Why Moving Averages

As a trader or investor, the only reason to investigate moving averages is to gain knowledge to increase profits. Like many other technical indicators, moving averages are meant to help us objectively tell the market status at any given time. This helps us see through the emotions of the day and make rational decisions, which we’re told will lead to greater profits and/or fewer losses over the long run. Moving averages (MAs) smooth the series of prices for a stock. MAs are most often used to identify the trend of market direction, and are classed as a trend-following indicator. This doesn’t mean that MAs are only for long-term investors - short term traders use them also. Moving averages can be used to screen stocks for good candidates, signal buying opportunities, and offer sell signals.

Why Backtest - A Story

The goal of backtesting is to find out if moving averages really do lead to better results and what are the most promising ways to apply MAs. Let me tell you a short story. While I was putting together the results for one of the moving average BackTesting Report issues, I happened to visit a friend. At her house, I came across some reading material from a well-advertised discount stock broker. In it was an article that advising its customers to use a particular moving average length applied in a certain way to get the best results. I had my comprehensive tests right in front of me and I can tell you that broker’s method did not get the best results although they did mention a MA length that is useful in other ways. I had in my hand test results that showed that the way that broker applied the moving average had a win rate worse than the baseline when tested on 7147 stocks over 14 years of stock market data. Clearly the broker wasn’t running that kind of testing. It’s up to the customers - us! - to fend for ourselves and find out what works versus what doesn’t.

How to Calculate MAs

When backtesting moving averages, the first decision is how to calculate the moving average. Do you want a simple moving average (SMA)? Or something designed to track price better such as an exponential moving average (EMA)? You might consider an experiment to compare the win rates of the two different averages. I did just that a couple years ago, and while I don’t have the results to publish, I came away with the notion that it didn’t make a big difference whether I chose SMA or EMA — just pick one and use it consistently. So for this project, I choose to use simple moving averages because I see them mentioned in commentary most often. To actually do the calculation, I relied on the built-in function which came with TradeStation. (The choice of backtesting engine is another decision which is general enough to write about in another post.)

How to Use MAs

Next you need to pin down how exactly you want to apply moving averages. How will you interpret the relationship between price and moving average? What rules will you use to decide when to buy and sell? You don’t have to read long about stocks before coming across a bullish reference to a stock trading above its 200-day moving average or its 50-day moving average, or even the 10- or 20-day MA. Or advice about buying stocks as they cross their 50-day or 200-day moving average. These are important rules to test in the backtesting engine. And then there’s the moving average crossover - a classic method of technical analysis. That makes three distinct ways of using moving averages to test.

Going more in-depth, some trading texts talk about the slope of a moving average. If you hark back to algebra and consider the MA as a line, to find its slope you would pick two points on the line and apply the usual formula ((x2-x1)/(y2-y1)). This brings up the question of how far apart to pick the two points which can make a difference to results. Really, since the MA is being used to identify the trend, we just want to know if it is sloping up or down. Then we can simplify the whole calculation by noticing that if the price is above the moving average, it must be pulling the average up, and a price below the MA pulls it down. Thus another reason to test the efficacy of price above the moving average.

Parameter settings

Once you decide on how to use the MAs, you need to pick a selection of various lengths to test. Beware of over-optimizing. Somewhere out there is a guy with backtesting results showing 3895% gain or whatever using just the right moving average. Too bad he doesn’t know what MA will produce those results in the future. That said, you need to try more than one length to make sure that your results aren’t a fluke. Stick with defaults settings or the ones you hear about most in the media. Finding the one perfect parameter setting is not going to make you rich. Finding a cluster of good, robust settings just might do you a great deal of good though.

As a practical matter when backtesting allow enough data lag before measuring. All tests must begin measuring at the same place for apples-to-apples comparison among different MA lengths. For example, if you’re testing a 200-day moving average, it will take the first 200-days of data to calculate the first point of that moving average. That means that the first day you could possibly have a signal is 200-days into the data set. To make a fair comparison with, say, the 10-day moving average, you need to make sure not to count any signals from the 10-day moving average before the 200-day is ready to go. Fortunately TradeStation has a way to set the “Maximum number of bars study will reference” in “Properties for All” strategies which forces the backtesting engine to wait that long before tabulating data.

More Profit from Buying or Selling?

Moving average rules, and in particular moving average crossover rules, are often discussed as a reversal system. This means that one signal, say the MAs crossing upwards is a buy signal and then its opposite, say MA lines crossing down, is not only a sell signal but also the trigger to go short. Theoretically, that’s just fine but many people are not interested in shorting the market. They are looking for techniques to help them buy and maybe sell. Even a person who regularly sells and sells short might use different techniques for buying and selling. For these reasons, it’s wise to test the buy signals separately from the sell signals.

This poses a dilemma because it’s hard to evaluate a buy signal in isolation. One way to do this is to use timed exits - that is, exit the trade or sell the stock after a certain amount of time elapses. I chose to run each backtest three times with three different times exits because different people have different styles and different needs. To produce backtesting results useful to swing traders, I exit after 2 days. To model position traders, 20 days. To meet the needs of active investors, backtesting holds each position for 200 days. This gives a way to isolate the buy signals and find out just how useful the moving average is to stock buyers of various temperaments.

Need to Define Goodness

One more very important thing to consider if you are backtesting moving averages to find out how well they do in the stock market: How will you know what is good? You need objective criteria for success. That means identifying the key statistics such as win rate, expectancy, hypothetical equity gains, etc. It also means setting standards for acceptable performance in each of these areas.

An example illustrates why this is important and why it’s not as easy as it first appears. Say your tests show a win rate of 55% for a particular indicator. That may might not be so good if, say, 62% of all stocks went up during the same period of time. Or if only 25% of stocks rose during that time period, your 55% win rate would be spectacular. What is good depends on how it compares to baseline market performance under the same conditions.

