A Look Back at the Performance of the Holy Grail

Originally Published March 20, 2012 in Advisor Perspectives

Back-tested results often look good on paper because stellar performance could have come from curve-fitting. If that were the case, then my "Holy Grail" model would not have withstood the test of time. But in the 32 months that have passed since its publication, investors who heeded its advice would have outperformed the market on a risk-adjusted basis.

I presented my Holy Grail model in a three-part series entitled Moving Average - Holy Grail or Fairy Tale (Part 1, Part 2, and Part 3) nearly three years ago. Let’s review the rationale behind my methodology, how the Holy Grail works and the out-of-sample results since its publication.

The Holy Grail is not market timing

Academically cited, empirical evidence has traditionally favored buy-and-hold over active or tactical investment strategies. That evidence shows that no one beats the market in the long run. But this conclusion is only correct if “the long run” means from the 1940s to the 1990s, the period over which most of this research was conducted.

The problem is that this conclusion was biased by the highly skewed data. This period encompassed two spectacular bull cycles (1940 to 1966 and 1982 to 1999). A more appropriate conclusion would have been, "buy-and-hold works in bull markets." The “Holy Grail” method captures as much of the bull markets as possible, while avoiding the worst of bear-market cycles. As a result, it outperforms buy-and-hold on a risk-adjusted-return basis in both bull and bear markets.

Market timing is generally misconstrued as synonymous with forecasting market turning points. By this definition, I am not a "market timer." I cannot anticipate market turning points in advance. My notion of market timing is similar to atmospheric monitoring. We do not need to forecast the weather in advance, but we must be observant of ever-changing weather patterns and be ready to act accordingly. To detect and track weather changes, meteorologists use temperature gauges, barometers, and computer models. To monitor investment climate, I use market-timing models. 

As a technical timing model, my Holy Grail model does not offer predictions. It follows price trends. In future articles, I will present other types of timing models that are driven by fundamental, macroeconomic, cyclical, and seasonal factors. These environmental gauges enable one to better assess the investment climate.

How the Holy Grail model works

My Holy Grail model is a six-month exponential moving-average crossover (EMAC) system. I use Professor Robert Shiller’s S&P 500 data series as the signal generator, because it has a long history dating back to 1871 and because it is accessible to the public. My Holy Grail model turns bullish when the Shiller S&P 500 crosses above its six- month EMA and bearish when it crosses below. When the model turns positive, one invests in the S&P 500 total-return index and collects dividends; when it turns negative, one sells the S&P 500 and puts the proceeds in cash. For a detailed description of my model, please refer to the three-part series to which I linked in the introduction.

It is not my intention to promote the Holy Grail as a trading tool; past performance cannot be assumed to prevail in the future. The Holy Grail is used as a counterexample, to disprove the claim that buy-and-hold is the only logical investment strategy. Holy Grail proves that one can beat the market by following trends, not by predicting market turning points.

Two refinements

After my 2009 articles, I received excellent feedback from many readers. Two of their suggestions are incorporated in this update. The Shiller Index I used previously was based on the monthly average of the daily close of the S&P 500 and, as such, it was not a tradable vehicle. My first refinement was to use the S&P 500 monthly close prices from Ultra Financial dating back to 1942 in performance calculations. Prior to 1942 (when Ultra’s data was not available), performance was calculated with the Shiller Index. The second refinement involved the sales proceeds. Instead of cash, the proceeds after all sell signals were placed in 90-day Treasury bills from 1934 to present and in the 10-year Treasury bonds prior to 1934.

Updated results from 1871 to 2012

The Holy Grail signals over the entire 140-year span are shown graphically in Figure 1. Green segments depict periods when the Shiller Index was above its six-month EMA, while pink signifies periods spent below that average. The blue line in Figure 2 shows the cumulative value of a portfolio following my Holy Grail model, and its value is based on three contributing factors: capital gains from the Holy Grail's buy signals, dividend reinvestment while in the markets, and proceeds from Treasury bills following the model's sell signals. 

A $1 investment in 1871 would have soared to $1.3 million by February 2012, a compound annual growth rate (CAGR) of 10.6% (this strategy is depicted by the blue curve). By comparison, $1 bought and held with dividend reinvestment (the orange curve) reached only $164,000 over the same period, a CAGR of 8.9%. That is a 162 bps gap in annual rate-of-return over the 140 years.

