What 14 Million Tests Say About MACDE-mini S&P 500 FuturesCME_MINI_DL:ES1!EdgeToolsThis paper is the fourth in a series. The first study tested RSI across 26 million configurations and found zero Bonferroni-significant results. The second documented a small but genuine Turn of the Month anomaly, with 21 significant results from 385 tests. The third examined VWAP and produced the strongest findings so far: 150,546 Bonferroni-significant results concentrated in mean reversion, with short signal edge of 0.89 percentage points, roughly six times transaction costs. MACD was always going to be next. The Moving Average Convergence Divergence indicator is the second-most popular technical analysis tool after RSI, present on virtually every charting platform, explained in every trading course, and defended with religious fervor. It has also been defended, occasionally, in the academic literature. Brock, Lakonishok and DeLoach (1992) found some evidence for moving average rules on the Dow Jones Industrial Average. That paper has been cited over three thousand times and forms the intellectual scaffolding for every MACD apologist who claims institutional backing. We tested MACD more thoroughly than it has been tested before. 14,310,400 parameter configurations across eight distinct strategies, 20 assets spanning six categories, 436 valid parameter pairs, eight signal periods, and 26 holding periods. The same Welch t-test framework with Bonferroni correction used for RSI, Turn of the Month, and VWAP. The results are unambiguous. MACD generates 3,235 Bonferroni-significant results from over 14 million tests, of which 2,844 concentrate in a single strategy type, histogram divergence, on the short side. The overall mean long edge is +0.054 percentage points and the mean short edge is +0.018 percentage points. Both are economically negligible, falling well below transaction costs. The standard 12/26/9 setup, the configuration taught in every introductory course, produces zero Bonferroni-significant results. The line crossover, the most commonly used MACD signal, also produces zero. MACD joins RSI in the category of indicators that fail systematic testing. Unlike RSI, which produced absolutely nothing, MACD shows a faint statistical pulse in divergence signals. That pulse is too weak and too concentrated to constitute a trading strategy, but it exists. Whether it constitutes a genuine edge or a statistical artifact at the boundary of detection is a question the data cannot definitively resolve. 1. Introduction Gerald Appel introduced the MACD indicator in 1979 as a tool for identifying changes in trend momentum (Appel, 1979). The calculation is straightforward: take the difference between a fast exponential moving average and a slow exponential moving average of price, then smooth that difference with a third exponential moving average called the signal line. The difference between the MACD line and the signal line forms the histogram. Appel recommended the 12/26/9 parameterization, meaning 12-period and 26-period EMAs with a 9-period signal smoothing. That combination has since become one of the most widely recognized parameter sets in all of technical analysis. The indicator spread quickly through the retail community. By the 1990s, MACD was included as a default indicator on nearly every charting platform. Murphy (1999) dedicated an entire chapter to it in his standard reference on technical analysis. Elder (1993) featured it prominently in his trading methodology. Pring (2002) described it as one of the most reliable momentum indicators available to traders. These endorsements were based on observation, pattern recognition, and discretionary experience, not systematic statistical testing. The academic treatment of MACD has been more cautious. Brock, Lakonishok and DeLoach (1992) tested simple moving average rules on the Dow Jones Industrial Average from 1897 to 1986 and found some evidence of predictive content in moving average signals. Their results applied to simple moving average crossovers, not specifically to MACD, but the paper became the most frequently cited academic justification for MACD-type strategies. Sullivan, Timmermann and White (1999) subsequently re-examined these results using the bootstrap reality check methodology and found that after correcting for data snooping, the evidence weakened substantially. Lo, Mamaysky and Wang (2000) applied computational pattern recognition to technical analysis and concluded that some technical patterns contain genuine information, while cautioning that the magnitude was economically small after costs. Park and Irwin (2007) surveyed 95 studies of technical analysis profitability and concluded that the evidence was mixed, with earlier studies tending to find profitability and later studies, using more rigorous methodology, finding less. The academic literature on MACD specifically, as distinct from simple moving average rules, is thin. Most quantitative studies lump MACD into broader examinations of moving average rules without testing its specific strategy variants independently. This gap leaves the retail community relying on decades-old endorsements from practitioners rather than on direct statistical evidence. The present study fills that gap with what we believe is the most comprehensive systematic test of MACD strategies in the available literature: 14,310,400 parameter configurations tested with Bonferroni correction across a diversified asset universe. 