Simple moving average (SMA)

Definition

The SMA is the arithmetic mean of the last N closing prices, recomputed each bar — the baseline trend-smoothing tool. Price relative to an SMA, SMA slope, and crossovers between two SMAs are the canonical trend-state definitions (trend_state, dist_sma_pct).

How it works / structure

• Formula: SMA_t(N) = (P_t + P_{t−1} + … + P_{t−N+1}) / N.
• Parameters (engine-executable): window N (common: 20/50/ 200-day), price input (close vs typical price), and the derived signals — price-vs-SMA state, SMA slope sign over k bars, fast/slow crossover pair (e.g. 50/200: the “golden/death cross” vocabulary).
• Properties: equal weighting makes it smooth but laggy — it responds to a shock N bars after entry AND exit of the window (the “drop-off” artifact: an old outlier leaving the window moves today’s SMA with no new information).
• Lag arithmetic: the SMA’s effective delay is ≈ (N−1)/2 bars — the cost paid for smoothness, and the reason crossover systems enter trends late by construction.

When it applies

Trend-state definition for regime filters (the platform’s trend_state uses SMA relationships), systematic trend entries (strategy-futures-trend-following MA variants), and as the mean in mean-reversion distance measures (strategy-mean-reversion, dist_sma_pct).

Risk profile & failure modes

• Whipsaw in ranges: crossover signals in sideways tape reverse repeatedly; the indicator has no range/trend awareness of its own — pair with a regime filter or accept the chop tax.
• Lag at turns: by the time a long SMA confirms, much of the move has passed; lag is structural, not tunable away (shorter N = less lag, more noise — the trade-off is the parameter).
• Round-number folklore: specific windows (200-day) carry self-referential lore; treat level effects as unproven unless cited.

Evidence & limits

Brock-Lakonishok-LeBaron (1992) found MA rules had predictive content on 90 years of Dow data — the study that legitimized academic testing of technical rules; Sullivan-Timmermann-White (1999) showed data-snooping adjustment weakens such results materially, and out-of-sample performance decayed post-1986. The honest summary: MA-defined trend states correlate with the documented time-series momentum effect; specific crossover timing rules are weak-to-unproven after costs and snooping.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X, above its rising 200-day SMA, will post a positive return over the next quarter” — falsified at horizon.
• “A 50/200 crossover system on universe U beats buy-and-hold after friction over this replay decade” — falsified by the paired replay.

Cross-references

• Weighted sibling: indicator-ema; derived: indicator-macd
• The effect it proxies: strategy-momentum (time-series)
• Platform bindings: trend_state, dist_sma_pct
• Method caveats: lens-technical (snooping, lag)