Besides higher returns, the Holy Grail model also offered significantly lower risk (volatility) measured by standard deviation. The annualized standard deviation of the Holy Grail system was 10.5%, a whopping 500 bps less volatile than buying and holding, which yielded a 15.3% standard deviation.

The Holy Grail diminished what would have been devastating losses from bear markets and allowed profits to run during bull markets, achieving the two most essential objectives in money management: capital preservation in bad times and capital appreciation in good times. 




Out-of-sample results from June 2009 to February 2012

How has Holy Grail fared in the current decade-long secular bear market, and – even more importantly – how has it done in the 32 months since its publication? Figure 3 updates the Holy Grail signals from June 2000 to February 2012, with a blue arrow to mark the month when Advisor Perspectives first published the Holy Grail.

All signals to the right of the marker represent out-of-sample data, including current results. If the promising historical back-test performance was merely a product of curve fitting, the results of the out-of-sample data should be noticeably worse.

There were two mini-bear markets during the 32-month out-of-sample period, one in 2010 and one in 2011. The Holy Grail sidestepped both of them. It did not sell at the peaks, but then a trend-following system is not expected to do that. The Holy Grail simply continued to offer downside risk protection and preserve principal through bad times. 




Figure 3 also demonstrates that the Holy Grail strategy accomplished its second objective, staying in the game in good times. Buy signals did not coincide with market bottoms, but once the rallies were confirmed buy signals followed. The latest buy signal came in December 2011, just before the January/February surge intensified.

Figure 4 compares the cumulative results of the Holy Grail over this period to those of the S&P 500 total-return index with dividend reinvestment. Each of the two strategies was assumed to begin with $1,000 in January 2000. Again, the blue arrow depicts the out-of- sample period. Holy Grail not only avoided both the dot-com crash and the sub-prime meltdown, it also softened the blows of the 2010 and the 2011 market corrections. Since June 2009, the CAGRs for the Holy Grail and buy-and-hold were 15.3% and 18.4%, respectively. The Holy Grail offered a much lower annualized standard deviation of 11.3% than the S&P 500’s 15.8%. Thirty-two months of live performance demonstrates that this simple trend-following system continued to add value. 




A disciplined approach to investing

How does one go about building timing models that monitor the investment climate? To begin answering that question, let’s begin by identifying the factors that underlie the Holy Grail model’s success. The Holy Grail is a technical model that follows price trends, but these features also apply to other tactical models that monitor seasonal, sentiment, macroeconomic and fundamental statistics. The common attributes shared by all working models are:

Simplicity: Moving-average crossover is the simplest system one can employ. In systems engineering design, the number of potential failure modes linked directly to the complexity of the system. In modern physics, simplicity and elegance are accepted as important contributors to proofs of concepts. Time and again, complex models may show great promise, but it is the simplest, most elegant systems that ultimately prove to have lasting relevance.

Commonsense rationale: Following market trends appeals to one’s common sense. All reliable models anchor on sound logic. Simplicity without rationale is naive. The Super Bowl Barometer may be simple and even look good statistically, but there is no logic behind it. Good models do not require the support of advanced theories or intricate algorithms, but they must have a cause-and-effect rationale.

Rule-based clarity: The buy/sell rules of Holy Grail are black-and-white. Being simple and logical would not be enough. The rationale must yield clear, actionable rules. If we cannot write buy/sell rules that a computer could compile, we do not have a rule-based model. Objective, quantitative models have no room for interpretation or ambiguity. The signals are either positive or negative, without qualifiers, provisos, or exceptions.

Sufficient sample size: The Holy Grail was tested over 140 years – a more-than- adequate sample size. Contrast this sample with that supporting the claim that "no one beats the market in a long run." If researchers extended their database beyond the study period of 1940 to 1999, they would have come to my conclusion: "buy-and-hold has only worked in bull markets."

Adequate data: Similarly, because the study period on which my evidence rests includes multiple bull and bear cycles, it represents an appropriate pool of underlying data on which to base conclusions. An example of inappropriate data would be the all-too-common practice of applying economic theory to the Great Recession using data from the post-WWII recoveries. The Great Recession was a balance-sheet recession that paralleled only the Great Depression. All other post- WWII recessions were business-cycle recessions. They were two different beasts.

