Portfolio Heat Calculator
Portfolio heat is every open position's risk added together. The naive sum overstates the exposure when positions are uncorrelated, and describes it accurately when they are not. Correlation, rather than the number of positions you hold, decides what you are genuinely exposed to.
What your open positions actually risk
Defaults are six positions at 1% each with high correlation — the situation that feels diversified and is not.
Effective risk is r × √(n + n(n−1)ρ). At ρ = 1 it equals the naive sum exactly; at ρ = 0 it falls to r × √n, which is where diversification actually lives.
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How the number is built
Portfolio heat is the total you would lose if every open position hit its stop. Adding the individual risks gives the worst case. What it does not give is the likely case, and the gap between those two is correlation.
The standard combination is:
Effective risk = r × √(n + n(n−1)ρ)
where r is the risk on each, n the number of positions and ρ the average correlation between them.
Check the two ends. At ρ = 1 the formula collapses to r × n — the naive sum, exactly. At ρ = 0 it becomes r × √n, which for six positions is 2.45% rather than 6%. The whole benefit of holding more than one thing lives in the distance between those two numbers.
A worked example
Take the defaults: six positions, 1% each, average correlation 0.9, on a 25,000 account.
The naive sum is 6%. Every position stopping out costs 1,500.
The effective risk is 1 × √(6 + 30 × 0.9) = √33 = 5.74%. Barely below the naive sum, because at 0.9 the positions are nearly the same trade.
And the diversification is 1.09 independent positions. Six carefully chosen trades are giving you the risk profile of one, plus a rounding error.
Run the same six positions across correlations and the effect is stark:
At ρ = 0 the effective risk is 2.45% and you hold 6.00 independent positions. At 0.3 it is 3.87% and 2.40. At 0.6, 4.90% and 1.50. At 0.9, 5.74% and 1.09. At 1.0, 6.00% and exactly 1.00.
Most of the diversification is gone by 0.3. That is the finding worth carrying: correlation does not have to be high to destroy the benefit — moderate correlation removes most of it, and moderate correlation is what a portfolio of same-sector, same-direction trades actually has.
Why the cap belongs on the total
A per-trade rule does not constrain a portfolio. One percent a position is a sensible rule and it places no limit at all on how many positions you open, so ten of them is a 10% exposure arrived at one careful decision at a time.
And losses do not arrive evenly spaced. A market that moves against a set of correlated positions moves against all of them in the same stretch.
Which turns six separate 1% decisions into one 6% day.
Setting the cap
A total-heat cap is a single number decided while flat, and the useful way to choose it is from the recovery arithmetic rather than from comfort. A 6% loss needs 6.4% to get back. A 20% loss needs 25%. A 33% loss needs 50%.
Pick the drawdown you could sit through without changing your method, then set the cap below it. If everything correlating to one and stopping together would take 15% and you know that 15% would make you abandon the plan, the cap is too high — and it is too high regardless of how carefully each individual position was sized.
A common answer is 6% total, which at 1% a position means six open trades. The number matters less than the fact that it exists and that it binds before the seventh position rather than after the sixth loss.
What recovery costs
Losses and gains are not symmetric. A 6% fall needs 6.4% to recover; a 20% fall needs 25%; a 50% fall needs 100%. The arithmetic gets worse faster than the loss does, which is the real argument for capping total heat rather than trusting per-trade discipline.
And exiting several correlated positions at once is harder than exiting one. They will be in similar instruments, moving the same way, at the same moment.
Each exit costs. The spread and any commission are paid six times rather than once.
The original data
Of the 24,971 unique videos in this site’s search study, position sizing appears in 195 at a median of 1,738 views, and correlation in 5 at 1,162.
The question: Six positions open, all the same way. Add a seventh?
195 videos on sizing a single position. Portfolio heat is the other half of risk management: an account can be damaged by positions that were each sized correctly but all move together.
The answer is that a seventh correlated position adds risk and no diversification at all. Effective risk goes from 5.74% to 6.69%, and the equivalent independent positions stay at 1.09. You are paying most of a percentage point of exposure for a spread figure that does not move.
When it fails
The correlation figure you enter is historical, and the number that matters is the future one. In ordinary conditions a set of positions may genuinely show low correlation; in a shock, correlations across almost everything move towards one, so the diversification you measured disappears at exactly the moment it was supposed to work. That is not a flaw in the formula — it is the reason a total-heat cap has to be set at a level that survives ρ = 1.
The second failure is estimating correlation by eye. Positions in different tickers can be the same bet on one interest-rate move.
A third is a per-trade rule with no total. It permits unlimited exposure one decision at a time.
A fourth is counting positions as diversification. Six at 0.9 is 1.09 independent positions, and counting them says six.
A fifth is ignoring that stops are requests. In a gap the actual loss exceeds the heat figure, because none of the stops filled where they were placed.
And a sixth is assuming the effective figure is the number to spend. It describes the likely case; the naive sum is still what happens if everything goes wrong at once, and sizing should survive that.
Related
Risk management is where total exposure sits among the other decisions. Position sizing is the per-trade half that this page is the missing complement to. And correlation is the input that does all the work in the formula above.
The number that changes how multiple positions look is 1.09. Six trades, each carefully sized, each with its own reason — and if they are all long the same sector they are carrying the diversification of barely more than one position. Counting positions and calling it spread is the trap. Counting them is not the measurement.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money. Some links on this page earn a commission if you buy through them. It costs you nothing and it does not decide what appears here or in what order — how these pages are made is set out in our methodology.