving average crossover indicator using the results of a backtested simulation. The test used close prices of 7072 US stocks from 4th January 1982 to 31st December 2007. Prices are in US Dollars (USD). The test reviews six (6) statistics: Profit Per Year, Simulated Portfolio Gain (in US Dollars), Median Signals Per Year, Median Profit %, Success Ratio and Maximum Drawdown Loss. Sell signal is placed at 15 % stop loss (after a 15% fall from any stock price).

 

Profitability

 

See attached worksheet

 

The purpose of any good study is to determine which indicator could make a good profit. We did this by using three (3) statistics: Profit per Year, Simulated Portfolio Gain and Median Signals per Year.

 

The Profit per Year column shows the average profit of simulated stock investment per year. This simply shows the return to investor of the money used to purchase the stock at the time of entry (simulation starting at $100k and investing 1% cash-at-hand for every buy). The next column shows the Simulated Portfolio Gain of each entire backtest over all stocks at the end of the historic data period. These two statistics measure the return of money or growth of investment as shown by increase in price of stock. In other words, these statistics tell us which technical indicator has historically yielded the highest possible profit for our investment. We are therefore interested with the indicator with the highest profit or portfolio gain.

 

The third column Median Signals per Year is quite different from the two statistics. It does not give us direct measure of profit but gives us an idea as to how often we get buy signals triggered. If the value is too low, we wouldn't be able to trade, as there'd be nothing to buy. If on the other hand, the value is too high, it could also be hard to manage, as it would be impossible to buy them all as an individual. Here we are interested with the indicator having an average to high value.

 

In terms of obtaining profit, two indicators (in green highlight) performed ahead of the pack (movx(c,5,w,c,50,w,1) and movx(c,10,w,c,50,w,1). These two are highly profitable technical indicators. Both indicators show an average of 12% Profit per Year compared to the others showing only 8-11% [1]. Also, we can see that both indicators are reactive. They triggered the buy signal 7000-8000 times a year. This means that stock trading is possible and manageable. This is even recommended for short-term trading as both indicators could easily alert the investor of an uptrend.

 

However, we have also identified three indicators (highlighted in rose) which did not perform well in terms of profitability movx(c,10,w,c,100,w,3), movx(c,10,w,c,150,w,3) and movx(c,25,w,c,200,w,5)) [2]. These indicators, while having an average yearly profit, have one of the lowest, if not the lowest portfolio gains among all. We are of course not interested in indicators which do not yield a high portfolio gain for the investment.

 

On a deeper note, it seems that group 1 in Table 1 is the group with highly profitable indicators compared to other groups. This group provides the highest gain, yearly profit and above average median signals per year compared to the last two groups. The best indicators for each of the statistic belong to such group. Thus, if we are looking for a profitable indicator, we should always look at the indicator with the shorter moving average (group 1 in Table 1).

 

It may be best to show you the increase in portfolio one may expect from highly profitable indicators we have recommended so far. The image shows portfolio growth simulated using indicator movx(c,10,w,c,50,w,1) (one of the best performing indicator in terms of profitability) with 15% stop loss as buy signal for US stocks from 1983 to 2007. You can see that in a matter of 24 years, the stock value went from 94k USD to 700k USD or almost 7 times its initial value. This is a reasonable return for the investment.

 

 

Risk Management

 

See attached worksheet

Table 2 shows moving average crossover indicators' performance in terms of risk management statistics

 

It is of such importance for an investor to consider risk in arriving at a financial decision. Investment entails gain or loss depending on the reliability of one's technique and experience. This section will help the investor ascertain which indicators provide the most and least win-to-loss ratio as well as the "worst case scenario" in terms of possible losses. A correct appreciation therefore of indicator performance could save an investor from undertaking ventures which may not return profit as much as expected.

 

If we are looking at risks, we should be interested first in measuring the likelihood of gain versus the likelihood of loss. This is shown by statistic Success Ratio (first column in Table 3). Technically, success here is where the stock price at the 15% stop loss sell point was above the buy price, and loss when the stop loss sell point was below the buy price. After determining the indicator which could provide more gain than loss, we also need to look at largest loss we can expect if we take the investment. This is maximum drawdown loss. It is simply the value of the portfolio after the largest string of losses assuming the investor acts according to the signals triggered. In other words, we need the indicator with a high success ratio because it is likely to gain which means safe investment for us. On the other hand, we are interested in the indicator with the lowest drawdown loss.

 

For easy reference, the least risky indicators are in green (movx(c,25,w,c,200,w,1), movx(c,25,w,c,200,w,3,0) and movx(c,25,w,c,200,w,5)), while the risky indicators are in red. The least risky indicators gave us the one of the highest success ratios and the lowest drawdown losses. By using these indicators, you can expect a more steady return of profit compared to all other indicators in the list. The risky indicators, on the other hand, are those which gave lower success ratios and highest drawdown losses. These risky indicators could result to quite unstable return and high losses.

 

Also, you will immediately notice how high the drawdown loss values are. Massive drawdowns like these suggest a risky market over a long historic period when investments are likely to lose a large portion of investment at some stage. This means that, using a moving average crossover alone is probably unwise. Some knowledge of market conditions would be quite helpful here. The image below shows yearly returns of US stocks from year 1983 to 2007 using indicator movx(c,10,w,c,50,w,1) with 15% stop loss as buy signal. The red line indicates the point where there is neither profit nor loss. Notice how the green line falls below the horizontal red line as much as it rises above it? This connotes that the stocks almost always have no returns as much as they profit. This suggests that there is just as much potential for wins as for losses during that period.

 

 

Recommendations

 

The moving average crossover is one of the most well-known technical analysis tools. It gives us an appreciation of the price direction of a stock. Knowing how and when to utilize an indicator such as the moving average crossover and what specific indicator to use fit for a particular trading purpose can delineate the line between potential gain or loss.

 

This article, I hope, goes into some of the statistics of real-world performance of the moving average crossover. We have come to know which indicators suit what aspect and which indicators will not be much of a help. Thus to summarise we'll rate indicators according to overall performance. Table 3 below shows us which indicators are best for short-term, medium-term or long-term trading highlighted in green.

 

From these simulations, I'd recommend indicator movx(c,10,w,c,50,w,1) for short-term trading. It performed ahead of the pack when it comes to profit and portfolio gain yet maintained an average success ratio and relatively high median signals per year value. It suits short term trading because it triggers buy signal more often and earlier. It reacts easily to price fluctuations. One downside is its high drawdown loss value but this only makes sense because the indicator only covers a very short period of time when there is yet no strong trend forming.

 

On the other hand, two indicators proved useful to medium-term trading (movx(c,25,w,c,100,w,3) and movx(c,25,w,c,100,w,5)). These two performed remarkably in profitability statistics but still show one of the highest success ratios and one of the lowest drawdown loss values. As for long-term trading, one indicator seem to outperform the other long-term indicators in terms of both profit and risk (movx(c,25,w,c,150,w,5)). This indicator gave one of the lowest drawdown values we seek for in terms of long-term trading. Also, it has 42.94% win-to-loss ratio; one of the highest likelihood of gain compared to other indicators in the list. Overall, these four indicators topped the others.

 

See attached worksheet

 

This is a very informative study you've done!! I'd be very interested in seeing the sell results as well.