Having simple, rule-based models that rely on common sense with ample and appropriate supporting data is only half the battle. The real challenge lies in execution. President Reagan's approach to the Soviet Union was "trust, but verify." If we anchor our trust on simple, logical and objective timing models, we can boldly pull the execution trigger.

Timing models are tools. Discipline in executing them makes money. Ned Davis, in his book Being Right or Making Money, confessed that his biggest flaw as a money manager was that he tended to let his personal ego affect his market view. What was his remedy? He entrusted his market view to mathematical timing models. The strict discipline they offered allowed him to take an objective approach, while avoiding the fool’s errand of trying to “beat” the market on guesswork alone.

With the right tools, Davis was able to see past the conventional academic wisdom that buy-and-hold is the only option. Are you? 


Moving Average: Holy Grail or Fairy Tale – Part 3

Originally Published July 28, 2009 in Advisor Perspectives

“If there was ever a good time to consider a new investment approach,” an advertisement for a mutual fund company proclaimed in a recent issue of a financial planning magazine, “it’s when the old ones have proven so fallible.” For a second, I thought that they had finally given up on the tired buy-and-hold (B/H) approach. It turned out they were just promoting a new kind of index fund.

Buy-and-hold remains deeply entrenched in the financial planning community, despite many of the flaws my previous articles have illustrated. Although many financial advisors suffer dearly from their B/H practices, they are reluctant to change their approach. Who dares to challenge investment sages like Bogle, Siegel, and Malkiel who emphatically support this long-standing investment principle? Academic research studies overwhelmingly endorse B/H. How can they all be wrong?

Perhaps the investment scholars and researchers are right to advocate B/H, but for the wrong reason, as I will explain later. But first, let me digress to respond to some of the feedback my previous articles received.

Let’s be clear

I am gratified to learn that many readers are able to replicate my results. My research is only credible if it passes peer reviews. A couple of readers, however, had difficulty reproducing my exact numbers. I use Professor Robert Shiller’s S&P500 Index primarily because his data is accessible to the public, so that my calculations can be checked. But Professor Shiller creates his monthly index by averaging daily closing prices. If you use actual daily or monthly closing prices, you will get different results.

Several analysts also inquired about the actual implementation of the Moving Average Crossover (MAC) system. For the record, it is not my intention to promote the MAC system as a trading tool. There are many trading systems used by active managers with proven track records. I use MAC as a demonstration to challenge the popular notion that no one can beat the markets in the long run. In science, it only takes one counterexample to invalidate a principle, no matter how well-established it might be.

Establishing a way to implement active investment management systems into a business practice exceeds the scope of my articles. For those planners new to the field of rule-based trading systems, my advice is to work with a reputable active investment firm or to use experienced consultants. It’s not a do-it-yourself project.

Let’s revisit market history

Implementation considerations aside, let’s turn to a more detailed analysis of the MAC system, and see how it compared to B/H pre- and post- the Great Depression, as well as during each of the last 14 decades.




The effectiveness of the 6-month MAC system is illustrated graphically in Figure 1. I present the 138-year history into two plots of seventy years each for better visual clarity. All the buy and sell signals are superimposed on the S&P500 Index in two colors. The red segments (sell) depict periods when the Index was below its 6-month moving average; and the green (buy), above. The blue curve shows equity accumulation from three contributing factors: capital gains resulting from MAC transactions, reinvestment of dividends while in the markets, and capital preservation in cash while out of the markets. A $1 investment in 1871 would have soared to $332,000 in June 2009. By comparison, $1 invested under the B/H approach with dividends reinvested earned only $105,000 over the same period. Note that without reinvesting dividends a $1 investment in the S&P500 Index itself only returns $211 (from $4.44 in 1871 to $938 in June 2009).

A tale of two periods




As we have seen, the 1929 crash gives MAC an advantage over B/H as seen in Figure 1. Several readers wanted to know how MAC would have fared if we removed the one- time impact of the Great Depression. In Figure 2, I show two separate investments with $1 each at the beginning of the two seventy-year periods. From 1871 to 1940, the B/H strategy returned 100-fold and MAC beat it by a factor of five, primarily a result of side- stepping the Great Depression. From 1941 to June 2009, without the impact of the Great Depression, both systems gain 1,000-fold and tie at the end. However, B/H outperforms MAC for most of the seven decades. So you may say that B/H is indeed unbeatable, if bear markets like the Great Depression, the Oil Embargo of 1974, the 2000 Internet Bubble, and the 2008 Sub-prime Meltdown can all be ignored. B/H can be considered as a bull market Holy Grail.

