Correlation and Portfolio Risk

The short answer

A per-trade risk limit controls one trade. It says nothing about what happens when several trades can go wrong at the same time, for the same reason.

Five positions at 1% each are five separate 1% risks only if they can lose on different days. If they share a driver, a single adverse move stops out all five, and you have taken a 5% loss from a rule book that says your maximum risk is 1%.

How risks actually combine

Two extremes bracket the problem.

If positions are genuinely independent, their swings partly cancel: some are up while others are down, and the typical combined move grows closer to the square root of the number of positions than to their sum. Five independent 1% risks feel, day to day, more like a bit over 2% than like 5%.

If positions are perfectly correlated, nothing cancels. Five 1% risks behave as one 5% risk, in both directions.

Real books sit somewhere between, usually much nearer the second extreme than traders assume. And note the asymmetry: the partial cancellation is the typical case, while the full 5% remains the worst case regardless of correlation. Independence makes a simultaneous loss unlikely, not impossible.

The percentages above are arithmetic illustrations, not measurements of any market.

Where correlation hides

Correlation is rarely announced. It arrives through a shared driver that is obvious in hindsight and invisible on a chart.

The same asset, twice. Two trading pairs quoted against different currencies, a stock and a fund that holds a large weight of it, a spot position and a futures position on the same underlying. These are frequently treated as separate trades.

The same sector or theme. Companies serving the same end market respond to the same news. Assets in the same corner of crypto respond to the same narrative.

The same macro driver. Interest-rate expectations, the direction of the dollar, an energy price. Positions in unrelated-looking instruments can all be, underneath, the same bet on one variable.

The same scheduled event. If four positions all depend on how one release is received, you have one position with four entry prices.

The same venue. Holding everything at one exchange adds a correlation that has nothing to do with price: an outage, a withdrawal halt or a solvency problem affects every position at once. See custody and exchange risk.

The same idea. The most common one. Five setups found by the same screen, filtered by the same criteria, are five expressions of a single thesis. When the thesis is wrong, they are all wrong.

What these share is that none of them shows up in the sizing calculation. Each position passes the per-trade rule on its own terms, and the aggregate is never computed, because nothing in the workflow asks for it.

Correlation is not a constant

Even if you measure it properly, the number is unstable.

A correlation coefficient is calculated over a chosen window using past data. Change the window and it changes. More importantly, correlations tend to rise during broad selling: when participants reduce exposure across the board, assets that previously moved independently start moving together, because the reason they are being sold has nothing to do with their individual characteristics.

The uncomfortable implication is that diversification thins out at precisely the moment you are counting on it. A book that looked well spread in calm conditions can behave like a single concentrated position in a disorderly one.

This is not a reason to ignore correlation. It is a reason not to build anything precise on top of a measured figure. Regulators describe diversification in the same broad terms for the same reason — the principle is reliable, the coefficient is not.

Managing it without pretending to measure it

You do not need a correlation matrix. You need two caps and one honest question.

Cap total open risk. Decide the maximum you can lose if every open position stops out on the same day, and hold to it. If your per-trade limit is 1% and your total cap is 3%, you hold three positions at full size, or six at half size. The number of open trades becomes a sizing input rather than a matter of how many ideas you happen to like.

Cap risk per driver. Group open positions by what would hurt them — not by ticker, sector label or asset class, but by the event or variable that would take them all out together. Then cap each group. A common shape is a group cap equal to or a little above the per-trade limit, which effectively says: a second position in the same theme must be paid for by shrinking the first.

Ask the question. Before adding a position: is there a single plausible piece of news that stops me out of this and something I already hold? If yes, the new trade is an increase in an existing position, and it should be sized as one.

A worked grouping

Invented for teaching. These are not recommendations, and the instruments are generic.

Suppose a 1% per-trade limit, a 3% total cap, and a 2% per-driver cap. The book holds three long positions in assets that all rise and fall with the same broad market direction, plus one long in something driven by a separate factor.

The three lookalikes form one group. At full size that group carries 3% — over the 2% driver cap. The resolution is not to refuse the trades but to size them together: roughly 0.67% each, so the group totals 2%. The fourth position sits in its own group at 1%. Total open risk is 3%, at the cap.

Nothing here required a statistic. It required deciding which positions belong in the same bucket, then letting the sizing arithmetic allocate within it.

What this does not fix

Grouping by driver is a judgement, and you will sometimes group wrongly — usually by missing a link that only becomes visible under stress. Caps also cost you: correctly identified independent opportunities get declined once the total cap is full.

That trade is deliberate. The cost of being too cautious is a smaller gain. The cost of discovering your correlations during a bad week is a drawdown several times the size you authorised, and the recovery arithmetic applies to the aggregate loss, not to the per-trade limit you thought you were running.

What to do with this

List your current open positions and write next to each one the single event that would hurt it most. Any two positions sharing an answer belong in the same group.

Then check the totals: what you lose if one group goes against you, and what you lose if everything does. If either number surprises you, the position count is doing work your risk rule was supposed to be doing.