Macro Sensitivity: Measuring How Much a Variable Moves an Outcome

A sensitivity is how much one outcome moves for a stated move in one variable. The stated move is what makes the figure usable at all: an effect quoted without the size of the move it answers cannot be compared with any other figure, cannot be scaled to any other move, and cannot be checked by anyone reading it.

Two things already built underneath carry the weight here. The first is the set of channels through which a macro variable reaches a company at all, and the leverage that gives them. Operating profitRevenue minus the day to day costs of producing and selling, stopping short of interest and tax. Because it is the small remainder left by two very large numbers, a slight move in either one lands on it heavily. is a thin residual sitting under two very large numbers. The second is the mapping work that produces the shares themselves: how much of revenue is exported, how much of the cost baseEverything a company pays out to make and move its product, taken together and stopping short of interest and tax. Exposure shares such as fuel or imports are normally quoted as a fraction of this total. is imported, how much of it is fuel. A sensitivity is not a new measurement. A sensitivity is those shares, arranged so that they can be compared.

Sensitivity work adds one discipline and one warning. The discipline is that every effect is written as an effect per stated move, against a named outcome. The warning is that a figure built this way is exact at exactly one point and nowhere else, and that nothing in the figure indicates how far from that point it still holds.

All the arithmetic below runs on Nirvi Engineering, an invented manufacturer inside the invented Republic of Sankhya. Its revenue line reads Rs 1,000 crore and its cost line Rs 900 crore, leaving operating profit at Rs 100 crore and a margin of 10.00 per cent. Exports are 30.00 per cent of revenue, so Rs 300 crore. Imported inputsMaterials, parts or fuel bought from outside the country and paid for in a foreign currency, so the rupee cost of them moves when the exchange rate moves even if the quantity does not. are 40.00 per cent of costs, so Rs 360 crore. Fuel is 10.00 per cent of costs, so Rs 90 crore. Borrowings stand at Rs 200 crore carrying 9.00 per cent, so the interest charge is Rs 18 crore.

Why is the size of the move part of the figure?

One sentence is heard often and is worth almost nothing. Someone says that a weaker Marut unit takes Rs 0.60 crore off Nirvi Engineering's profit.

The only question that matters is the obvious one. A weaker Marut unit by how much? A move of one per cent? Five? Twenty six? Until that is answered the number cannot be used at all. The figure cannot be ranked against another variable. The other variable was measured against a move of its own size. The move it came from is unknown, so the figure cannot be carried to a bigger move either. Nobody can reproduce a calculation whose input is missing, so the figure cannot even be checked.

An effect quoted without the size of the move it responds to is an anecdote. An effect quoted with that size is a measurement. Written properly the sentence reads: a 1.00 per cent depreciation of the Marut unit changes Nirvi Engineering's operating profit by minus Rs 0.60 crore, which is minus 0.60 per cent of that profit.

Where does the Rs 0.60 crore come from? Two parts, and both are published above and can be rebuilt from there. Exports of Rs 300 crore rise by 1.00 per cent, adding Rs 3.00 crore of revenue. Imported inputs of Rs 360 crore rise by 1.00 per cent, adding Rs 3.60 crore of cost. Net that off and profit is Rs 0.60 crore lower. The direction of the sensitivity is decided by which of the two rupee amounts is larger, and here the cost side is larger even though the company exports.

Why does a sensitivity have to name the outcome as well?

With the currency move held fixed at 1.00 per cent and nothing else changed, what it did to Nirvi Engineering depends entirely on which line the question is asked about.

Revenue rises. Exports of Rs 300 crore gain Rs 3.00 crore, lifting the revenue line to Rs 1,003 crore off a base of Rs 1,000 crore, and that is plus 0.30 per cent. Operating profit falls to Rs 99.40 crore against a base of Rs 100 crore, a fall of 0.60 per cent. The operating marginOperating profit divided by revenue, written as a per cent. Because revenue is the divisor, a margin can fall even in a period when profit in rupees has risen, if revenue rose faster. falls further than either, arriving at 9.91 per cent where it began the day at 10.00, a drop of 0.09 percentage pointsThe plain arithmetic difference between two percentages. A move from 10.00 per cent to 9.91 per cent is a fall of 0.09 percentage points, and it is also a fall of 0.90 per cent of the original 10.00. The two are different statements about the same move., and 0.09 against a starting 10.00 is minus 0.90 per cent of the margin.

Three figures. Plus 0.30, minus 0.60, minus 0.90. One variable, one move, one day, and even the sign is not the same across the three. A reader handed any one of them without the outcome attached has been handed half a figure and has no way to know which half.

A sensitivity names two things and not one: the variable that moved and the outcome that was measured, and dropping either one makes the number unquotable. The margin falls hardest because revenue is sitting underneath it as a divisor, and the divisor went up while the numerator went down. The moving divisor is worth holding on to, and it returns below as the reason a sensitivity stops behaving when it is pushed hard.