Dissecting the decades 

Let’s examine market history in a different light. In Part 2, I compared MAC’s monthly and annual performance to that of B/H. MAC beat B/H on both counts. But by looking at monthly and even yearly perfromance you could miss the forest for the trees. Examining decadal performance, thought, one gains new insight from a longer-term perspective.




Figure 3 shows Compound Annual Growth Rate (CAGR) by decade. The 138 years cover fourteen decades. The upper graph compares B/H to MAC. The lower graph is more instructive, as it shows the net CAGRs (MAC minus B/H). Out of fourteen decades, B/H outperforms MAC in only six, and by small margins. Five of those six decades occurred after 1941. In those decades when MAC outperforms B/H, the margins are quite significant. Finally, for more than a century, the current decade is the only one that B/H has shown a loss, although the current decade is not over yet.

The Emperor has no clothes! 

I mentioned earlier that researchers are right to endorse B/H, but they do so for the wrong reason. They are right that B/H has an impeccable track record over six decades. But they are wrong to declare B/H as the best way to invest at all times. B/H underperfomed more than half of the time in 138 years. They are also wrong when they justify their argument with theories such as the Modern Portfolio Theory and the Efficient Market Hypothesis. The markets were quite efficient during all bear markets so why didn’t B/H work then? History and simple logic tell us why B/H didn’t work in many decades before the ’40s, why it has worked for so long after the ’40s, and why it has stopped working since 2000. You don’t need advanced economic theories to explain the obvious.

After World War II, the West, led by the United States, unleashed the power of the free market system. Capitalism fueled technological innovation, which in turn bolstered global economic expansion. As a result, the stock markets enjoyed the most powerful and the longest advance in human history. The unprecedented secular bull markets skyrocketed 1,000-fold and lasted six decades. All academic research sudies focused on this post-WWII era naturally concluded that no one can beat the markets. The efficient market theories had little to do with B/H’s success. The B/H strategy was the Holy Grail simply because of the secular bull markets.

Then came 2000. The markets tumbled and B/H faltered. Researchers who clung to six decades of flawless records with a seemingly sound theoretical underpinning were perplexed. Since bull markets always returned in the past, they waited, only to get hit again in 2008. They continue to hold, wait, and hope.

As an engineer surrounded by financial scholars and investment geniuses, I feel like the little boy watching the naked Emperor in the parade. I point out the obvious with no fear of embarrassing myself. President Clinton once said, “It’s the economy, stupid!” I holler, “It’s the bull markets, Professors!” The truth is that B/H works wonders during economic expansions, but it underperforms during economic slowdowns or contractions. If there were no bear markets, B/H would indeed be the Holy Grail!

Diversification in time

The Modern Portfolio Theory tells us not to put all your eggs in one basket. The B/H strategy calls for holding all your eggs in one continuous “basket” of time. That sounds like a risky proposition to me. Market timing is not witchcraft. It reduces risk through temporal diversification. There are times to hold, and there are times to fold.

Active investment management with market timing works not by forecasting the future, but by following major market trends. By way of example, let me illustrate how the 6- month MAC system described in Part 1 and Part 2 realizes temporal diversification. Figure 4 shows the difference between $1 investments in B/H and in MAC made in

January 2000. How have the two systems performed through the 2000 Internet Bubble and the 2008 Systemic Meltdown, to June 2009? I’ll let you be the judge. The MAC system doesn’t predict the markets, it follows the trends. It doesn’t sell at peaks or buy




at bottoms. But it’s effective in preserving wealth in bear markets and accumulating wealth in good times.

Now you know why the B/H strategy that worked so well in the past has proven so fallible since 2000. The question is whether you believe the secular bull of the past is likely to return after the current recession is over. If you think that the next decades will not match the good fortune of the post-WWII era, you should start looking for an alternative investment approach.


UPDATE: Read the original Advisor Perspectives replies to this article.



Moving Average: Holy Grail or Fairy Tale – Part 2

Originally Published June 16, 2009 in Advisor Perspectives

Prominent Nobel laureates in economics often point to a large body of evidence that supports the Efficient Market Hypothesis (EMH), which states that no one can beat the markets over the long haul. Many renowned financial experts further declare that passive investing in a diversified index like the S&P500 is the only sensible way to manage money. I respect their opinions but I am unable to verify their claims. By examining the evidence, I show that the Moving Average Crossover (MAC) system offers a superior risk-return profile to a buy-and-hold strategy.

