Guide · Risk management · Updated 2026-09-19

The sum of your stops is not your open risk, and it is wrong in both directions

Every figure on this page was computed from the exchange daily index close files rather than quoted, and the method is set out at the bottom so the work can be redone. The dataset is eleven sector indices over 2,686 daily observations. No figure here is an example chosen to make a point; the two books were selected by searching all 462 five sector combinations for the lowest and the highest average pairwise correlation.

The definition, and the word doing all the work

Heat is a single number describing a whole book: the loss that would be realised if every open position were closed at its own exit, divided by capital. It is not exposure, which is what the positions are worth. It is not margin, which is what the clearing system asks you to post. A book holding the whole of capital in five positions carries no heat at all if every exit sits at the entry, and a book holding a tenth of capital in one position can carry several per cent if the exit is far enough away.

That much is uncontroversial and it is where most explanations stop, usually with an instruction to add up the per position risk and keep the total below some figure. The instruction is not wrong so much as incomplete, because the definition contains a condition nobody checks. Every position at its exit at the same moment is an event, and events have frequencies. If it happens once a quarter the number describes something you will live through. If it is essentially impossible for your particular book, the number describes nothing and you have been managing a quantity with no referent.

So the honest way to read the definition is as a question rather than a sum: how correlated does the book have to be for the plain total to be the right number, and how correlated is it actually? That is a measurement, and Indian sector data is enough to make it.

Two books, one number, and the number is wrong twice

Take eleven Indian sector indices and their daily closing changes from 2015-11-10 to 2026-09-18. The average correlation across all 55 pairs is +0.509, which is the first thing worth knowing: Indian sectors are positively related to each other by default, and a portfolio assembled without regard to that is more concentrated than it looks. Now search every five sector combination for the two extremes.

Read the first error off the table. Both books carry a plain heat of 5.00 units, and the loss from one correlated adverse move of the same size is 3.52 units in the spread book against 4.30 in the clustered one. As a description of a bad correlated day the plain sum is 42 per cent too high for Book A and 16 per cent too high for Book B. It is not conservative in any useful sense, because the size of its error depends on the book. It is close to right for the book that is really one bet and badly wrong for the book that is not, which means it charges a genuinely diversifying position the full price of another unit of what you already hold.

The effective position count makes the point sharper. Book A holds five names and carries 2.01 independent bets. Book B holds five and carries 1.35. One of the sectors, public sector banks, appears in both books, and it is not the same holding in the two: surrounded by unrelated sectors it adds real breadth, and surrounded by its own kind it adds almost nothing. No per position calculation can see that, because the quantity is not a property of the position.

How often the heat event actually happened

The correlation arithmetic is an argument about an average day. The stronger test is to walk the sessions and count. Size every position so that a move to its exit costs exactly one unit of capital, set each exit at twice a trailing sixty session volatility estimate, and ask on each of 2,626 sessions how many of the five positions reached an exit. The volatility estimate uses only prior sessions, so nothing in the walk knows the future.

Two results are worth separating. The first is that the event the definition names is rare in both books and 2.7 times more common in the clustered one: 19 sessions against 51, or roughly one in 138 against one in 51. A single number that is handed to both books cannot be describing the same thing.

The second is that the columns cross. Book A had more sessions with at least one position at an exit, 487 against 349, because its members include individually volatile sectors. It had far fewer sessions on which three or more went together. This is what diversification looks like from the inside and it is the opposite of comfortable: the spread book stops out more often, and it stops out alone. A trader judging a book by how frequently positions are closed at a loss will reliably prefer the more dangerous one.

The exits set the number, so heat moves when you move a stop

Heat is position size multiplied by the distance to the exit. Both factors matter, and the second is the one that escapes attention because it does not involve an order. The distance to an exit is measured in the instrument's own volatility, which is why the same rupee position carries very different heat in different sectors.

The spread between the quietest and the most volatile of these sectors is 2.02 times, so an identical position size carries 2.02 times the heat in one than in the other at the same exit multiple. A book described as five equal positions is not carrying five equal risks unless the exits were placed to make it so.

