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Moving-average-crossover strategies have worked out very well in recent years. They prevented their followers from being invested in equities during the tech bubble and the financial crisis. Nevertheless, most of those strategies have underperformed the broad equity market since 2009. In this article, I will analyze all possible moving-average-crossover signals for the S&P 500 since 1928, to see if these strategies provide any value for investors.

### Introduction

Mebane Faber’s 2007 paper “A Quantitative Approach to Tactical Asset Allocation“ has become quite popular among the investment community. In this paper, he demonstrated that a very simple 10-month moving average could be used as an effective investment strategy. To be more precise, Faber used a 10-month moving average to determine if an investor should enter or exit a position within a specific asset class. When the closing price of any given underlying closes above its 10-month moving average (10 months is approximately 200 trading days), the investor should buy, and when the price closes below the 10-month moving average, the investor should sell. As this strategy has worked out very well in the past and is very easy to follow, many investors have adopted similar moving-average-crossover strategies for their personal portfolios. A lot of articles have been published about how to apply or improve on Faber’s ideas.

Another famous moving-average-crossover pattern is called the "golden cross." It occurs when the 50-day moving average of a specific underlying security crosses above its 200-day moving average. The claim is that this signifies an improvement in the underlying trend structure of any given security. Investors should move into cash if the golden cross turns into a "death cross," in which the 50-day moving average crosses below the 200-day moving average. Within the last decade, most of those moving-average-crossover strategies have worked out very well, as shown in the chart below. This was mainly because those moving average strategies prevented their followers from being invested in equities during the tech bubble and the financial crisis.

Nevertheless, most of those crossover strategies have underperformed the broad equity market since 2009, as shown in the chart below, where the payoff from the golden cross since 2009 is depicted. This was mainly because we have not seen any longer-lasting downturn since then.

The recent underperformance of such strategies is not a big surprise at all, as all trend-following strategies are facing the typical “late in, late out” effect. Therefore, such an approach can only outperform a simple buy-and-hold strategy during longer lasting bear markets. However, many investors try to avoid the typical late-in-late-out effect by choosing shorter moving-average combinations, which has, of course, the negative effect of increased trading activities.

Despite the fact that those moving-average-crossover signals are quite popular, I have not found any research paper that evaluates all possible moving-average-crossover combinations to determine whether such strategies provide any additional value for investors.

### Methodology

Let’s analyze all possible moving-average-crossover signals for the S&P 500 from Dec. 31, 1928, until June 11, 2014, to get an unbiased view of the pros and cons of such crossover signals. In addition, I would like to determine if the recent underperformance of those crossover signals compared to a simple buy-and-hold strategy is typical or just a temporary phenomenon. Moreover, I would like to find out if the outcome of a specific crossover strategy tends to be stable or more random in its nature. For simplicity, I have assumed a zero nominal rate of return if a specific strategy was invested in cash. Moreover, in our example there is no allowance for transaction costs or brokerage fees.

### Results

In the following charts I analyze different kind of key metrics (z-axis), and the time frame for each single moving average is plotted on the x and y axis, respectively. For example, the key metric for the golden cross strategy (50:200) can be found if you search the crossing point of the 50 day moving average (x-axis=50) and the 200 day moving average (y-axis=200). I tested all combinations of lengths (in days) of moving averages crossing over one another.

All moving crossover strategies provide some form of maximum loss reduction. If we consider the fact that the biggest decline from the S&P 500 was 86% during the 1930s, the main advantage of such strategies become quite obvious.

In total, there were only three combinations of days (70/75, 65/80 and 70/80) that faced a maximum loss exceeding the maximum loss from the S&P 500. All other combinations faced losses less than a typical buy-and-hold strategy. Especially in the range from 50/240 days to 220/240 days, the maximum loss ranged between -40% and 060%, which is quite an encouraging ratio if we consider the 86.1% from the S&P 500. Moreover, as we can see that in that region, this drawdown reduction was or tends to be quite stable over time — this area can be described as a plateau. If this effect was a random variable within that specific time range, there would have been many more spikes in that area. Therefore, small adjustments within the time frames of any moving average are likely to have not a big impact at all, regarding to this ratio. The case is quite different if we analyze the area around 1/100 days to 1/200 days. In that area, small adjustments within the time frame of each moving average could lead to quite different results and are therefore highly likely to be random.