I tested the simplest form of active investing, the MAC system, against a buy-and-hold approach on the S&P500 total return index from January 1871 to April 2009. With no data mining or systems optimization, such that anyone analyzing the same S&P500 database would have made the same investment decisions, this basic trend-following system beats the markets.

“How dare you challenge the Canon of Finance with such heresy as ‘beating the markets?’” the experts are sure to respond.

I must have found the Holy Grail, or else the buy-and-hold logic is flawed!

Before I continue, let me recap my key findings in Part 1. I tested different moving average lengths from 2-months to 23-months. By comparing the results of the best of class (6-months) and the worst of class (23-months) to those of the buy-and-hold benchmark, I can make an objective assessment on the MAC system as a whole relative to the markets.

MAC performances that beat the buy-and-hold benchmarks are in green; those that don’t are in red. 




CAGR is the Compound Annual Growth Rate. Terminal Equity Value is how much $1 invested in January 1871 would grow to at the end of April 2009. Risk-adjusted return is the average annualized monthly return divided by the standard deviation of annualized returns. Drawdown is the percentage decline in equity value from its recent peak.

Aggregate versus periodic performance

The table above compares aggregate performance over 138 years. But aggregate results are not the only information pertinent to investing. You want to know periodic performance as well. For example, how did the systems perform during bear markets? How often and how brutally did the markets turn against you when the systems told you to stay the course? What were the monthly, annual, and decadal performances?

Bear market risks

Let’s first find out which system protects us better from the wrath of bear markets. Three growth curves are shown in Figure 1. The red one is the buy-and-hold benchmark. The 6- and 23-month MACs are shown by the blue and the green curve, respectively. 




Each curve represents how an initial investment grows over time. A smooth and rising curve is preferred. All three investors invested $1 in the S&P500 total return index in January 1871. The buy-and-holder reinvested his dividends at all times. The two active investors reinvested dividends only when the S&P500 index was above its moving average but otherwise kept the proceeds in non-interest bearing cash.

Figure 1 not only shows which investment wins the race in wealth accumulation (6- month MAC), but also graphically illustrates how the three systems play out in historical bear markets. MACs won’t get you out at every market peak, but they would have preserved some – if not most – of your accumulated wealth. In contrast, passive advisors willingly handed over their clients’ hard-earned money to every hungry bear they encountered! Worse, by the time a passive investor realizes that a bear is eating his lunch, his strategy calls for him to do nothing to try to stanch his losses, lest he miss the market’s rebound. Don’t laugh! That’s the passive experts’ “Missing out” logic!

Market exposure risks

Full market exposure is risky – even during bull markets – because it increases the risk of drawdown. There is a material difference between actual loss and drawdown. Actual loss is painful but the healing process begins as soon as the investor realizes the loss. 

Drawdown, on the other hand, is like an open wound. It represents the pain of holding stocks when the markets turn against us. The pain continues to grow with every additional price decline. Exposure to uncertain and unfriendly markets is more harmful to investors’ mental health than actual loss is to their wallets.

Both the duration and the magnitude of drawdown for the two MAC systems are shown in Figure 2. The blue stripes are the 6-month MAC and the green are the 23-month. The average drawdowns for the two systems are 2 and 4 percent, respectively. Drawdowns of greater than ten percent were rare during the 138-year period. In comparison, the average drawdown of the buy-and-hold system was a painful 26 percent. 




Figure 2 shows that the MAC system would never expose investors to an unfriendly market for more than a few months at a time. On the contrary, buy-and-holders could be underwater for over ten or even twenty-five years before breakeven, as shown in Figure 5 in my “Missing out” article. The mental anguish of suffering in a hostile market environment for such a prolonged period of time is unimaginable.

Active investments offer much lower market exposure risks than the buy-and-hold approach, both in magnitude and in duration of drawdown. Which camp would you rather join? 

Annual performance tradeoffs

Markowitz’s Efficient Frontier is an instructive way to compare monthly performance because it shows risk-reward tradeoffs on a single diagram. Figure 3 shows annualized monthly returns (reward) versus standard deviations of annualized monthly returns (risk). To keep the graph legible, I show only the 6-month MAC (green squares) against the buy-and-hold (red squares) benchmark. 




