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Turning Five Returns Into a Volatility Estimate

Daily percentage changes of a pair over five days: plus 0.3, minus 0.2, plus 0.5, minus 0.4, plus 0.1.

Compute the standard deviation. Mean: the sum is 0.3, so the mean is 0.06 percent. Deviations from the mean: 0.24, minus 0.26, 0.44, minus 0.46, 0.04. Squares: 0.0576, 0.0676, 0.1936, 0.2116, 0.0016. Sum: 0.532. Divide by n minus 1, which is 4: 0.133. Square root: about 0.365 percent.

The daily volatility is about 0.37 percent. Annualize by multiplying by the square root of 252, roughly 16: about 5.8 percent. That is in the range typical of major currency pairs.

What can you do with it? On a pair at 1.1000, one standard deviation is 0.365 percent, about 40 pips. So a move of 40 pips is an ordinary day. A 120-pip day is three standard deviations, which would be rare if returns were normal, though real markets have fat tails.

Use it to judge targets. A 20-pip scalp target is half a standard deviation, plausible within hours. A 150-pip swing target is almost four standard deviations of one day, so it needs multiple days.

Five data points are far too few for a reliable estimate. Use 20 or more for practical purposes.

The exercise shows how simple volatility is: a spread measure of recent changes.

Try this: compute the 20-day standard deviation for your pair and convert it to pips.

Nice walk through. One caution on annualising with square root of 252: it assumes the daily returns are independent. FX returns are close to that, but volatility clusters, so five days is a very noisy estimate. The real annual volatility could easily be half or double the 5.8 figure.

For practical use, 20 or 60 days gives a more stable number, and many people prefer an exponentially weighted estimate that reacts to recent changes but does not jump around as much as a 5 day sample.

A pair that averages five ticks per second doesn't produce five ticks every second. The ticks arrive in bursts: nothing for 800 ms, then twenty in 200 ms.

These microbursts come from the way the market works. A single large order triggers a cascade of quote updates from many providers. Algorithms react to each other, producing a flurry that lasts a fraction of a second.

For a scalper, microbursts determine what's possible. An order sent during a burst meets a rapidly changing price. The fill might be 0.4 pips away from the quote seen when clicking. An order sent between bursts sees a stable price.

Backtests that assume uniform time can't capture this. A simulation might say a stop was hit at a certain price, when in reality the burst jumped over it.

Analyzing tick data for burst structure, such as the distribution of inter-tick intervals, gives a more realistic picture of execution risk. The tail of that distribution, the shortest intervals, is where slippage lives.

What does the inter-tick interval distribution look like on the pairs traded here?

The calculation is correct, and walking through it step by step shows how straightforward the standard deviation is. The deviations from the mean of 0.06 percent, squared and summed, give 0.532. Dividing by four, which is n minus 1 for a sample, gives 0.133, and the square root is about 0.365 percent. Annualising with the square root of 252 gives about 5.8 percent, which sits at the lower end of the range typical for major pairs. EUR/USD has often had annual volatility between about 5 and 10 percent in recent years, so this is a calm reading.

The part I'd stress is how much the sample length changes the answer, because I learned that on my own data. I computed daily volatility on EURUSD using five days, twenty days and sixty days across about a year, and the five day figure ranged from 0.18 to 0.61 percent depending on the week. The twenty day figure stayed between 0.3 and 0.45, which is far more usable for choosing targets.

What I do now is convert the number straight into pips each morning and compare it with my planned stop. If one standard deviation of the last twenty days is about 55 pips on GBPUSD, I know that a 12 pip scalp target is a small fraction of a normal day, and a 100 pip target is almost two full days of typical movement.

I also keep a separate figure for the London session only, since the daily number hides how quiet Asia is. It made my target setting much more honest.

The pip conversion makes the number practical. One daily standard deviation of 0.365 percent on 1.1000 is about 40 pips. So on a normal day, a move of 40 pips in either direction is ordinary. Scalp targets of 10 or 20 pips are well within that range and plausible within hours. A swing target of 150 pips is nearly four daily standard deviations, which would need several days of consistent movement. Using volatility like this to sanity check targets helps avoid setting goals the market is unlikely to reach in the intended holding period.

The point about fat tails is important. Under a normal distribution, a three standard deviation day would happen about once every 370 days, roughly once in a year and a half of trading days. In currency markets, such days happen more often than that, especially around central bank decisions or unexpected news. So a 120 pip day on this pair would be uncommon but not shocking. Sizing positions to survive moves of four or five standard deviations, rather than three, gives a more realistic margin for the tail events that real markets produce.

The caution that five data points are too few is right. The standard deviation from five values can easily be half or double the true value. Twenty days gives a much more stable estimate, and sixty days more stable still, though a longer window responds more slowly to changes in conditions. Many traders use twenty days as a practical balance. Has anyone here compared the twenty day standard deviation with ATR for their pair? I'd be interested in how closely they tracked and which one you found more useful for setting stops and targets.