The Magic of the Moving Average

I can no longer count the times I have heard the words, moving average, golden cross, death cross and MACD (moving average convergence divergence) on financial TV of late. Sue “explained” the move up in gold was due to a signal from the MACD indicator, while Carter Worth, Fast Money Halftime and others repeated, “Now it’s all about whether the S&P closes above or below the 200-day – about 1115.”
The moving average crossover has seen spectacular resurrection as a trading signal:

  • Euro to Reach 11-Week High Against Yen on Golden Cross
    Europe’s currency is likely to extend last month’s 4.3 percent rally versus the yen to at least the 100-day moving average of 116.74 yen, a level that capped its gains after a previous golden cross was triggered in April, Ng said. The golden cross occurred on July 27, when the 20-day moving average passed above the 50-day moving average, according to data compiled by Bloomberg.
  • The Death Cross, or, Questioning What You Read
    It is fairly simple to test this thesis that “moving averages no longer work since 1990?. Below is a chart of the S&P500 total return vs a timing system that uses the simple 50/200 day SMA crossover mentioned in the article. The portfolio moves into a Vanguard Bond mutual fund when not on a buy signal. Transaction costs and taxes are ignored. As you can see, the conclusions the professor has made are somewhat curious. It looks like timing improves every metric from CAGR to vol and maximum drawdown reduction. It also looks like the timing model did an impressive job of sidestepping two devastating bear markets and the psychological damage that causes.
  • The Death Cross
    This ominous-sounding event occurs when the 50-day moving average crosses under the 200-day, and to some technicians it signals the start of a long-term bearish bias.
  • Death Cross in S&P 500 May Not Lead to Rout
    Since 1970, death crosses in the stock index preceded an average decline of 0.4 percent in the next month and three- and six-month gains of 2.5 percent and 4.8 percent, respectively, according to the Montreal-based brokerage. Eleven of the 21 occurrences preceded a one-month rally, the firm found.
  • The kiss of the death cross
    It turns out that the death cross has had a mediocre track record at best over the last two decades. To be sure, it’s had some great recent successes — such as the one that occurred in December 2007, very early in the 2007-2009 bear market. But there have been a number of other failures — such as one that occurred in October 2005, in the middle of the 2002-2007 bull market.
  • Investment Strategy – “Don`t Worry, Be Happy” Analyst(s): Jeffrey D. Saut
    August 4, 2010: The call for this week: Since the SPX’s rally began in early July I have suggested the first upside challenges would come at the 50-DMA (currently at 1081.54) and then the 200-DMA (currently at 1114.37). The 50-DMA indeed took some time to surmount. Last week the 200-DMA also proved difficult to surpass. Nonetheless, I think it will eventually be breached to the upside, bringing into view the June reaction high of 1131. As the Lowry’s organization opines, “In summary, as the major price indexes have moved sideways since the May 25th low, market conditions have showed clear signs of strengthening, not weakening. While overbought readings on short-term indicators suggest the potential for a near-term pullback, any decline should act only as a temporary setback in the rally from the July 2nd low and is unlikely to represent the next leg of a more prolonged move lower.” Plainly I agree . . .

A moving average is nothing more than the average of a series of prices. The uninformed investor or trader does not know that this technique is from a discipline called time series analysis. Defined by the U.K. Office for National Statistics,

A time series is broadly defined as a series of measurements of a variable taken at regular time intervals.
. . .
The information provided by any time series can be used as input for further analysis through time series modelling. There are two main goals of time series modelling. Firstly, it is used to identify and formalise the dynamic behaviour observed in time series data. This is known as time series estimation.
. . .
Secondly, it is used to predict the future values of time series variables. This is known as time series forecasting. Time series forecasting is based on the idea that the past behaviour of a variable may continue into the future. Consequently, current and past data may provide useful information for predicting future values.
. . .
Time series models can be broadly grouped into two categories: univariate and multivariate time series models.
Univariate time series models focus on a single variable. Their goal is to identify and estimate the relationship between the current value of a variable and its own past values.

In short, it’s forecasting the future based on current and past numbers. In Time-Series Forecasting [DOWNLOAD PDF], Christopher Chatfield wrote:

[Univariate methods are particularly appropriate when there is a large number of series to forecast, when the analyst’s skill is limited or when multivariate methods require forecasts to be made of explanatory variables.
. . .
[I]t is important to distinguish between a forecasting method and a model. A model is a mathematical representation of reality, while a method is a rule or formula for computing a forecast. The latter may, or may not, depend on a model. Arising from this distinction, we look in turn at univariate forecasting methods based on fitting a univariate model to the given data . . . and then at intuitively reasonable, but essentially ad-hoc, computational procedures. These two types of method are quite different in character.

Note Chatfield’s distinction between a forecasting method and a model. Uninformed traders are using moving averages as a forecasting method even though there is no reason to believe stock price behaviour can be modeled as a moving average process. For more information, see Introduction to Time Series Analysis, in particular, Univariate Time Series Models.
But let’s not stop here. I found a paper — written by a CFA no less — that comes up with a theoretical foundation for the moving average as a model of asset prices. Click the Open in New Window button to launch a full-size version.
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To use Mordecai Kurz’s Theory of Rational Belief as a basis for price movements that can be traded with moving averages is one of the most bizarre claims I have come across in a long time.

Can you see the fallacy of the arguments found in the articles featured on this page? If anyone wants to spot them, I’m game. Just post your comments below.
RELATED: Because They Only Worked by Coincidence


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  1. “According to RBE, cycles emerge in asset markets whenever the mistakes we make as investors become correlated.” Well, if it’s the case, I would use a mean-reverting rather than a momentum-based system such as the MAC.
    Second: the article dismisses the following statement “why should anyone expect the MAC System to be effective in the future just because it worked during a small sample period of (ahem) 137 years?” Which begs the question: how do you differentiate skill vs. luck if you don’t have some kind of an explanation for the results of a given strategy. This is at odd with the scientific method: 1) ask a question, 2) do background research, 3) construct a hypothesis, 4) test the hypothesis, 4) analysis the data and draw conclusions. This article tackles the problem from the wrong end: 1) draw a conclusion, 2) fit whatever theory to explain your observation.

  2. I took the easy one. I found the five differences in the Pirate flags. The other is too hard but can we say all crossing theories, etc. to a degree may cause the correlation of beliefs and thus cause the incorrect pricing making us suspecious of magnitude of price change after one occurs. We had a death cross this summer and it did not turn out to be nearly as bad as the consensus (correlated) view of S&P well below 1000 (yet). Should the correlated thinking have made us suspecious?

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