The Efficient Frontier lies at the top-left portion of the graph where most green squares reside. This means that MAC’s annual returns are generally higher than those of buy- and-hold at the same level of risk. The undesirable portions of the graph (bottom and right) are mostly occupied by red squares. All except one of the extremely high volatility years are in red. If Markowitz favors investments at the Efficient Frontier, then he would surely prefer the MAC system to the buy-and-hold approach.

Doesn’t Modern Portfolio Theory call for absolute correlations between return and risk? Hence any investment offering high returns with low risks must be flawed. On the contrary, Modern Portfolio Theory does not postulate that high intrinsic risks are an inherent characteristic of high-return investments. Rather, it simply points out that rational investors would logically ask for additional risk premium to compensate for the extra risk they are taking. The performance of the MAC system is theoretically sound.

Based on the risk-and-return tradeoffs presented in Figure 3, no rational investor would subscribe to the buy-and-hold scheme as it offers no adequate risk premium to compensate for its enormous volatilities.

Monthly performance comparisons

The monthly performance comparisons between the MAC and the buy-and-hold method are best illustrated with a histogram. Again, I show only the 6-month MAC to keep the graph legible. The horizontal axis in Figure 4 shows different increments of monthly percentage change. The vertical axis tabulates the number of occurrences of each of these increments in 1,659 months. 




On the positive-return side of the distribution, green squares capture all the winning months of the markets, including the few unusually strong rallies of 10 to 30 percent. When the markets are bullish, the MAC system does not miss the best months.

On the negative-return side, there is a sizable gap between the two systems. The MAC system is able to elegantly sidestep the markets during most of the losing months. Proceeds from all these bad months are safely kept in cash as reflected by the single green square floating at the very top of the vertical axis. Many red triangles suffer worse than fifteen percent losses, while green squares rarely incur losses of more than five percent.

Figure 4 illustrates graphically how the 6-month MAC system beats the markets. There is no fairy tale if a system can consistently avoid the losers but stay with the winners 1,659 times over 138 years.

Holy Grail or fairy tale?

I am not trying to persuade anyone that the MAC system is the Holy Grail. Indeed, I discovered MAC’s limitations when evaluating its decadal performances, which I will discuss in Part 3. Stay tuned!

What I have tried to convey is that all claims should be treated as hypotheses until they are proven by objective evidence - even a claim as sacred as the eminent passive investment doctrine. Perhaps the generally accepted buy-and-hold investment principle is only a fairy tale! 


UPDATE: Read the original Advisor Perspectives replies to this article



Moving Average: Holy Grail or Fairy Tale – Part 1

Originally Published June 16, 2009 in Advisor Perspectives

Buying and holding a diversified portfolio works well during good times, but falls short when supposedly uncorrelated asset classes drop in unison in bear markets. Are there alternative investment strategies that work for all seasons? The 10-month Moving Average Crossover (MAC) system is a solid candidate, as it sidestepped two recent bear markets in 2000 and 2008. But did it work in previous bear markets? Is 10 months the optimum length?

Let’s examine historical evidence to find out if MAC is the Holy Grail or just a fairy tale.


Electrical engineers routinely use moving average as a low-pass filter in analog and digital signal processing. It blocks transient perturbations from the input and only allows the core signals to pass, hence the term low-pass filter. Transient perturbation is a fancy name for short-lived popcorn noise that obscures the underlying signal.

Random spikes in an otherwise smooth signal are undesirable. We can reduce the amplitude of these noisy spikes by averaging the values of the data points neighboring on either side of the spike. Figure 1 shows how the filtered output closely tracks the original signal but the unwanted spikes are attenuated. The degree of noise suppression depends on the number of points used in the averaging. The longer the averaging period, the smoother the output. Because we can’t predict when random spikes will appear, we slide the filter block across the entire data stream from start to finish. The term moving average literally describes this function.


mac_part1_fig1-2   As an engineer, I have always been skeptical of the way stock market technicians plot MA curves. Traditionally, engineers align the midpoint of the MA curve with the center of the original data curve. This way, the MA curve is centered with respect to the original time series as shown by the red curve in Figure 2. Technicians, on the other hand, shift the end of the MA curve to match the most recent price point as shown by the blue curve in Figure 2. The lag between the original data curve and the shifted MA curve created by this peculiar plotting convention is the core of the MAC system. Without shifting the MA, there is no lag. Without the lag, there is no crossover.