2. What MACD measures MACD is built from three exponential moving averages. The MACD line equals the fast EMA minus the slow EMA: MACD line = EMA(close, fast period) minus EMA(close, slow period) The signal line smooths the MACD line: Signal line = EMA(MACD line, signal period) The histogram equals the difference: Histogram = MACD line minus Signal line When the fast EMA exceeds the slow EMA, the MACD line is positive, indicating that recent prices are higher than prices over the longer lookback. When the MACD line exceeds the signal line, the histogram is positive, indicating that the trend is accelerating. Traders interpret these relationships as momentum signals. The standard 12/26/9 parameterization uses alpha equal to 2/(n+1) for each EMA, giving the fast EMA a smoothing factor of approximately 0.154, the slow EMA approximately 0.074, and the signal line approximately 0.20. These are not derived from any optimization or theoretical framework. Appel (1979) selected them based on his visual examination of stock charts. The combination stuck because it was published first, not because it was demonstrated to be optimal. At its core, MACD measures the difference between two lagged representations of the same price series. Both the fast and slow EMAs are functions of past closing prices, weighted by geometrically declining coefficients. The MACD line captures the difference in how quickly these two representations respond to recent price changes. When price moves sharply, the fast EMA reacts first, creating a gap that the MACD line registers. The signal line further smooths this gap. The critical question is whether this double-differenced, triple-smoothed transformation of price adds information that the original price series does not contain. Moving averages are linear combinations of past prices. Taking the difference of two moving averages produces another linear combination of past prices. Smoothing that difference with a third moving average produces yet another linear combination. At every step, the input is price, and the output is a weighted average of past prices. No new information enters the calculation at any stage. This is the same structural problem documented in our RSI study. RSI computes a ratio of recent up moves to recent down moves, which is a nonlinear transformation of price, and still produces zero Bonferroni-significant results. MACD performs a purely linear transformation, which is theoretically even less likely to extract latent information. The question is whether the empirical evidence agrees with this theoretical expectation. 3. Common MACD strategies Retail MACD education centers on eight interpretive frameworks. Some are taught in every introductory course. Others appear in more advanced material. All eight are represented in our test battery. The line crossover interprets the MACD line crossing above the signal line as a buy signal and crossing below as a sell signal. This is the canonical MACD trade and the first strategy every tutorial teaches. The zero-line cross interprets the MACD line crossing above zero as bullish, meaning the fast EMA has overtaken the slow EMA, and crossing below zero as bearish. The histogram direction change interprets the histogram crossing from negative to positive as a buy signal and positive to negative as a sell signal. Because the histogram equals MACD line minus signal line, this is equivalent to the line crossover with one bar less lag. The histogram divergence compares price action with histogram behavior over a lookback window. When price makes a new low but the histogram does not, this is interpreted as bullish divergence. When price makes a new high but the histogram does not, bearish divergence. The price-MACD divergence is similar but compares price against the MACD line itself rather than the histogram. Price making a new low while the MACD line does not suggests weakening downward momentum. The histogram momentum strategy looks for three or more consecutive bars of increasing or decreasing histogram value, interpreting sustained directional movement in the histogram as acceleration in the underlying trend. The above-zero filtered crossover restricts the standard line crossover to signals occurring when the MACD line is above zero for longs and below zero for shorts. The logic is that a crossover above the zero line represents a stronger confirmation because it occurs within an established trend rather than against one. The histogram peak-trough reversal identifies local extrema in the histogram and enters when the histogram reverses from a peak or trough. A trough followed by a rising bar generates a long signal. A peak followed by a falling bar generates a short signal. None of these strategies has a theoretical derivation. They are all interpretive frameworks applied to a derived indicator, based on the assumption that various patterns in the MACD-signal-histogram relationship predict future price direction. The divergence strategies have the weakest theoretical basis of all, requiring price and momentum to disagree in a specific way and treating the disagreement as predictive. Whether any of them contain information is an empirical question. 