Margin of Safety: Building In Room to Be Wrong

A margin of safety is a deliberate deduction taken off a finished estimate, sized by how uncertain that estimate is rather than by how wrong anybody expects it to be. Benjamin Graham set the idea out in The Intelligent Investor in 1949. Deduct 25 per cent from Sankalp Industrial Systems Limited's base case of Rs 2,128.14 crore and Rs 1,596.10 crore is left.

Everything that follows is an elaboration of one uncomfortable admission: the estimate is wrong, and nothing inside it says which way. If the working itself could say which direction it leaned, no deduction would be needed. The working would simply be corrected. A deduction is the response that remains once the error is accepted as having an unknown sign, and that is why its size is set by how far the answer could travel rather than by where anybody thinks it is going.

The habit is already familiar from days that have nothing to do with valuation. A traveller leaves for the station twenty minutes earlier than the journey needs. The early start is not a prediction of a twenty minute delay. A prediction would simply say the journey takes twenty minutes longer and leave it there. The early departure answers the auto that might not come, or the road that might be dug up, and there is no saying which. The twenty minutes is sized by the spread of what could happen, not by an average of it, and that single distinction carries the whole of this guide.

Whose idea was this, and what did he actually claim?

Benjamin Graham set out the margin of safety in The Intelligent Investor in 1949, and he treated it as the central idea of the whole discipline rather than as one technique among several. His claim was narrower than the phrase now suggests. He did not say that a deduction makes an estimate better. He said that an estimate is an opinion about the future dressed in arithmetic, that opinions about the future are unreliable in ways nobody can measure in advance, and that the sensible response is to require a gap between the calculated figure and the figure anybody would be willing to act on.

Notice what that leaves out. Graham's idea says nothing about the size of the gap. The idea says nothing about which businesses deserve larger gaps. No percentage appears anywhere in it. The idea supplies the shape of the response, and every decision about magnitude is left to whoever will live with the answer. The silence is not a gap in the idea. The silence is the idea being honest about what it can and cannot settle, and any treatment that hands over a recommended percentage has quietly added something Graham never put there.

There is a second thing in his framing that gets lost. Graham was writing about the difference between an estimate and a decision, and the deduction is where the two are kept apart. An enterprise valueEverything the operating business is worth, before splitting it between the lenders and the shareholders. produced by a model is a piece of arithmetic. The decision that follows is a separate act, made by a person, under conditions the model knows nothing about. The deduction sits in the seam between them, and it is the only place in the whole sequence where somebody is allowed to admit a doubt about their own working and attach a number to it.

Where in the sequence is the deduction allowed to sit?

The mechanics matter more than they look. A margin of safety is applied to an estimate. A margin of safety is not computed inside one. Applying and computing are different operations, and mixing them up destroys what is being built.

The sequence runs on Sankalp Industrial Systems Limited, invented, a listed manufacturer of industrial valves and precision castings. Four things had already happened before the deduction arises. The table names them so that not one of them has to be argued again here.

How that model is built is covered separately. All that matters now is that the arithmetic is over. The figure exists. Only now does anybody deduct anything.

Move the deduction one step earlier and it stops being a margin of safety and becomes part of the model. Suppose that instead of finishing at Rs 2,128.14 crore and taking 25 per cent off, an analyst quietly lowers the assumed growth after Year 5 because the forecast makes them uneasy. The output is smaller. The shortfall might even be the size the deduction would have been. But it is no longer an estimate with a deduction sitting beside it. The output is a different estimate, and a reader who picks it up has no way of separating the analyst's view of the business from the analyst's discomfort with their own working. The two have been stirred together and cannot be pulled apart again.

The reverse mistake is rarer and just as damaging. A deduction that is decided on but never actually taken off before the figure is used is a note in a file. Somebody wrote down that they were uncomfortable, everybody agreed, and then the number that travelled onward was the undeducted one. Between an assumption nobody can unpick and a deduction nobody applied, the second is the more common failure in practice. The unapplied deduction requires no error at all, only the working and the conversation sitting in two different documents.

What exactly is the deduction taken off?

The object being deducted from is one figure, and it deserves naming precisely. The figure is the base caseWhichever set of assumptions a team is prepared to put its name to before anybody argues about it. enterprise value of Rs 2,128.14 crore for Sankalp Industrial Systems Limited. The base case is the sum of two very unequal parts, and their split is what gives the rest of the argument something to work on.

