Scenario vs Sensitivity: One Variable or a Coherent Set

A sensitivity moves one variable and holds everything else exactly where it was. A scenario moves a set of variables together because one condition would move all of them. On the worked case, giving back 2.0 points of gross margin alone costs about Rs 52.7 crore of gross profit. The same give back, with revenue per unit no longer growing alongside it, costs about Rs 86.5 crore, roughly 64 per cent more.

The gap between the two figures is not a disagreement about arithmetic. Both are correct. The two figures answer two different questions, and the trouble starts when the easier question gets asked and the harder answer gets reported. A model is a set of lines that are connected to each other. RealisationThe revenue a company gets for each unit it sells. If volumes are flat and realisation rises, the extra revenue came from price or from a richer blend of products., volume, margin and cost are not independent dials that happen to sit on the same sheet. Realisation, volume, margin and cost sit downstream of conditions in the world, and one condition typically reaches several of them at once. A tool that moves one dial is measuring something real, but it is not measuring a year.

What is a sensitivity, and what exactly does it hold still?

A sensitivity takes one input, moves it by a stated amount, leaves every other input untouched, and reports what happened to the answer. The whole definition sits in those four steps, and the second one carries the weight. The move is trivial. The holding still is the design.

The holding still buys attributionBeing able to say which input caused a change in the answer, rather than only that the answer changed.: the entire change in the answer belongs to the one thing that was moved, and nothing else can be blamed for it. If gross profit falls by a certain number of crore and only one input was touched, no argument is possible about where the fall came from. There is a clean line from the input to the output with nothing else standing in it.

Working out whether the fan in a house is what pushed the electricity bill up runs on the same logic. Changing the fan, the air conditioner, the geyser and the number of people in the house all in the same month and then looking at the bill settles nothing. Leaving everything else alone and running the fan differently for one month settles it. The answer that comes back is narrow and it is clean, and the narrowness is not a defect. The narrowness is what makes the answer worth anything at all.

So a sensitivity is an attribution instrument. A sensitivity is built to answer which input matters, and it answers precisely because it refuses to let anything else move. Hold on to that. Everything that goes wrong later comes from asking a sensitivity a completely different question and being handed the same clean number.

What is a scenario, and what makes one coherent rather than merely pessimistic?

A scenario moves a set of variables together, and it moves them together because a single underlying condition in the world would move all of them. The set is not chosen. The set is discovered by asking what the condition touches and then following it.

The word doing all the work is coherent: a scenario is not several sensitivities added up, it is one statement about the world with its consequences traced through the sheet. That distinction sounds fussy until someone tries to build one. Adding three sensitivities together produces a number, but nobody can say what the number describes. The three moves were chosen separately, and there is no reason they would arrive on the same day. Tracing one condition produces a set that arrives together by construction.

The household version is the one everybody has lived through. A person loses a job, and the loss of salary is the sensitivity. The scenario is what actually happens: the salary stops, the medical cover attached to the job stops with it, the loan the household was planning becomes harder to get because there is no salary slip, and the emergency fund starts being spent at exactly the moment it stopped being added to. Nobody sat down and chose four bad things. One condition arrived and four consequences followed it, and any honest description of that year has to carry all four.

The finance version behaves identically. If the reason the margin fell is that pricing across the whole field weakened, then that same weakening is also the reason the company stopped being able to push realisation ahead of its costs. Whether the second consequence is included is not a matter of choice. The consequence was already inside the condition.

Why does moving one variable understate a change that actually happens?

The variables in a real model are not independent. A condition that pushes one of them usually pushes the others in the same direction, and a single move therefore measures the smallest possible version of the change rather than the likely one. The mechanism is worth being slow about. The arithmetic is never wrong, and being right is exactly what makes it convincing.

Holding everything else still is not conservatism. Holding everything else still asserts independenceThe assumption that one number can move without dragging any other number along with it., silently, in the background, with nothing written down anywhere. The assertion is that a world exists in which the margin falls and absolutely nothing else does. Sometimes that world exists. Usually it does not, and nobody checked. The assertion was never written down in the first place.

Notice where the understatement actually enters. The understatement does not enter when the sensitivity is computed. The understatement enters at the moment somebody labels the result a downside case. Up to that point the number is an honest, narrow measurement of one line. The label is what converts it into a claim about a year, and the claim is where it stops being true.

How much does one variable understate it, on the worked case?

A claim about direction is cheap. The size follows, on the invented case, with every step written out so that it can be repeated on a calculator.

Start from what the forecast year already holds. Sarvani Coatings Limited, an invented maker of industrial coatings, published revenue of Rs 2,415 crore in year three, its most recent completed year to 31 March, with a gross margin of 46.0 per cent. The worked view carries volume rising 6.0 per cent, with realisation adding a further 3.0 per cent on top of that. Volume and realisation compound rather than add: 1.06 multiplied by 1.03 is 1.0918, so revenue growth is 9.18 per cent and not 9.0. Forecast revenue is therefore about Rs 2,636.7 crore, and holding the margin flat at 46.0 per cent gives gross profit of about Rs 1,212.9 crore.