The consequence for a live book is the part generic pages omit. Widen every exit on Book A from twice the daily volatility to three times and its plain heat moves from 1.46 to 2.19 per cent of capital. Nothing was bought. Nothing was sold. The broker statement is unchanged and the open risk rose by half. The reverse is equally true: tightening exits reduces heat, which is why a book that looks safe on a heat report can be one that has quietly moved its exits inside the ordinary noise of the instrument and will be shaken out by it. Heat says nothing about whether the exit is in a sensible place, only what it costs if it is reached.

Because heat responds to exits, it is a quantity that changes on days when you did not trade. A trailing exit that moves with price changes heat every session. A volatility based exit changes heat when volatility changes, even if the exit level is untouched, because the same distance is now a different number of standard moves. Any process that recomputes heat only when an order is placed is measuring a stale book.

Heat is a floor on the loss, not a ceiling

Everything so far has assumed that an exit is honoured at the exit price. It is not a promise. A resting stop becomes a market order when it is triggered, and a market that opens below the level fills where the market is, not where the instruction was. The pre-market call auction sets that opening price on the day's accumulated orders, and a price band or a surveillance restriction can move the boundary of what is even possible. This is why the loss on a book can exceed its heat, and the excess is not small.

A stop is an instruction to trade, not a guarantee of a price, and the distance between the two is widest on the sessions when every position needs it at once. In the delivery segment an exit that does not complete carries a further mechanism of its own, because settlement obligations do not wait for a convenient price.

Read the third column as a multiple of what was planned. Across the eleven sectors the opening print was past the exit on 167 occasions in total, which is under one per cent of sessions for every sector, and on those occasions the realised loss averaged 1.59 times the intended one. The worst single instance, in realty, cost 3.45 times the planned loss on one position.

For a whole book the effect compounds, because the sessions on which sectors open past their exits are the same sessions. Running the walk again with fills at the opening print rather than at the exit, the plain sum of 5.00 units was exceeded on 14 sessions for Book A and 21 for Book B. On those sessions the loss averaged 7.34 and 7.28 units. The worst session in the sample cost Book A 13.05 units and Book B 14.35 units, which are 2.61 and 2.87 times their own plain heat.

That is the second direction of the error, and it is the one that matters. A trader who believes heat is the worst case has the sign of the residual backwards. The plain sum is above the loss from an ordinary correlated move and below the loss from the move that clears the exits before the market opens. It is a number in the middle of a distribution, being used as though it were the end of one.

Wider exits make the full heat event rarer and make the overshoot smaller relative to a larger planned loss, which is exactly what should happen. The ordering between the two books survives at every exit distance tested, and so does the fact that the worst observed session cost more than the plain sum in both books at all three.

A constraint that is checked afterwards is a report

The useful form of heat is not a figure on a weekly summary. It is a number computed before an order goes in, and a limit that refuses the order. The distinction is not administrative. A heat figure produced after the fill can tell you the book is over its limit, and by then the only remedies available are to carry the excess or to close something at a price you did not choose. Neither is the decision you would have made with the number in front of you, and the second one converts a risk problem into a realised loss.

Computing it before the order requires the marginal quantity rather than the total: how much does this position add to the book that is already open. On the plain sum that question has a trivial answer, because every position adds its own risk and nothing else. On the adjusted number it does not, and the difference is the whole point of the exercise.

The identical trade costs between 0.490 and 0.944 units of headroom depending on what is already open. More of a sector the book already holds costs close to the full unit; a sector that moves apart from the book costs around half. Nothing about the candidate position changed between those two figures. Its risk, its size and its exit are the same. The price it pays in the constraint is set by the rest of the book.

Put a limit on that number and the process acquires a refusal. Take a limit of 4.50 adjusted units, chosen here only to make the arithmetic visible. Book A sits at 3.52 with 0.98 units of headroom and accepts the candidate. Book B sits at 4.30 with 0.20 units and refuses the same candidate, even though the candidate is the cheapest available addition at 0.490 units. What the limit permits instead is the same position at 0.45 units of risk, which is under half the intended size. That is the constraint doing its work: it does not argue with the idea, it prices the idea against the book and returns a size or a refusal.