The Moving Average Crossover system

MAC is the simplest and probably the oldest trading system. You buy when the price rises above its moving average, and you sell when it drops below. Although there are several forms of moving averages, I prefer the Exponential Moving Average (EMA) to the Simple Moving Average (SMA) because EMA gives slightly smaller lag.

My assumptions

To keep things simple, I made three assumptions:

  1. All proceeds after sales are kept in non-interest-bearing cash.
  2. No transaction fees.
  3. No taxes.

The first assumption penalizes MAC in favor of buy-and-hold. Parking proceeds in Treasury Bills would obscure the central focus of my study because short-term interest rates varied widely throughout history.

The second assumption has a small positive bias toward MAC. But fees on index funds and ETFs (which I assume, for the purpose of my analysis, have been around since the Civil War) are less than 10 basis points and will not significantly affect my results.

I exclude tax effects for several reasons. First, tax rates vary with income levels. Second, top marginal tax rates changed dramatically in the past 138 years, from below ten percent before 1910 to above ninety percent in the 1950s. Third, buy-and-holders are not exempt from tax; tax payments are merely deferred. When they eventually sell their holdings, their entire cumulative gains will be taxed. Ignoring taxes is a balanced compromise, and does not give the MAC system an unfair advantage.

I will revisit the fee and tax assumptions after presenting my results.

Let the contest begin: MAC versus buy-and-hold

To compare performance between MAC and buy-and-hold, I used Compound Annual Growth Rates (CAGRs) and 138 years of monthly data for the S&P500 total return index (with dividend reinvestment) from 1871 to 2009. I examined a wide range of MA lengths, from two to twenty-three months.

The buy-and-hold benchmark returned 8.6 percent over this period, and is represented by the red bar in Figure 2. The green bars represent the CAGRs for different moving average lengths. CAGRs below 11 months consistently beat buy-and-hold. Above that, they reach diminishing returns. The quasi bell-shaped curve suggests that the distribution is not random.




Figure 4 provides even more compelling support for the MAC system. I calculated risk- adjusted returns using the ratio of CAGR to its standard deviation, measured monthly from January 1871 to April 2009. Standard deviation of returns is a generally accepted measure of risk. By this definition, the MAC system beats buy-and-hold hands down across all MA lengths. The stability in risk adjusted return performance and their insensitivity to the MA length show that MAC is a robust system.

Standard deviation treats both up and down volatility as risk. Judging from the “missing out the best days” argument buy-and-holders embrace, I presume that

they don’t consider upside volatility as risk - only downside volatility. A more relevant measure of downside risk is equity drawdown. Drawdown is the percentage decline from the most recent equity peak. There are two ways to evaluate drawdown: average drawdown and maximum drawdown. Figures 5 and 6 respectively show the results of the two methods.




If you don’t view price surges as hazardous and consider only price plunges as risky, then you surely won’t care for the buy-and-hold approach. Buy-and-hold delivers a whopping negative 85 percent maximum drawdown, courtesy of the Super Crash from the 1929 peak to the 1932 trough. Even the average drawdown is a painful negative 26 percent. In comparison, the maximum drawdown for MAC is only negative 15 percent and the average drawdown is no worse than negative 4 percent.

I ignored both transaction costs and taxes, so now let’s check on these assumptions. Figure 7 shows the number of round-trip trades (from buy to sell) for the different MA lengths. The average is 0.38 trades per year, or one round-trip every 2.6 years. Even with the 2-month MA, MAC generates only 0.9 round-trip per year, or a holding period of 1.1 years. The low trading frequency of MAC not only keeps transaction costs low, but lowers the tax rates from ordinary income rates to long-term capital gain rates.



Have we found the Holy Grail?

Based on aggregate performance over the entire 138-year period, the MAC system beats buy-and-hold in both abosulte performance and risk-adjusted return. Have we indeed found the Holy Grail that works for all seasons? To find out, stay tuned for Part 2, in which I examine MAC and buy-and-hold on a monthly basis and by decade to see how they compare in all bull and bear markets since 1871.


UPDATE: Read the first set of original Advisor Perspectives replies to this article.

UPDATE: Read the second set of original Advisor Perspectives replies to this article.