Now the sensitivity. Take 2.0 points off the gross margin, to 44.0 per cent, and hold every other line exactly where it was. Two points of a Rs 2,636.7 crore revenue line is about Rs 52.7 crore of gross profit. Clean, attributable, correct.

State the base yearThe year whose figures a calculation sits on. Change the year and the same percentage move is worth a different number of rupees. beside it or the figure is not finished, because the same 2.0 points on the published year of Rs 2,415 crore is about Rs 48.3 crore. The two differ by about Rs 4.43 crore, and it is worth seeing why: the value of one margin point is simply revenue divided by a hundred, so the ratio between the two answers is exactly the revenue growth between the two years, 9.18 per cent, and the margin level itself cancels out of that comparison entirely. A sensitivity quoted with no base attached is not finished. The figure is a percentage wearing a rupee sign.

Now the scenario. The build starts somewhere else entirely. Do not ask what happens if the margin falls. Ask what condition would take 2.0 points off it. On this case the honest answer, and it is the one the earlier work already established rather than one invented here, is that the pricing environment across the whole field weakens. Sarvani Coatings gained margin because realisation outran its input costs, not because those costs fell, so the condition that removes the gain is the one that stops realisation running ahead.

Follow that condition rather than stopping at the margin. If the field stops letting realisation run ahead of input cost, realisation growth does not stay at 3.0 per cent. Realisation growth goes to zero, and revenue then grows on volume alone at 6.0 per cent, giving about Rs 2,559.9 crore. At a gross margin of 44.0 per cent that is gross profit of about Rs 1,126.4 crore.

Against the thesis case of about Rs 1,212.9 crore, the coherent scenario costs about Rs 86.5 crore while the one variable move showed about Rs 52.7 crore, so the scenario is about 64 per cent larger and the whole of the extra came from a second consequence nobody moved. The extra is not a mystery and it is not a fudge. Revenue that did not arrive is Rs 2,636.7 crore less Rs 2,559.9 crore, or about Rs 76.8 crore. The missing revenue would have carried the new margin of 44.0 per cent, worth about Rs 33.8 crore of gross profit. Added to the Rs 52.7 crore, that comes to the Rs 86.5 crore exactly. Two parts, both checkable, no rounding gap.

One more thing about that 2.0 points. Whether the exercise is honest turns on where the figure came from, and nobody picked it for sounding like a reasonable amount of bad news. The published ladder puts gross margin at 43.0 per cent on revenue of Rs 1,840 crore in the first of the three completed years, then 44.0 per cent on Rs 2,120 crore, then 46.0 per cent on Rs 2,415 crore, where gross profit came to Rs 1,111 crore. A 2.0 point give backA measure travelling part of the way back towards where it started, after having improved. is exactly one year of the gain, and it lands the margin precisely where year two left it. A reader can argue with a size like that, and arguing is the point. A number chosen for feeling bad is a number nobody can argue with. Being unarguable sounds like a strength and is the opposite of one.

When is a sensitivity exactly the right tool, and when does it fail?

A sensitivity is the correct instrument for exactly one job: ranking the variables by how much each of them moves the answer. The ranking is precisely what the earlier work on drivers needed. For establishing whether the answer hangs on the margin, on volume or on the share gain, there is no better method available. Each one moves alone, by the same relative amount, the effect on the answer is written down, and the list is sorted. The independence assumption that makes a sensitivity a poor description of a year is exactly what makes it a clean ranking device. A ranking is a comparison between inputs, and every input is being treated the same way.

A sensitivity fails everywhere else, and particularly at describing a bad year. Describing a bad year is unfortunately what it is most often used for. The failure is not statistical subtlety. The failure is a category error. The question asked was which line matters most, and it was answered honestly. The honest answer was then printed under a heading that promised something else.

How is a scenario built without inventing a story?

The discipline is one sentence long: start from a condition, never from a mood. A weakening pricing environment across the field is a condition. The condition is a describable state of the world, somebody could disagree about whether it is likely, and it has consequences that can be traced line by line. A bear case is a mood. A mood produces numbers chosen for feeling bad, and a mood is unfalsifiable in the worst way. No evidence could ever arrive to show a mood wrong.

The difference in what each one produces is plain. The condition yields three things, and none of them has to be imagined. First, realisation growth stops, and stopping is exactly what the condition means. Second, the margin gives back the gain, because the gain was realisation outrunning input cost per unitWhat the materials for one unit of output cost, kept separate from what the materials bill came to in total. in the first place. Third, volume may or may not move, and that has to be decided openly. The mood yields a number about a fifth lower than the base case and no way at all to say what would have to happen for it to occur.