How are sensitivities to different variables compared?

Nirvi Engineering is exposed to three macro variables already built. The Marut unit. The rupee cost of fuel. The rate it borrows at. Any operator asked which of the three matters most will offer an opinion. Getting an answer instead of an opinion needs the three written on one basis.

Look at how each of the three usually turns up in conversation. The fuel exposure gets quoted in rupees of cost. The currency exposure gets quoted in rupees of profit. The borrowing rate gets quoted in basis pointsThere are a hundred of them inside one percentage point, so a rate stepping from 9.00 per cent to 9.50 per cent has stepped fifty. Rate markets count this way to keep small moves in whole numbers.. Three quantities in three units, none of which can be set beside another. There is no arithmetic that ranks Rs 0.90 crore against fifty basis points, and pretending otherwise is where most of the confusion in this subject lives.

The fix is mechanical. Take one per cent as the move, apply it to each variable in proportion to itself, and express every result against the same outcome. Operating profit is the outcome worth using here, for the reason the channels themselves established: profit is the thin residual that macro leverage shows up in. The fix gives one rule and three numbers, and every share behind them is published above.

The rule is short, so read it off the table rather than off the rows. The effect on profit of a 1.00 per cent move, as a per cent of profit, is the exposed rupee amount divided by profit. Rs 90 crore over Rs 100 crore gives 0.90. Rs 60 crore over Rs 100 crore gives 0.60. Rs 18 crore over Rs 100 crore gives 0.18. Only once every effect is a per cent of the same outcome for the same size of move can two variables be set beside each other at all, and the ranking that then appears is the first genuinely useful result.

Two notes about that table before it gets used. The first is that the fuel and currency rows sit inside operating profit while the interest row sits below it, and the rate effect is set against the same Rs 100 crore purely so that the three can be compared. The shared base is a convention stated openly, not a claim that interest is an operating cost. The second is that the three rows are not added up. Adding them would assume all three variables moved 1.00 per cent on the same day, a claim nobody has made. The sum would also mix an operating effect with a financing effect as though the two came off one line.

One caution about the rate row, the one that trips people. A 1.00 per cent move in the borrowing rate here means a move of one per cent of the rate itself, from 9.00 per cent to 9.09 per cent, or nine basis points. The move is not one percentage point. Check the rate row against the interest rate case already worked: a fifty basis point rise is 5.5556 per cent of a 9.00 per cent rate, and 5.5556 times minus 0.18 gives minus 1.00 per cent of profit, exactly the figure that case reports when the interest charge steps up from Rs 18 crore to Rs 19 crore. The two routes agree because they are the same division written twice, and what that agreement shows is that the proportional basis carries a basis point figure correctly rather than that anything has been independently confirmed.

Why does a sensitivity change as the variable moves?

Here is where the discipline starts to bite. A sensitivity is computed at one starting point. The figure describes the arithmetic in the neighbourhood of that point and makes no promise about the neighbourhood of any other. Whether it survives being carried a long way is not a matter of opinion, and it is not a property of the variable either. The deciding question is whether anything under the figure moves when the variable does.

The answer turns out to be different for two channels built from the same figures, so it is worked rather than asserted. Both start from a stated sensitivity of minus 0.90 per cent per 1.00 per cent. The compounded rupee fuel move already carried is 26.00 per cent, so both get multiplied by twenty six.

Take the fuel channel against profit first. The stated minus 0.90 multiplied by twenty six gives minus 23.40 per cent of profit. Measured directly instead: fuel of Rs 90 crore rising 26.00 per cent adds Rs 23.40 crore of cost, profit falls from Rs 100 crore to Rs 76.60 crore, and that is minus 23.40 per cent of profit. The scaled estimate and the direct measurement are the same number. The gap is nothing at all.

The match is not luck, and it is worth knowing exactly why it held. The quantity of fuel did not change. The share was applied to a cost base that did not move. The denominatorThe number a quantity is divided by. In a per cent of profit figure the denominator is the starting profit; in a margin figure it is revenue. Whether a denominator moves with the variable is what decides whether a relationship is straight. was the starting profit, which by construction does not move either. Nothing in the arithmetic shifted, so the relationship really is a straight line and scaling it really is exact.

Now take the currency channel against the margin, also stated at minus 0.90 per cent per 1.00 per cent. Multiplied by twenty six the same way, it gives minus 23.40 per cent again. Measured directly at a 26.00 per cent depreciation, something else happens. Profit falls to Rs 84.40 crore, revenue rises to Rs 1,078 crore, and the margin lands at 7.83 per cent against a starting 10.00 per cent. The margin fall is minus 21.71 per cent, not minus 23.40. The scaled estimate overstates the fall by 1.69 percentage points.