4. Data and methodology 4.1 Asset universe We constructed a universe of 20 ETFs across six categories covering the major liquid segments of global financial markets. US large cap equities comprised SPY, QQQ, IWM, DIA, and VTI, providing exposure from the S&P 500 to the total market. Sector ETFs included XLF, XLK, XLE, XLV, and XLU, spanning financials, technology, energy, healthcare, and utilities. International equities included EFA and EEM, covering developed and emerging markets. Fixed income comprised TLT, IEF, and AGG, spanning long-duration treasuries, intermediate treasuries, and the aggregate bond market. Commodities included GLD, SLV, and USO, covering gold, silver, and oil. Real assets comprised VNQ and DJP, covering REITs and a broad commodity index. All data is daily, sourced from TwelveData with Tiingo as fallback, covering approximately 5,000 trading days per asset. 4.2 Parameter grid We tested the full practical range of MACD parameters: Fast period: 2 through 20 in steps of 1, giving 19 values. Slow period: 10 through 60 in steps of 2, giving 26 values. Valid parameter pairs require the slow period to exceed the fast period by at least 5, producing 436 valid combinations. Signal period: 3, 5, 7, 9, 12, 15, 18, and 21, giving 8 values. Holding period: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 30, 40, 50, 60, 75, 90, 120, 150, 180, and 252 trading days, giving 26 values from one day to one full year. The total configuration space is 8 strategies multiplied by 20 assets multiplied by 436 parameter pairs multiplied by 8 signal periods multiplied by 26 holding periods, equalling 14,510,080 target tests. After filtering for minimum data length and minimum signal counts, 14,310,400 valid test results remained. 4.3 Strategy implementation For each asset and parameter combination, MACD is calculated once using pandas ewm with adjust=False, which produces the standard exponential moving average with alpha equal to 2/(n+1). All eight strategies generate their signals from this single MACD calculation. Forward returns are computed as close-to-close returns over the specified holding period. This avoids look-ahead bias: the signal fires at bar t, and the return is measured from the close of bar t to the close of bar t plus the holding period. 4.4 Statistical framework Edge equals the mean forward return following a signal minus the mean forward return over all bars in the same asset sample. This baseline-adjusted approach ensures that a strategy in a rising market does not receive credit for beta. Significance is assessed using Welch's t-test for unequal variances. A minimum of 10 signals per configuration is required. Given 14,310,400 valid tests, the Bonferroni-corrected significance threshold at alpha equal to 0.05 is 3.49 times ten to the negative ninth power. Surviving this threshold requires a result so extreme that it would occur by chance fewer than once in 300 million tries under the null hypothesis. 5. Results 5.1 Aggregate findings Figure 1 presents the overall picture, and it is a quiet one. Mean edges cluster near zero for most strategies. No strategy produces mean edge exceeding 0.35 percentage points on either side. Histogram divergence and price-MACD divergence are the only strategies with visible positive bars on the long side. The annotations beneath each strategy name show Bonferroni-significant test counts, and most read zero. Across all 14,310,400 tests, mean long edge is +0.054 percentage points and mean short edge is +0.018 percentage points. Both figures are below the 0.10 to 0.15 percentage points required to cover round-trip transaction costs for liquid ETFs. Even if these edges were statistically robust, they would not survive implementation. Figure 2 decomposes by asset category and shows that the weak aggregate results are not masking strong effects in subgroups. US equities show the most positive numbers: long edge +0.209 percentage points and short edge +0.128 percentage points. But even these figures are marginal relative to transaction costs and do not achieve significance after Bonferroni correction in the vast majority of configurations. 5.2 Statistical significance Figure 3 maps the parameter space. The heatmap is dominated by colors near zero, with no clearly defined region of strong positive or negative edge. The standard 12/26 position sits in an unremarkable part of the landscape, neither at a local optimum nor at a local minimum. There is no hidden sweet spot that traders are missing. The parameter space is uniformly mediocre. Figure 4 examines whether edge develops at longer holding horizons, as it did for VWAP mean reversion. The answer is no. Long and short edges show no consistent monotonic pattern across holding periods. Some strategies show mild positive edge at very long holding periods above 120 days, but the effects are small, inconsistent across strategies, and could plausibly reflect equity risk premium rather than MACD signal content. Figure 5 shows the p-value distribution. Under the null hypothesis, p-values distribute uniformly. The observed distribution is close to uniform, with a mild excess at low values that is much less pronounced than the sharp spike documented in the VWAP study. The excess represents the 391 long-side and 2,844 short-side Bonferroni-significant results. These are not zero, which distinguishes MACD from RSI, but they are not the kind of departure from uniformity that characterizes a robust indicator. 