Moving Averages: SMA and EMA

A moving average converts a price series into a smoother reference series. A common input is the close, but other inputs are possible. State the input, number of periods and chart interval: a 20-period average on a weekly chart differs from a 20-day average.

An n-period SMA gives each of the latest n observations weight 1/n. On the next observation, the oldest value leaves the window and the newest enters.

The SMA’s update depends on the entering and leaving prices. A change in its slope need not mean the latest price alone changed sharply.

An EMA updates its previous value using the new price and a smoothing coefficient. Under a common convention, α = 2/(n + 1). The recursive weighting declines geometrically as observations age.

This lesson seeds the first EMA with the average of the first n closes, on observation n. Later values use the recurrence. Some software starts from the first price or uses an adjusted weighting method. Those choices can produce different early values, so document the seed and warm-up history when comparing outputs.

Neither average must always lie closer to the latest close or turn first on every possible path. The EMA’s faster typical response is a weighting property, not a universal ranking of every observation.

The row-6 result corresponds to observation 5 because row 1 is a header. Store outputs as formulas if students will edit the prices; cached values alone will not recalculate.

A close above a rising average describes a different state from a close above a falling average. Use both location and slope alongside the wider chart. Being above the 200-day average alone does not formally establish a bull market, and a close below it does not mechanically establish a primary reversal.

A bullish price crossover occurs when price moves from at/below the selected average to above it. A bearish crossover reverses that relation. Compare consecutive observations; “price is above the average” describes a state, not necessarily a new crossing event.

A commonly taught golden cross occurs when the 50-day SMA crosses above the 200-day SMA. A death cross is the reverse. Specify whether SMA or EMA is used. These are delayed trend signals, and a strategy must define execution, position size and exit rules separately.

In a daily-close backtest, a signal using the final close becomes known at that close. Model an achievable execution time rather than silently assuming an earlier fill.

Traders sometimes watch pullbacks near a rising average or rallies toward a falling average. These are dynamic reference areas that can fail. The selected period should follow an explicit method rather than be chosen after observing which line price respected.

See support, resistance and role-reversal diagrams →

A whipsaw is a signal that reverses quickly, such as price crossing above a moving average and soon falling back below. Sideways fluctuations can generate repeated crossings and costs. A shorter period typically follows prices more closely but can produce more frequent signals.

Match the period to a stated purpose, then test stability over multiple periods and market conditions. A single best historical parameter can reflect overfitting.

Use identical data, corporate-action treatment, starting dates and execution assumptions. Include the warm-up period, turnover, fees, slippage, drawdowns and a relevant benchmark. Separate parameter development from out-of-sample evaluation and distinguish missing observations from genuine trading sessions.