Two channels, the same stated figure, the same multiplication, and one of them is exact while the other is out by 1.69 points. Whether a sensitivity scales is a question about the shares underneath it and never about the size of the move. The margin has revenue as its denominator, revenue rose 7.80 per cent along with the currency, and the divisor at a 26.00 per cent move is simply not the divisor the small figure was measured against. The two stated figures happened to be the same minus 0.90, a coincidence of the shares in this case and not a rule about anything.

What is the difference between a sensitivity and a forecast?

Read the properly written sentence once more and notice what shape it has. If the Marut unit depreciates by 1.00 per cent, and nothing else moves, then Nirvi Engineering's operating profit moves by minus 0.60 per cent. The sentence is an if and a then. Both halves are stated. Neither half asserts that the Marut unit is going to do anything.

The distinction gets lost fastest in a room, and the reason is that a sensitivity and a forecast run on exactly the same arithmetic. The difference is not in the calculation and not in the number. The difference is in whether anybody has claimed the input. Take the sensitivity and add the words this yearWords like this year, next quarter or by December convert a stated assumption into a claim about the future. Such words are the entire difference between an if and a prediction, and they are usually added without anyone noticing. to the if, and the sentence has quietly become something else entirely.

A sensitivity is an if and a then, and it contains no claim whatever that the variable will move. Deciding what a variable might do, attaching a size to it, and holding several such settings side by side is the separate discipline of building scenarios, which is covered separately. A sensitivity supplies the then. Somebody else has to bring the if, and when they do, the honest thing is to keep saying it out loud.

What does a sensitivity leave out?

Everything a sensitivity leaves out sits inside four words that never get written down: everything else held still. The phrase is not a caveat bolted on afterwards. Holding everything else still is load bearing, and the figure would not exist without it.

Go back through the minus 0.60 per cent and count what was pinned. The export share stayed at 30.00 per cent of revenue. The imported share stayed at 40.00 per cent of costs. The fuel share stayed at 10.00 per cent. Volumes did not move, selling prices did not move, and every other macro variable in Sankhya sat exactly where it was. Five things held for one thing allowed to move.

A real 1.00 per cent currency move looks rather different from inside a business. A buyer abroad may respond to the new price. A purchasing head may look again at a supplier who quotes in Marut units. A fuel bill and a currency move are often stirred by the same thing, so the second variable may not sit still while the first is being measured. None of that is a prediction. The list is only the plain observation that the world does not come with the other five things pinned.

Assuming everything else stays still is built into every sensitivity ever quoted, and in a real move nothing else does. Three more things the figure is silent about, and each one gets asked of it constantly. A sensitivity says nothing about how probable the move is. A sensitivity says nothing about which other variables travel alongside. A sensitivity says nothing about what the business would do in response, and a business that can reprice or re-source is a business whose shares were never fixed in the first place.

How does an analyst actually use these figures?

A working analyst almost never quotes a sensitivity on its own. A sheet is kept instead. Every channel that reaches the company, every one written per 1.00 per cent, every one against operating profit, and the date and the shares the whole sheet was measured from written across the top.

The reason is the locality point, taken seriously. Any single row on that sheet is only as good as the starting point it was measured at, and starting points move: a company that changes a supplier has changed its imported share, and every currency row on the sheet is stale the day it does. The order in which the channels bite is far more stable than the size of any one of them, so what survives is the ranking rather than any individual figure. Knowing that fuel bites harder than currency, and currency harder than the borrowing rate, shows where the next hour should be spent. Knowing that the fuel figure is exactly 0.90 says very little by comparison.

A lender reads the same sheet the other way round. The question there is not which channel is largest but how far one of them can travel before the interest cover looks different, and that is a question about the size of the move rather than about the sensitivity. An operator inside the business reads it a third way, as a list of the exposures worth doing something about, and doing something about an exposure changes the share and therefore retires the row.

The same arithmetic works at household scale, and doing it once by hand makes it feel obvious. Take a household bringing home Rs 80,000/- a month. Fixed outgoings are Rs 65,000/-, made up of a home loan instalment of Rs 32,000/-, groceries of Rs 12,000/- and everything else at Rs 21,000/-. Rs 15,000/- is left. Now put the two exposures on one basis. A 1.00 per cent rise in the grocery bill costs Rs 120/-, or 0.80 per cent of what is left. A 1.00 per cent rise in the instalment costs Rs 320/-, or 2.13 per cent of what is left. The same one per cent move, the same outcome, and the loan is more than two and a half times the groceries. The household has just ranked its channels, and the arithmetic is identical to the one Nirvi Engineering runs at a thousand crore.

The Republic of Sankhya, its currency the Marut unit, Nirvi Engineering and the household budget are invented.
Educational material. Not advice on any investment, tax, budget or market position.