5.3 Results by strategy Histogram divergence is the only strategy with a meaningful number of significant results. Of 1,788,800 histogram divergence tests, 255 long signals and 2,844 short signals survive Bonferroni correction. Mean long edge is +0.323 percentage points, mean short edge is +0.102 percentage points. The long edge is above transaction costs. The short edge is not. The mechanism behind histogram divergence is that price makes a new low over a lookback window while the MACD histogram does not. This is interpreted as weakening selling pressure. The data suggests this interpretation has some validity: when selling pressure weakens as measured by the histogram failing to confirm a price low, subsequent long returns are modestly above baseline. The effect is real in the statistical sense of surviving strict correction. Whether it is robust enough to build a strategy around is another question: 255 Bonferroni-significant long results from 1.79 million tests is a survival rate of 0.014 percent. Price-MACD divergence produces 136 Bonferroni-significant long results with mean long edge of +0.347 percentage points. This is structurally similar to histogram divergence but uses the MACD line itself rather than the histogram. The slightly higher mean edge and lower survival count suggest a less consistent but occasionally stronger signal. Line crossover produces zero Bonferroni-significant results from 1,788,800 tests. The canonical MACD trade, the one drawn first on every tutorial chart, has no statistical support. Zero-line cross produces zero Bonferroni-significant results. The idea that the fast EMA overtaking the slow EMA predicts future returns is not supported. Histogram direction change produces zero Bonferroni-significant results. This is equivalent to the line crossover with slightly different timing, and the data treats them identically: both fail. Histogram momentum produces zero Bonferroni-significant results. Three consecutive bars of histogram acceleration predict nothing. Above-zero filtered crossover produces zero Bonferroni-significant results. Adding a trend filter to a crossover that does not work does not produce a crossover that works. Histogram peak-trough reversal produces zero Bonferroni-significant results. Identifying local extrema in the histogram and trading the reversal generates random outcomes. Figure 7 presents the complete numerical summary. Six of eight strategies produce zero Bonferroni-significant results. The two that produce significant results, histogram divergence and price-MACD divergence, account for a total of 3,235 significant tests from 14.3 million, a rate of 0.023 percent. For comparison, VWAP mean reversion alone produced 100,765 significant results from 1.68 million tests, a rate of 6.0 percent. 5.4 Results by asset category US equities show the strongest effects: long edge of +0.209 percentage points and short edge of +0.128 percentage points. This is consistent with US equities being the most liquid, most traded, and most studied market, where any residual signal is most likely to appear. International equities show modest long edge of +0.028 percentage points but more interesting short edge of +0.193 percentage points. Sector ETFs show positive long edge of +0.134 percentage points with short edge near zero. Commodities show negative edge on both sides: long negative 0.175 percentage points and short negative 0.180 percentage points. This means MACD signals applied to commodity ETFs actively destroy value on both the long and the short side. The commodity result is consistent with the lack of volume-based microstructure dynamics in commodity ETFs, where price movements are driven by supply-demand fundamentals rather than by institutional execution patterns. Fixed income shows mildly negative edge on both sides. Real assets show negligible edge in both directions. 5.5 The standard 12/26/9 setup Figure 8 isolates the question every MACD user wants answered: is the standard setup at least better than the average parameter combination? From 4,160 tests using exactly the 12/26/9 parameterization, mean long edge is +0.060 percentage points and mean short edge is negative 0.012 percentage points. Bonferroni-significant results: zero on both sides. The violin plots show the 12/26/9 distribution sitting squarely in the middle of the full parameter distribution. It is not worse than average. It is not better than average. Appel's original recommendation, selected from visual chart examination in 1979, performs almost exactly at the median of the parameter space. There is no hidden better combination waiting to be discovered either: the best mean long edge across all parameter combinations is +0.656 percentage points (price-MACD divergence, fast=20, slow=26, signal=3), which sounds like progress until you realize it is a mean across 20 assets and 26 holding periods and that the best-looking aggregate can easily emerge from random variation when 3,488 parameter triplets are evaluated. 