Roughly four rupees in every five of this answer come from the part nobody wrote out year by year. Nothing about the split is unusual, and none of it is a criticism of the model. A discounted cash flow of a growing company looks like this whenever it is taken apart, and the lopsidedness is the first of three specific facts a deduction responds to. To the rupee the two pieces are Rs 4,68,41,43,564 and Rs 16,59,72,35,530, and they add to Rs 21,28,13,79,094 with nothing left over.

Why does a ladder of deductions fall in a straight line?

Take the same Rs 2,128.14 crore and apply deductions of increasing size to it. Every row below is the identical figure multiplied by one less the percentage in the first column. Nothing else changes between rows, and holding everything else still is the whole point of showing them together.

Every five points of deduction removes Rs 1,06,40,68,955 to the nearest rupee, being five per cent of one fixed figure and therefore never moving from row to row. The ladder is a straight line by construction, and that evenness is precisely what a flat percentage gives up in exchange for being carried anywhere. The step never looked at a single assumption, so it knows nothing about which one is fragile.

The gaps in the column above alternate, and the alternation looks at first like a slip. The printed gaps read 106.40 and 106.41 in turn. The step has not changed. Each row is rounded once on its own from the full-precision product, and two of those roundings land on the lower paisa. Rounding once and saying so is the discipline. Nudging a figure until a column looks tidy would hide the arithmetic rather than show it.

What ought to set the size, on this estimate in particular?

Here is where most treatments of the subject go quiet, and where a reader is usually handed a percentage instead of a reason. The size of a deduction is a judgement. The judgement is about something specific, though, and the specific thing can be described even when the number cannot be prescribed.

Three properties of this estimate are the ones a deduction is responding to. Read them carefully and notice what they have in common.

The first is that the larger part of this answer, 77.99 per cent of it, is generated after the last forecast year has passed. Rs 1,659.72 crore of the Rs 2,128.14 crore comes from the terminal blockWhatever value sits past the last forecast year, gathered into a single figure at that point., and the forecast years contribute Rs 468.41 crore. An answer weighted like that rests on a period nobody has described in detail. An answer built mostly out of years somebody actually wrote out has less room to be wrong.

The second is that the cases already disagree with each other by a wide margin before anybody deducts anything. The bull case for this company stands at Rs 2,626.89 crore and the bear caseA worst story somebody has actually written down, with each assumption in it named and open to dispute. at Rs 1,654.94 crore. The distance between them is Rs 9,71,95,53,742, or Rs 971.96 crore, and set against the bear case that distance runs to 58.73 per cent of it. A team that already cannot agree within three fifths of its own lowest figure has said something about the estimate before anybody asks.

Take that spread figure carefully. Subtracting the two printed two decimal crore figures gives Rs 971.95 crore, and it is a paisa out because both ends were rounded before the subtraction. The full-precision difference is Rs 971.9553742 crore, and one rounding of that gives Rs 971.96 crore. On a figure this size the paisa carries no information, but the habit does: a number derived from two already rounded numbers has been rounded twice and is not the figure it claims to be.

The third is that a single input moves the answer a long way. Holding everything else and shifting the 12.00 per cent cost of capital by half a percentage point, the estimate does not merely move: it moves by different amounts in the two directions. Down to 11.50 per cent it becomes Rs 2,302.69 crore, a rise of Rs 174.55 crore. Up to 12.50 per cent it becomes Rs 1,977.06 crore, a fall of Rs 151.07 crore. Dividing by a smaller denominator does more than dividing by a larger one, so half a point in either direction leaves Rs 23.47 crore of difference between the two consequences. Subtracting the two printed figures gives Rs 23.48 crore. Carried to four decimals the difference is Rs 23.4742 crore, and one rounding of that gives the Rs 23.47 crore above. How that rate is estimated, and why shifting a single input differs from shifting four together, are both covered separately; the half point appears here only as a measurement of how loosely the answer is pinned.

Not one of those three facts is a fact about industrial valves. The three are facts about a piece of arithmetic: where its weight sits, how much its authors disagree, and how tightly it is pinned to one input. The distinction is the sharpest way to hold the whole idea. A deduction is not a view about the business. A deduction is a view about the working, and a reader who understands that will never again ask whether a good company deserves a smaller one.

