What Is a Z-Score? Positioning Against Its Own History

What is a z-score? It measures how unusual a number is against its own history: how many standard deviations it sits above or below its average. In positioning, it turns a raw net position, which means little on its own, into a measure of how stretched that position is, on the same scale for every market.

The positions it is calculated from are the CFTC’s, week by week, on COT report for forex and on each currency’s page, such as the New Zealand dollar COT report.

The calculation

You need three things:

• today’s value;
• the average over the lookback window;
• the standard deviation: how much the series normally moves around that average.

Subtract the average from today’s value, and divide by the standard deviation.

A z-score of 0 is exactly average. If the values were normally distributed, +1 would sit at about the 84th percentile, +2 at about the 97.7th, and about 95% of readings would fall between −2 and +2 (NIST normal table).

COT positioning is not normally distributed. It can be lopsided and sit near one end for long stretches. Read those percentages as a rough guide, not as the real share of history. A percentile, which ranks a week against the actual history, assumes no distribution at all.

Why rescale at all

A net long of 150,000 contracts in euro futures and one of 30,000 in New Zealand dollar futures cannot be compared directly: the markets are different sizes. Their z-scores can. That is what makes the measure useful across a list of currencies.

A worked example, with invented numbers

Say a market’s net position has averaged +20,000 contracts over the window, with a standard deviation of 35,000, and this week it prints +115,000.

The z-score is (115,000 − 20,000) ÷ 35,000 ≈ +2.7.

Most of the traders who wanted this position already hold it. If the story behind it cracks, a lot of positions may need to close at once.

Common mistakes

• Using it as a timer. Selling a +2.5 reading because “it must revert”. Stretched positioning can stretch further, and strong trends can hold extreme readings for months.
• Ignoring the window. A z-score against two years of history can say something very different from one against ten. A short window can make an ordinary week look extreme.

How an extreme fits with the other warning signs is in COT Data Reversals.