Standard Deviation as a Risk Gauge

[Fairman]

Standard Deviation as a Risk Gauge

Standard deviation is a measure of how widely values spread around their average. Applied to price changes, it quantifies volatility, and gives a statistically grounded way to think about expected movement.

To compute daily volatility, take the daily percentage changes over a period, such as the last 20 days, and calculate their standard deviation. If it equals 0.5 percent, a typical daily move is about half a percent. Roughly two-thirds of days fall within one standard deviation of the average if returns were normally distributed, and about 95 percent within two. Real markets have fatter tails, so extreme moves occur more often than the normal curve suggests.

You can annualize the figure by multiplying by the square root of trading days, about 16 for a daily to annual conversion with 252 days. A daily deviation of 0.5 percent corresponds to about 8 percent annualized, which is typical for major currency pairs.

Uses include setting stops and targets in terms of expected movement, scaling position sizes inversely to volatility, and judging whether a move is unusual. A candle of three standard deviations is rare and often attracts attention.

Bollinger Bands and ATR are related tools, each with slightly different calculation.

Remember that volatility changes over time and clusters, with quiet and active periods.

Practical step: compute the 20-day standard deviation of daily returns for your pair, and convert it to pips at the current price.

[Fairman]

The fat tails point is important for risk. A three standard deviation day happens a lot more often in currencies than the bell curve says, so don't size as if it's a once a decade event. Under a normal distribution, a three sigma day should show up roughly once every year or so of trading days. In practice, major pairs tend to produce several of them a year, usually around central bank surprises, big data misses or sudden risk off moves. So when you check what a bad day could cost, use the biggest real moves from the last couple of years on your pair, not the textbook number. The real history is always a bit uglier.

[Fairman]

Converting the number to pips makes it much more practical. Then you can compare it directly with your stop and see if your stop is inside normal noise. Example: if the 20 day standard deviation on EURUSD is 0.45 percent and the price is 1.10, one standard deviation is about 50 pips a day. On a 15 minute chart you'd scale that down a lot, but the idea is the same. If your stop is smaller than the typical movement over the time you expect to hold the trade, you're likely to get stopped by noise. That's a useful sanity check before you blame your entries for every stop out.