What happens when one unease is charged in two places at once?

Now the problem that costs practitioners the most, and it never announces itself. Uncertainty can be charged in more than one place in a valuation, and the places do not know about each other.

Here is the sequence as it actually happens. An analyst builds the model and feels uneasy about the forecast. So the discount rate goes up half a point, to 12.50 per cent, on the reasoning that a shakier forecast deserves a higher risk-adjusted rateSomebody has already lifted this one because they were uneasy, which makes it one place unease gets charged.. The raised rate alone takes the answer to Rs 1,977.06 crore. Then, at the review meeting, somebody asks for a margin of safety, and 25 per cent is applied to the output. Rs 1,482.80 crore.

The same discomfort has now been priced twice, and neither charge knows the other happened. Nothing in the working is wrong. The half point is defensible on its own. The quarter is defensible on its own. Applied together, the total deduction is the product of two independent judgements neither of which was made in the light of the other, and no reader afterwards can say how much of the shortfall came from which.

The test to apply is simple, and it is a question about provenance rather than about arithmetic. For every rupee of distance between the model's output and the figure that will actually be used, the single place that rupee was charged has to be nameable. If a rupee can be traced to two places, one of the two is a duplicate. The second charge is the one that has to go. The first is already inside the working where a reader can see it.

What does the bear case look like on the same axis as the ladder?

The bear case for this company is Rs 1,654.94 crore, and it was built somewhere else by moving four assumptions together: the yearly increase in revenue down to Rs 80.00 crore, the margin on earnings before interest, tax, depreciation and amortisation (EBITDA) down to 22.5 per cent, the cost of capital up to 12.50 per cent and the terminal growth rateHow fast the never-ending stream is assumed to keep growing once the forecast has run out. down to 4.00 per cent. The bear case is taken here exactly as it stands, and its construction is covered separately.

The bear case and the ladder have not yet stood on the same axis. Do that and something falls out immediately. A 20 per cent deduction leaves Rs 1,702.51 crore, Rs 47.57 crore above the bear case. A 25 per cent deduction leaves Rs 1,596.10 crore, Rs 58.83 crore below it. The worst story anybody actually wrote down for this company falls between a fifth and a quarter off the base case, closer to the fifth.

Both distances were rounded down, so the two add to Rs 106.40 crore against a true five point step of Rs 106.41 crore. Unrounded they add to the step exactly.

Is the crossing an identity or a coincidence?

Pushed until it stops being an observation and becomes arithmetic, the last point runs like this. If a 20 per cent deduction lands above the bear case and a 25 per cent deduction lands below it, then somewhere between the two there is a deduction that lands exactly on it. The crossing percentage is where the two techniques meet at one number.

The crossing is 22.24 per cent. The bear case sits Rs 473.20 crore below the base case, and Rs 4,73,20,11,928 divided by Rs 21,28,13,79,094 comes to 22.2355 per cent at four decimals, written 22.24. Saying that the bear case is 22.24 per cent below the base case and saying that a 22.24 per cent deduction has been applied to the base case are the same sentence read from its two ends. Nothing had to be arranged for that to be true. A percentage is simply that relation read from either end.

The rounded 22.24 per cent applied to the base case gives Rs 1,654.84 crore, against the bear case's Rs 1,654.94 crore. The Rs 0.10 crore between them is the rounding in the percentage, not a defect in either figure, and it is stated rather than tidied away. A reader who wants the exact landing uses the unrounded 22.2355 per cent.

Every locked reading is printed below as well. Nothing on the axis hides behind the slider, and the table is the whole of it.

Are a deduction and a bear case two protections, or two attempts at one job?

Now the honest conclusion, and it is not the one most readers expect. The bear case and the deduction are not two different protections that add up. The two are attempts at the same job, done differently, and the useful thing is not to choose between them but to see both at once.

The difference between them is not severity. On this company they can be made to give the identical figure, as the last section showed. The difference is whether there is anything inside to disagree with.

Carrying easily and being open to argument are the same property with its sign flipped, which is why no amount of care makes one technique dominate the other. A percentage travels because it refers to nothing. A bear case refuses to travel because it refers to four things. Both properties cannot be had at once, and the reason for stating both figures is that together they say something neither can say alone: whether the deduction somebody chose is harsher or gentler than the worst coherent story anybody bothered to write down.