Two more things make the condition on this case a real one rather than a convenient one. First, the condition was established before any of this arithmetic: the published statements simply cannot separate a pricing environment across the whole field from Sarvani Coatings deciding its own prices, or from a mix shiftThe blend of what gets sold changing, which shifts an average price even though no individual price moved. towards industrial work. Second, the peers point the same way. Measured across year one to year three, a two year span, Nandivarman Paints Limited gained 2.4 points of gross margin and Kesaria Surface Solutions Limited gained 3.6, against 3.0 points for Sarvani Coatings over that identical two year span. All three rose. The shared direction narrows the question without resolving it. A shared environment explains a gain that everybody had, and Sarvani Coatings sits between the two peers, so nothing there separates its own pricing from its mix.

The scenario also leaves one line alone. Volume growth stays at 6.0 per cent in both columns, even though a weaker pricing environment might well arrive alongside softer demand. Holding volume still was a choice, and the choice makes the scenario a conservative one rather than a maximal one. Choices like that belong in writing alongside the numbers. A scenario that quietly moves every line it can find is a mood again, wearing a condition as a disguise.

Why does a three column table usually contain only one real scenario?

Almost any model has three columns headed downside, base and upside. The thing to examine is what actually differs between them. The base case is the model, the upside is the model with better numbers typed in and the downside is the model with worse ones, so all three share every mechanism and only one of the three was ever built.

The test is short and it is brutal. Do any two of the columns disagree about how the world works, or do they only disagree about a percentage? If the downside column says volume grows at 4.0 per cent instead of 6.0 per cent for no stated reason, it is not a scenario. The column is the base case with a smaller number in one cell. If the downside column says the pricing environment weakens and therefore realisation stops and therefore the margin gives back and therefore the working capital cycle behaves differently, that is a different account of the world, and it deserves its own column.

There is a tell that costs nothing to check. In a genuine set of scenarios, the columns will disagree about the direction of at least one line, not merely its size. Everything moving the same way in every column, only by different amounts, means one mechanism has been scaled up and down three times.

What is actually done with the pair of them?

A sensitivity ranks and a scenario sizes, so the working order is the sensitivity first to find which variables carry the answer and the scenario second to see what a coherent move in those variables costs. Run the other way around, both are wasted. A scenario built before the ranking exists will trace the lines the builder happened to think of that morning, and it will look thorough while quietly leaving out the one line that mattered. A ranking run after the scenario has been written reveals what should have been traced. Finding out in that order is slower.

On this case the order shows up plainly. The ranking is what identified the margin as the line the answer hangs on, out of everything in the forecast. Only then does it make sense to ask what condition would move the margin. The second consequence appears at that point, with the right line already in view.

How does a working analyst actually use the two of them in a week?

Meghna Iyer, covering the coatings names, has a model with about forty inputs in it. On Monday she is not building scenarios, she is ranking. She moves each of the top dozen inputs alone by the same relative amount and writes down what happens to forecast gross profit. The ranking takes an afternoon and produces a sorted list, and the list tells her that three lines carry the answer and the other nine are decoration. Everything she does for the rest of the week is aimed at those three.

The scenario work only starts once the ranking has told her where to point it, and its output is a size rather than a ranking. She asks what condition would move the margin, traces it to realisation and to revenue, and arrives at about Rs 86.5 crore of gross profit rather than about Rs 52.7 crore. The larger number is the figure that goes to an investment committee. A committee is not asking which line matters. A committee is asking how much a bad version of the world costs, and the sensitivity was never designed to answer that.

The same split shows up outside research entirely. A lender assessing a working capital limit runs sensitivities to find whether the borrower's repayment capacity hangs on the receivable cycle or on the margin, then builds one scenario in which the borrower's largest customer delays payment and traces that single condition through the cycle, the interest cost and the covenant. A household does it without any of the vocabulary: what if the school fee rises is a sensitivity, and what if one earner in the house stops earning is a scenario, and everybody instinctively knows the second question is the one that keeps them awake. Ravindra Setlur, sitting on the other side as a chief financial officer, runs the identical pair when deciding whether a new line can be funded from internal accruals.

The worked case supports one narrow claim, and the limits of it are worth stating. The thesis being taken apart holds that the margin gain was a level shiftSomething that moves once and then stays where it landed, unlike a rate which would keep adding year on year. rather than a rate that repeats, and the scenario here does not test that claim. The scenario only sizes what happens if part of the gain reverses. Sizing and testing are different jobs, and running them together is how a sized reversal gets mistaken for a tested claim. The 64 per cent is a fact about these invented figures on this give back and nothing more. The 64 per cent is a coincidence of the numbers chosen, it moves as the give back moves, and it is not a rule of thumb about anything.

Sarvani Coatings Limited, Nandivarman Paints Limited, Kesaria Surface Solutions Limited, Meghna Iyer and Ravindra Setlur are invented.
Educational material. Not advice on any investment, tax, budget or market position.