6. Comparison with previous studies Four indicators, 46 million tests, one consistent framework. The scoreboard: RSI: zero Bonferroni-significant results from 26 million tests. The most popular technical indicator generates random output. Turn of the Month: 21 Bonferroni-significant results from 385 tests. A small test universe with a real effect driven by identifiable institutional flow cycles. VWAP: 150,546 Bonferroni-significant results from 5.8 million tests. Mean reversion short signals deliver 0.89 percentage points of edge, roughly six times transaction costs. A genuine, economically meaningful finding with a clear microstructure mechanism. MACD: 3,235 Bonferroni-significant results from 14.3 million tests. Concentrated in histogram divergence with mean long edge of +0.323 percentage points. Marginal relative to transaction costs. No strategy variant approaches the economic significance of VWAP mean reversion. The pattern that emerges across these four studies is now well established. Price-only transformations, RSI and MACD, fail. Both indicators take closing prices, apply mathematical operations, and return a derived series that contains no information beyond what the original price series already carried. The EMAs in MACD are linear weighted averages of past prices. Their differences are linear combinations of linear combinations. No transformation in this chain can create information that the input did not contain. Volume-incorporating indicators, specifically VWAP, succeed. VWAP integrates volume with price and thereby accesses information about market participation that price alone does not capture. The institutional execution patterns around VWAP create genuine supply-demand dynamics that a price-only indicator cannot detect. Calendar effects, Turn of the Month, succeed because they proxy for institutional flow patterns anchored to economic payment cycles. The information comes from the calendar, not from price. The lesson is consistent: indicators predict when they access information beyond the price series. Indicators that merely transform price cannot create information the price did not already contain. This is not a philosophical position. It is a consistent empirical finding across 46 million tests. 7. Why MACD fails and why divergence partially survives 7.1 The mathematical constraint MACD is a linear function of past prices. The fast EMA, the slow EMA, the MACD line, the signal line, and the histogram are all linear combinations of the same closing price series with different weighting schemes. In the framework of Lo, Mamaysky and Wang (2000), the question is whether the specific weighting scheme applied by MACD isolates information that raw price data obscures. For linear filters applied to the same underlying series, the answer is generally no. A linear filter can redistribute information across frequencies but cannot create it. The EMA emphasizes recent prices relative to older prices. The MACD line computes the difference between two such emphases. The result is a signal that is correlated with recent price momentum but carries no independent information about future returns. This is different from VWAP, which multiplies price by volume before averaging. That multiplication introduces a genuinely new data dimension. MACD multiplies price by nothing except predetermined decay weights that are functions of the chosen period parameters. 7.2 Why divergence is different Histogram divergence and price-MACD divergence are structurally different from the other six strategies because they compare two separate quantities: price level and an oscillator derived from price. When price makes a new low but the histogram does not confirm that low, the signal is detecting a nonlinear discrepancy between raw price and the smoothed momentum measure. This is a second-order relationship that goes beyond the simple linear filtering of the crossover strategies. The divergence detection involves comparing local extrema in two different series, a comparison that introduces a nonlinearity the other MACD strategies lack. Price can make new lows while smoothed momentum improves because the rate of decline is slowing even as the level continues to fall. This is economically interpretable: weakening selling pressure before a price reversal. The divergence signals survive Bonferroni correction, but barely. 255 long and 2,844 short results from 3.58 million divergence tests is a survival rate of 0.087 percent. For context, VWAP mean reversion produces a survival rate of 6.0 percent, roughly 70 times higher. The divergence effect is real in the statistical sense but sits at the edge of what can be confidently distinguished from multiple testing artifacts at this scale. 7.3 What Brock, Lakonishok and DeLoach actually found The most cited academic defense of MACD-type strategies is Brock, Lakonishok and DeLoach (1992), who tested simple moving average crossover rules on the DJIA from 1897 to 1986. Their results showed buy signals following moving average crossovers generated higher returns than sell signals. Three qualifications limit the applicability of those results to modern MACD trading. First, the study tested simple moving averages, not exponential moving averages with a signal line. MACD's triple-EMA structure is a more complex filter than anything Brock and colleagues examined. Second, the study used a single asset, the DJIA, over a single period. Sullivan, Timmermann and White (1999) applied the bootstrap reality check to an expanded set of technical trading