On Sankalp Industrial Systems Limited that comparison has a clean answer. A quarter off the base case lands Rs 58.83 crore below the bear case. Whoever chose 25 per cent chose to deduct more than the four pessimistic assumptions together produce. Choosing that may be exactly what they intended. Either way it is worth knowing that they did it, and without both figures set side by side nobody could tell.

There is a second demonstration of the same point, and it is arithmetic rather than assertion. Carry the identical 25 per cent onto each of the three cases for this company and see what it does. On the bear case it gives Rs 1,241.20 crore. On the base case, Rs 1,596.10 crore. On the bull case at Rs 2,626.89 crore, it gives Rs 1,970.17 crore. The three results are Rs 728.97 crore apart, or three quarters of the Rs 971.96 crore the cases were already apart by. A flat proportion preserves every gap it is applied across, so the deduction has done nothing whatsoever to narrow the disagreement. A flat proportion moves the whole range down and leaves its shape untouched. An operation that never looked at a single assumption could not be expected to do anything else.

What can a deduction not repair?

The last thing to fix in place is the limit, and it is a hard one. A deduction answers an estimate that is out by an amount. The same deduction does nothing at all about an estimate that was built the wrong way.

Return to the station. Leaving twenty minutes early protects against the auto being late, the road being dug up and the queue at the counter. The same twenty minutes protects against none of it once the traveller has gone to the wrong station. Because the error is not in the size of the allowance, no quantity of margin on the time converts a wrong platform into a right one. The error is in what was being measured.

Valuation has the same two categories and they are worth naming apart. An estimate can be out by an amount: the growth is a little high, the margin a little touch generous, the rate a touch low. An error of degree has a size, and a deduction is a coherent response to it. An estimate can also be built the wrong way: the terminal block is a perpetuityAn arithmetic shortcut that treats a stream of cash as going on with no last payment. when the business has a finite asset life, or the cash flows being discounted belong to a different claimant than the rate assumes. The second is an error of kind. An error of kind has no size, and no percentage taken off the answer touches it.

The uncomfortable part is that the two look identical from outside. Both produce a number that is wrong. Only somebody who opens the working can tell which they are looking at, and a deduction applied without opening the working is a bet that the error was of the first sort. Graham's idea is a response to imprecision. The idea was never offered as a response to a wrong model, and treating it as one is the most consequential misreading of it in circulation.

How does somebody who has to sign the note actually use this?

Set the theory down and watch the idea do its work in a room. An analyst covering Sankalp Industrial Systems Limited has finished the model, has the base case at Rs 2,128.14 crore, has the three cases, and now has to write something a reviewer will initial.

The deduction gives them a place in the note rather than a number. The line is where they are permitted to write down how much of their own working they distrust, in a form somebody senior can read in three seconds. Having that line is genuinely useful and it is not what most people think a margin of safety is for. Everything else in the note is an argument about the business. The deduction alone is an argument about the note.

The reviewer's job, correspondingly, is to ask two questions and only two. First: is this percentage the analyst's judgement about the working, or is it the percentage that puts the answer where somebody wanted it to land? The two are indistinguishable on the face of it and completely different in kind, and the only defence is that the three fragility facts were written down before the percentage was chosen rather than after. Second: has this uncertainty already been charged somewhere upstream? If the rate was lifted, the deduction is a second charge for the first feeling.

A lender reads the same thing differently, and the difference is instructive. A lender is not deducting from a value in order to decide a price; a lender is asking how far the borrower's own figure can fall before the loan stops being covered. So the lender's version of this arithmetic runs backwards: not what deduction should be taken, but what deduction the structure survives. The mechanism is identical and only the question changes. Running it backwards is a decent test of whether the idea has been understood rather than the ladder memorised.

The household version comes long before the technique. Anybody running a home on one salary keeps a few months of expenses aside. The size of that buffer is not set by what they expect to spend. The buffer is set by how unpredictable the salary is, how many people depend on it, and how quickly another one could be found. Three properties of the situation, not one prediction about it, and exactly the structure the three fragility facts have. Nobody in that household has heard of Graham, and every one of them is doing what he described.

Sankalp Industrial Systems Limited is invented.
Educational material. Not advice on any investment, tax, budget or market position.