You can download a free copy of the BackTesting Report Baseline issue by clicking here.

Test Set

For a meaningful backtest, you need to have enough data to make a statistically valid comparison. At the minimum, that means 30 trades. Even if you are trading just one instrument - just one stock or just one currency pair - I think it’s important to test your trading strategy on many different instruments to prove its robustness. I went over the top with an extremely large test set — 7147 stocks over 14 years — to make sure my results would apply in a wide variety of market conditions.

You can get your copy of my backtesting reports on moving average buy signals by clicking here.

Tags: backtesting, baseline, data, day, exit, expectancy, goals, indicator, linkedin, long, loss, moving average, selling, short, signal, statistics, strategy, system, technical, TradeStation, trading, trend following

Click here to download the baseline issue of BackTesting Report free without registration.  

The Baseline is the backtesting results from a very simple trading strategy.  We use this as a basis for comparision.   We do this to weed out the trading strategies that look good because they happened by chance to be in sync with the market over the test period.   Instead we want to find the strategies that add value other than just riding the market.

Trading strategies must test out better than the baseline to be considered for live trading.

For example, an entry strategy with a 55% win rate might sound good by itself.   But if the baseline had a 60% win rate over the same stocks and time period, that 55% strategy is actually a loser!

Extra Insight:

We test a simple strategy that enters the market at every opportunity and blindly exits at the end of specified hold periods.   We choose the hold periods to match popular trading styles.  This gives a win rate baseline.   It also shows the market’s directional bias for the test period.  We calculate the expectancy although this is not a real trading strategy.

This sample strategy has some dependence on the start date.    We can measure it to see the impact.   We can also reduce the start date impact by doing a random re-sampling using Monte Carlo simulation to get a more robust baseline.

The difference between “buy and hold” of a benchmark index and the baseline strategy is that the baseline takes into account the transaction costs of commission and slippage.  The baseline also spends a fraction of the time out of the market between trades — overnight in the case of End-of-Day data.

Win rate is my comparision metric for entry strategies.  

Expectancy is my metric for comparison for exit strategies.

Last updated 02/04/09.

Tags: baseline, data, expectancy, monte carlo, trading, win rate

Expectancy measures a trading strategy’s profit potential.   It considers both the reliability or win rate as well as the amount gained by each win.    That way, it can compare trading strategies that often win small gains with strategies that rarely win but win big when they do. 

Expectancy = (win_rate * avg_win) - (loss_rate * avg_loss)

Van Tharp defines expectancy in terms of risk here, as the average of the R-multiples returned by trading or backtesting the system.

Extra Insight:

Over a large number of trades, the expectancy is the expected gain of the trading strategy.  Higher expectancy is generally better.  Always avoid trading strategies with negative expectancy.

Scaling the expectancy by risk is indeed useful, especially when it comes time to compare different systems.  I use the R-multiples as suggested by Van Tharp for ease of calculation.

Expectancy is also known as the Kelly Criterion for the Bell Labs researcher who proved the equation as an upper bound on the amount to risk.     A common language way to say it is to risk an amount proportional to the expected gain.   So if the expectancy is 45%, Kelly advocated risking 45% of the account value.   This may be mathematically optimal over a large number of trades but it can have a very vicious drawdown!   Imagine trading a high expectancy system, say 80% and the first trade is a loss.  For a $100k account, that would leave only $20k in the account and a long road to make a 4x gain to break even.

Expectancy is not the be-all and end-all of a trading system.   The standard deviation or variance of the results is important.  The win rate is too.  Both give insight into how psychologically difficult it is to stick to the trading strategy.

Updated: 11/12/08.

Tags: backtesting, expectancy, Kelly criterion, long, R-Multiple, risk, strategy, system, trading, Van Tharp

The Probability section of my backtesting report breaks down into two mathematical constructs: expectancy and standard deviation.  The intent is to give insight into the relative performance of a trading strategy over a large number of trades, and to help traders select profitable strategies (positive expectancy).  

Extra Insight: 

The most desirable case is a high expectancy with a low standard deviation.

Like the toss of a coin, a strategy may vary considerably from the reported results for a small sample of trades.

For a full definition of probability theory, get a textbook on the topic.

(Backtesting Blog is an Amazon Associate.)

Updated on 11/12/08.

Tags: expectancy, probability, standard deviation

Size Matters

Sizing is the rule for deciding how many shares or contracts to buy.

Extra Insight:

Sizing is critical to risk management, worthwhile returns, and also making comparisions between backtesting runs.   For the backtesting runs, I use a very common and straightforward sizing:

• If there is no stop loss for the strategy under test, my backtesting trade size is 1000 shares (and the amount at risk is the total amount of the trade).
• If there is a stop loss, my backtesting trade size is the nominal risk amount of $1000 divided by the distance from the expected entry price to the stop price.   If its a next-day market order then today’s close serves as the expected entry price.   This way, the risk amount is constant for every trade but the trade size varies in both dollar amount and number of shares.

(Backtesting Blog is an Amazon Associate.)

Updated 11/13/08.

Tags: backtesting, expectancy, loss, management, risk, sizing, stop, strategy, trade size, trading

StdDev is an abbreviation for Standard Deviation - a widely used mathematical formula.   The Wikipedia entry contains a section on finance about halfway down.   In one sentence, StdDev gives an idea how much the trade results vary and a smaller StdDev is generally better.

Extra Insight:

In the backtesting results, I apply the Excel formula Stdev.

Smaller standard deviations generally make for  better trading strategies, provided the strategy also has a positive expectancy to indicate potential profits.

Updated 11/13/08.

Tags: backtesting, expectancy, indicator, risk, standard deviation, strategy, trading