Another typical relationship is that as the number of trades increases, both moving averages become shorter. This, of course, is due to transaction costs. For that reason, most followers of such a strategy prefer a combination of short-term-oriented and long-term-oriented moving averages to reduce the total number of trades.

If we focus on the annualized performance of those moving-average-crossover signals since 1929, we can see that all combinations delivered a positive return since then. This outcome is not a big surprise at all, as the S&P 500 has risen by nearly 8,000% since then. Therefore, any continuous participation within the market should have led to a positive performance.

Another interesting point is the historical ability of those crossover signals to outperform a simple buy-and-hold strategy. In the second graph, we only highlighted those moving-average-crossover combinations that have been able to outperform a buy-and hold-strategy. We can see that the best combination (5/186) was able to generate a yearly outperformance of 1.4% on average, with no transaction costs included. Nevertheless, we can see a lot of spikes in that graph. Most outcomes are highly likely to be random by their nature. For example, the 5/175 combination delivered a yearly outperformance of 1.3% on average, while the 10/175 crossover outperformance was only 0.3% and the 20/175 underperformed the market by almost 0.5% on average.

Therefore, the outperformance of most crossover signals depends on pure luck. The case is slightly different if we focus on the area between 1:100/ 200:240, as all combinations in that range managed to outperform the S&P 500. The outperformance was quite stable over time, as small adjustments within the timeframe of each moving average did not lead to big differences in terms of outperformance. Nevertheless, the yearly outperformance in that region was only 0.58% on average. Please bear in mind that I have not included any transaction costs in our example.

### Generating absolute returns

Outperformance is just one side of the story. Investors might be also interested in generating absolute rather than relative positive returns. I looked at the ability of any moving-average-crossover combination to generate absolute positive returns. I analyzed how many signals of each moving-average-crossover combination were profitable in the past, expressed in percentage terms. A lot of combinations delivered long signals, which have been profitable more than 50% of the time. The area around 50/120 days to 200/240 days tends to be pretty stable, as the percentage of absolute positive signals is slowly increasing to the top. It looks like some moving-average combinations have the ability to forecast rising markets.

Unfortunately, this does not hold in most cases, as the percentage of absolute positive signals strongly depends on the number of days each moving-average combination was invested in the S&P 500. This becomes quite obvious if we consider that the S&P 500 has risen slightly less than 8,000% since 1929. Any exposure to the market in that time period is highly likely to produce a positive return! This effect can be seen on the second graph below, which shows the average long-signal length of each moving crossover combination, measured in days. If we compare both graphs, we can see a strong relationship between the average signal length and the percentage of positive performing signals. Nevertheless, some combinations tend to be better suitable for catching a positive trend than others.

As any moving-average combination could only outperform the market during a longer-lasting downturn, it is also interesting to examine how often a cash signal (negative crossover signal) was able to outperform the market. In such a case, the S&P 500 must have performed negative during that specific time period. The ratio can be also seen as the probability that a bearish crossover signal indicates a longer-lasting downturn. As you can see in the graph below, the S&P 500 performed negative in less than 50% of all cases after any moving-average-crossover combination flashed a bearish crossover signal. In addition, the graph is extremely spiked, indicating that this poor outcome tends to be completely random.

### The bottom line

Despite the fact that most moving-average-crossover signals provide some form of maximum loss reduction in comparison to a buy-and-hold strategy, their ability to outperform the underlying market is limited. Furthermore, the recent underperformance of such crossover signals since 2009 is a typical phenomenon rather than a temporarily one. This is because a negative crossover signal does not necessarily predict significant and longer-lasting downturns, or bear markets. Nevertheless, if investors are more focused on maximum draw-down reduction, such crossover signals are worth looking at, though they should definitely not be the sole source of information.

*Paul Allen is the head of quantitative/technical market analysis of **WallStreetCourier.com**, an independent research- and investment advisor for selected stock market information.*

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