Research

Moving-average indicators are ubiquitous in practice but usually collapse price behavior into directional crossover events, discarding the dynamics of displacement from trend. This paper introduces Moving Average Distance (MAD), a novel displacement indicator. MAD measures the signed percentage distance between price and a moving-average reference; standardizing it by a trailing volatility estimate yields a series comparable across time. The standardized series is recast as a regime process by discretizing it into six ordered states. On this foundation, the MAD-Markov Model provides an interpretable semi-Markov framework for forecasting regime transitions. Analysis of the regime sequence reveals that dwell times are not memoryless: the hazard of leaving a regime declines with time already spent, a duration dependence that a first-order Markov chain cannot represent. The central result is that the continuous position of price within its current band—information the discrete chain discards—conditions the direction of the next transition in a strong, monotone, and well-calibrated manner. On 26 years of daily S&P 500 (SPY) data, this relationship replicates across three independent market eras and produces out-of-sample transition probabilities that lie on the calibration diagonal, improving Brier score and log-loss over a memoryless base-rate chain by approximately 10%. The contribution is an interpretable, calibrated model of how displacement regimes form, persist, and give way.

A companion study, the MAD-Markov Model, established that a security’s continuous position within its displacement band forecasts the direction of its next regime transition in a strong, monotone, and well-calibrated manner; it stopped short of asking whether that structure can be traded. This paper extends the work from forecasting to trading, and profitability hinges on a distinction the forecast never required: whether displacement is changing because price is moving, or because the average is catching up to it. A first-order decomposition separates each change in Moving Average Distance (MAD) into a price-driven component and a moving-average artifact. The composition inverts with position in the band. Deep-oversold “improvements” are roughly two-thirds artifact, and at the re-crossing of the trend the ratio flips—roughly two-thirds genuine price movement. That decomposition converts directly into a signal. Gating trend re-crossing entries on price dominance beats each name’s own buy-and-hold, measured per day of capital deployed and gross of costs, on 59.8% of 672 point-in-time S&P 500 constituents (2016–2025, delisted members included) against 55.8% for the ungated rule (paired test, p = 0.021). On the index, an anticipatory variant that enters below trend, before the re-cross confirms, outperforms three decades of buy-and-hold on deployed capital (13.4% versus 10.9% annualized; in-trade Sharpe 0.74 versus 0.65) while invested 69% of days. The companion’s calibrated transition forecast adds nothing beyond identifying the state. The composition and timing of the entry, not the forecast, carry the signal.

Two companion studies established that a security’s displacement from its moving average carries structure. Position within the displacement band forecasts the direction of the next regime transition; the composition of a displacement change—price moving versus the average catching up—converts into a tradeable entry gate. This paper asks the question both results imply: taken together, as position and velocity, what kind of object are displacement dynamics? Each security is embedded in the phase plane of standardized displacement and its five-day change, and every statistic is tested against autoregressive surrogates matched to the series’ own persistence. The answer arrives in two halves. The orbit’s geometry is unremarkable—its size and preferred radius are exactly what calibrated linear mean reversion produces. The traffic on the orbit is not. The circulation is clockwise, time-irreversible, and asymmetric; the rising and falling branches of the mean cycle fail to mirror one another (p < 0.005), irreversibility appears at two distinct timescales with opposite sign, and the asymmetry holds in both halves of three decades of SPY. Across 715 point-in-time S&P 500 constituents and 2.9 million daily observations, one flow field fits the whole universe—disjoint random halves of the cross-section yield fields with cosine similarity 0.99, the field is equally stable across decades, and 90% of individual names carry the same positive loop asymmetry where matched surrogates split evenly. Displacement dynamics evolve on a shared, stationary surface whose shape linear models explain and whose flow they cannot.

Three companion studies developed and validated a trading signal built on Moving Average Distance—the percentage displacement of price from its 20-day average, standardized by trailing volatility—evaluating it one security at a time on unconstrained capital. This paper addresses the portfolio problem that design leaves open. Applied to 728 point-in-time S&P 500 constituents over 2016–2025, the gated entry generates a median of twelve simultaneous candidacies per signal day and exceeds the capacity of a concentrated book on 95% of days, so realized performance is determined largely by selection among simultaneous candidacies. Selection rules are evaluated in three stages: a cross-sectional ranking study over 42,340 resolved signal trades; nested scoring models fit strictly walk-forward; and dollar simulations under realistic execution, judged against matched random-selection envelopes and against capitalization-weighted (SPY) and equal-weight (RSP) index controls, with January 2022–December 2025 reported separately as the primary out-of-sample evidence. Trailing returns exhibit no predictive content for signal outcomes at any horizon examined; a displacement-based filter previously used in live trading selects no better than random draws; and fitted models attain the highest trade-level information coefficients but trail the unfitted volume rank in dollar simulation at every book size. The most robust selector is daily trading volume (monthly-mean t of 4.2 and 5.5 on its two statistics): conditional on a signal firing, heavily traded names earn materially more per trade over comparable holding times. The resulting estimation-free rule—eligibility restricted to the 100 highest-volume names, candidates accepted in volume order, ten equal slots—compounds $100,000 to $552,888 over 2016–2025 (18.7% annualized, Sharpe 0.90) and is the only simulated configuration whose confirmation window exceeds its full window: 19.7% annualized, Sharpe 0.97, and a −19.1% maximum drawdown, versus 9.5% annualized for SPY and 4.2% for RSP on the same dividend-free basis. All results are walk-forward, and all headline numbers reproduce from fixed seeds.