The same limit also hands the two books different allowances. Expressed in plain risk, a limit of 4.50 adjusted units permits 6.38 units of plain risk in Book A and 5.23 in Book B, a difference of 22 per cent. A limit on the plain sum would have given both the same allowance, which is the same as saying diversification is worth nothing. This is the practical reason to care which number the limit is stated in, and it bears on how an individual position is sized in the first place, which is a separate subject with its own arithmetic.

What a heat limit actually buys

It bounds the worst correlated session, and it does so before the session arrives.

That sentence is the entire case and it is worth unpacking, because the benefit is easy to state in a way that sounds smaller than it is. Accounts are not usually ended by a sequence of ordinary losses. They are ended by one session on which everything held turns out to have been the same position, and the aggregate loss is a multiple of anything in the recent record. The measurements above put numbers on that session: on the worst in 2,626 sessions the clustered book lost 14.35 units against a plain heat of 5.00, and the fourth worst still lost 9.56. Whether that is survivable is decided entirely by what the unit was worth, and the unit was set the last time a position was opened.

A limit is therefore a decision taken in advance about a session you cannot forecast. It does not predict the correlated day, reduce its probability, or say anything about when it will happen. It fixes what it costs. The alternative is to decide the same question on the morning of the event, with the positions already on and every incentive pointing the wrong way, which is the circumstance under which people reliably decide to wait.

It buys one more thing, less obvious and at least as valuable: it makes the size of the book a consequence rather than a mood. Under a heat limit the number of positions you can hold is not a preference. It falls out of how correlated they are and how far away the exits are, and it changes on its own when volatility rises, because a volatility based exit widens and consumes more of the same allowance. The book contracts in conditions that warrant contraction without anyone having to decide to be careful.

The failure the generic pages omit

Adjusted heat is computed from a correlation matrix, and a correlation matrix is an estimate over a window somebody chose. Every weakness of that estimate is inherited by the heat number built on it, and the weaknesses do not point in random directions.

On the worst decile of broad market sessions the average pairwise correlation inside Book A rose from +0.243 to +0.354, a relative increase of 46 per cent, and the heat computed from the ordinary day estimate understated the stressed day figure by 10.7 per cent. Book B moved less in relative terms, from +0.554 to +0.655 and 6.1 per cent on heat, for the simple reason that it had less diversification available to lose.

That asymmetry is the uncomfortable part. The book that benefits most from the adjustment is the book whose benefit erodes most when the adjustment matters. A measured heat number is therefore systematically too low in precisely the conditions under which the limit is binding, and the error is largest for the trader who took the most care over diversification.

None of this argues for abandoning the adjustment and going back to the plain sum, which is wrong by a larger margin in the other direction and wrong by an amount that varies with the book. It argues for knowing which way the residual points, and for testing a book against a correlation estimate taken from difficult sessions rather than from all sessions, which is a calculation of the same shape run on a different sample. How far correlation moves, how much of that movement is the measuring instrument rather than the market, and what window length is defensible are a subject in their own right and are measured separately.

What heat is actually for

Heat is not a forecast and it is not a performance statistic. It is the answer to one narrow question asked at one specific moment: given everything already open, what does this next position cost, and is there room for it. A number that cannot refuse a trade is not performing that function no matter how carefully it is computed.

Three things follow from the measurements on this page. The plain sum is not a conservative approximation of open risk; it is wrong by an amount that depends on the book, too high against an ordinary correlated move and too low against the session that clears every exit at the open. The correlation adjustment is worth making and is weakest under stress, so the number it produces is a floor that should be treated as one. And the exits are half of the quantity, which means heat is a live number that changes on days with no trading at all.

What remains after the arithmetic is judgement about where the exits belong and which positions are genuinely different bets rather than one bet held five ways, and that judgement is what the measurement is for. Bharath Shiksha teaches risk as a constraint you build and test rather than a figure you quote, because the difference between the two is visible only on the sessions that matter.