rules and found that after correcting for the full universe of rules that could have been tested, the significance of the best-performing rule was substantially reduced. Third, the study period ended in 1986. Markets in 1986 were structurally different from markets in 2026: spreads were wider, execution was slower, algorithmic trading was non-existent, and information dissemination operated on fundamentally different timescales. A moving average rule that exploited slow information diffusion in 1960 would face a radically different environment today. Our results on 14.3 million tests across 20 assets and 40 years of more recent data find no support for MACD crossover strategies. This is not inconsistent with Brock and colleagues finding weak support for simple moving average rules on one asset ending in 1986. It simply means that any signal that may have existed has been arbitraged away, or that it was specific to the asset, period, and methodology of the original study. 8. Implications For traders using MACD crossover: 1,788,800 configurations tested. Zero Bonferroni-significant results. This is the same outcome as VWAP crossover and the same outcome as RSI in general. Crossover strategies applied to momentum oscillators do not predict future returns. The consistency of this null result across three independent indicators tested in three separate studies suggests that the finding is not specific to any one indicator. It is a property of crossover signals derived from price transformations. For traders using MACD divergence: the data shows a statistically real but economically marginal effect. Histogram divergence long signals average +0.323 percentage points, which exceeds transaction costs but only modestly. The effect concentrates in specific assets and parameter combinations rather than being broadly available across the universe. A trader who restricts MACD usage exclusively to divergence signals on US equities with carefully selected parameters might extract a small positive edge. Whether that edge justifies the complexity of implementation relative to alternatives such as VWAP mean reversion, which delivers nearly three times the edge with 70 times the significant configurations, is a question of opportunity cost. For systematic strategy developers: MACD does not belong in the toolbox as a primary signal generator. The 14.3 million tests produce no evidence of consistent, economically meaningful prediction from any MACD strategy variant. This does not preclude MACD as a filter or auxiliary input in a broader system, but the data does not support building a strategy around MACD signals. Resources allocated to MACD-based strategy development would generate substantially higher expected returns if redirected to VWAP mean reversion or calendar-based approaches. For trading educators: the standard MACD curriculum, centered on line crossovers and the 12/26/9 setup, teaches strategies that have been tested across 14 million configurations and produce nothing. If MACD must remain in curricula for completeness, the honest presentation would acknowledge that crossover signals have no statistical support, that the 12/26/9 setup is no better than the median parameter combination, and that the only variant with any empirical basis is divergence, which even then produces marginal edge. Teaching the standard MACD crossover as a viable trading strategy is, at this point, not supported by the evidence. 9. Limitations Several constraints bound the conclusions. First, this study tests daily data only. MACD behavior on intraday timeframes was not examined. The VWAP study showed that timeframe matters substantially, and it is possible that MACD performs differently on 4-hour or weekly data, though there is no theoretical reason to expect it would. Second, we tested MACD in isolation. Some practitioners combine MACD with other indicators, support and resistance levels, or fundamental filters. These combinations were not evaluated. It is possible that MACD contributes useful information as one component of a multi-factor system even though it fails as a standalone signal, though the same could be said of any random variable. Third, the divergence lookback was fixed at 14 bars. Variable lookback periods for divergence detection might produce different results. Fourth, execution was assumed at bar close. Real execution involves slippage that would further reduce the already-marginal edge values. Fifth, this study does not test whether MACD had predictive value in earlier historical periods that has since been arbitraged away. It is possible that MACD signals were informative in the 1980s and 1990s when markets were less efficient and algorithmic trading did not exist. That hypothesis is not testable with the data horizon available. References Appel, G. (1979). The Moving Average Convergence-Divergence Trading Method. Signalert Corporation, Great Neck, NY. Appel, G. (2005). Technical Analysis: Power Tools for Active Investors. Financial Times/Prentice Hall, Upper Saddle River, NJ. Brock, W., Lakonishok, J. and DeLoach, S. (1992). Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance, 47(5), pp. 1731-1764. Elder, A. (1993). Trading for a Living: Psychology, Trading Tactics, Money Management. John Wiley and Sons, New York. 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