Average Daily Move

Average Daily Move is the arithmetic mean of absolute close-to-close daily returns. It answers a simple question: over this period, how much did the asset's closing price move on an average day, regardless of direction?

A +2% day and a -2% day both count as a 2% move. Direction is removed before the values are averaged.

The formula

Start with daily simple returns:

$$r_t = \frac{P_t}{P_{t-1}} - 1$$

Then take the absolute value of each daily return and calculate the arithmetic mean:

$$\text{Average Daily Move} = \frac{1}{T}\sum_{t=1}^{T}|r_t|$$

Where:

• $P_t$ is the closing price on day $t$.
• $r_t$ is the close-to-close daily simple return.
• $T$ is the number of daily return observations in the period.

If the daily returns were +2.0%, -1.0%, +0.5%, and -3.0%, the Average Daily Move would be:

$$\frac{|2.0| + |-1.0| + |0.5| + |-3.0|}{4} = 1.625\%$$

Mean, not geometric mean

Average Daily Move uses an arithmetic mean, not a geometric mean.

Geometric means are useful when returns compound over time. This metric is not trying to measure compounded growth. It is measuring the average magnitude of one-day moves after direction has been removed.

Mean vs median

We use the mean because large jump days matter when you are asking how much an asset moved on average. A few unusually large days should pull the number higher because those days were part of the experienced price path.

Median daily move is a different, useful companion metric. It answers a slightly different question: "what did a more typical day look like?" The median is less affected by outliers, but it also downplays jump risk. If Gale Finance shows both in the future, Average Daily Move should be read as the average realized movement, while Median Daily Move should be read as the typical day.

Average Daily Move vs volatility

Average Daily Move is not the same as volatility.

• Average Daily Move measures the mean absolute size of daily close-to-close moves.
• Volatility measures the standard deviation of signed daily returns around their average.

Both are useful. Average Daily Move is easier to explain to readers. Volatility is the standard statistical input used in Sharpe ratio, Sortino ratio, risk models, and portfolio sizing.

For a return distribution centered near zero, Average Daily Move will often be lower than one-standard-deviation daily volatility. Under a perfectly normal zero-mean distribution, the average absolute move is about $\sqrt{2/\pi}$ of the standard deviation, or roughly 80%. Real markets are not perfectly normal, so this is only intuition, not a conversion rule.

Average Daily Move vs ATR

Average Daily Move is also not the same as Average True Range (ATR).

ATR uses high, low, and close data to estimate the trading range within each period. Average Daily Move uses closing prices only. It does not know whether an asset traded far above or below the close during the day.

If you want to say "the closing price changed by X% per day on average," Average Daily Move is appropriate. If you want to measure intraday trading range, ATR is the better metric, but it requires OHLC data.

How to interpret it

If an asset has a 1.8% Average Daily Move over a one-year period, the plain-English reading is:

Over this period, the asset's closing price changed by about 1.8% per day on average.

That does not mean tomorrow's move is expected to be 1.8%. It is a historical period statistic, not a forecast.

Limitations

• It uses daily closes only, so it ignores intraday highs and lows.
• It is not directional: +3% and -3% count the same.
• It is sensitive to outliers because it uses the mean.
• It does not describe tail risk by itself. Pair it with max drawdown, Value at Risk, and Expected Shortfall when downside behavior matters.