Probability-weighted valuation

By now you can build a valuation. You can discount cash flows, cross-check a multiple, normalise a cyclical. Each of those methods hands you a single number — "this business is worth ₹200 a share" — and that single number has a problem it does not advertise: it pretends to know things it cannot.

The future is not one story. It is a fan of possibilities. The company might execute beautifully, or stumble, or land somewhere ordinary in between. A single valuation quietly picks one of those futures — usually the one the analyst finds most plausible — and then presents it with a false air of certainty, as if the other futures had been considered and dismissed. They were not considered. They were flattened.

This module is about un-flattening the estimate. Instead of one number, you build three — a bad case, a middle case, a good case — and you attach to each an honest guess at how likely it is. Out of that comes two things a single number can never give you: an expected value that respects all the outcomes, and a range that shows you, out loud, how uncertain you really are.

A point estimate is a lie of omission. When you say a stock is worth ₹200, the listener hears confidence — as if the future had been settled. But behind that ₹200 sat dozens of assumptions about growth, margins and the discount rate, and every one of them could have gone otherwise. Change the growth assumption by two points and the ₹200 becomes ₹240 or ₹160. The single number hid all of that motion inside itself.

Scenario analysis — the practice of valuing a company under a few clearly different futures instead of one — puts the motion back on the table where you can see it. The convention is three cases:

• a bear case, where things go poorly but not catastrophically — the demand slows, the margin slips, a competitor bites;
• a base case, the future you think most likely — steady, unremarkable, the world roughly continuing;
• a bull case, where things go well — the market grows, the company gains share, the margin expands.

Each case is a complete valuation with its own consistent assumptions, not the base case with one number nudged. And then the crucial step, the one that separates this from daydreaming: you attach a probability to each — how likely, honestly, do you think this outcome is? Those probabilities must sum to 100%.

Why bother? Because it forces two kinds of honesty at once. It forces you to actually imagine the bad case — most beginners never write theirs down, so it never restrains them. And it forces you to price your own uncertainty: if your three cases are ₹80, ₹200 and ₹360, you have just admitted, in numbers, that you barely know what this business is worth — and that admission should change how much you are willing to pay. This is reading the range of expectations rather than pretending to forecast one future.

The machinery is one line of arithmetic, and it rests on a single idea: expected value — the probability-weighted average of all the possible outcomes, or what you would get on average if the same situation played out many times over. You multiply each scenario's value by its probability, and add them up.

Take a composite consumer company. illustrative You have built three honest valuations:

• Bear — demand disappoints, a price war compresses margins: worth ₹120 a share. You put this at 25%.
• Base — the business grows with the category, margins hold: worth ₹200 a share. You put this at 50%.
• Bull — it gains share and premiumises, margins widen: worth ₹340 a share. You put this at 25%.

The probability-weighted value — the expected value — is:

(₹120 × 0.25) + (₹200 × 0.50) + (₹340 × 0.25) = ₹30 + ₹100 + ₹85 = ₹215 a share.

Notice two things at once. First, the expected value, ₹215, sits a little above the base case of ₹200, because in this example the bull case is further from the middle than the bear case — the upside outcome is bigger than the downside is small. Skew matters, and a point estimate would have missed it entirely. Second, and more important, the range is ₹120 to ₹340. That spread is not a nuisance to be averaged away — it is the headline. It says: even after all this work, the true value could plausibly be anywhere across a wide band, so treat ₹215 as the middle of a cloud, not a bull's-eye.

One discipline keeps this from becoming a game. The value that goes into each scenario should be built on the cash the owner can actually take out — owner earnings: the reported profit, plus non-cash charges like depreciation, minus the capital spending the business truly needs just to keep its competitive position. That is what an owner really pockets, and it is usually less than reported profit, because accounting profit ignores the capex a business must keep feeding in to stand still. Build your scenarios on owner earnings, not on headline profit, and the whole exercise rests on cash rather than on an accounting number that can flatter.

Watch how the weights, not just the values, do the work. illustrative

Two readers value the same composite company and agree on the three scenario values exactly: bear ₹120, base ₹200, bull ₹340. They disagree only on the probabilities.

Reader A, cautious, weights them 40% / 45% / 15%. Her expected value:

(₹120 × 0.40) + (₹200 × 0.45) + (₹340 × 0.15) = ₹48 + ₹90 + ₹51 = ₹189.

Reader B, optimistic, weights them 15% / 45% / 40%:

(₹120 × 0.15) + (₹200 × 0.45) + (₹340 × 0.40) = ₹18 + ₹90 + ₹136 = ₹244.

Same three futures, same three values — and an expected value ₹55 apart, purely from how likely each thinks the good and bad cases are. This is the honest heart of the method: it shows you exactly where your disagreement with someone else lives. It is not in the arithmetic and often not even in the scenarios — it is in the probabilities, which are judgements, not facts. When you and the market disagree about a stock's worth, this technique lets you find the precise assumption you are betting against.

And it disciplines the optimist in yourself. Reader B should have to ask: what do I know that justifies a 40% chance of the bull case? If the answer is "nothing specific, it just feels likely," the weight is enthusiasm wearing the costume of analysis. The probabilities are where wishful thinking hides, so they are where you should look hardest.

Probability-weighting looks rigorous, and that is its most dangerous feature. The arithmetic is exact; the inputs are guesses; and exact arithmetic on guesses produces a number that feels far more solid than it is.

The probabilities are made up. There is no data that tells you the bull case is 25% likely rather than 20% or 35%. You are quantifying a hunch, and dressing a hunch in a percentage does not make it knowledge. The discipline is worth it — it forces you to state your hunch and be consistent — but never mistake the resulting ₹215 for a measurement.

Three scenarios do not cover the future. Reality has a thousand branches, not three, and the genuinely important outcomes are often the ones no scenario imagined — the fraud, the regulatory shock, the technology that made the product obsolete. A tidy bear-base-bull can lull you into feeling you have "covered the downside" when your bear case was merely a mild disappointment, not a real disaster.

The expected value can be an outcome that cannot happen. ₹215 was nobody's scenario — it is a mathematical balance point between ₹120, ₹200 and ₹340. For a stock that either wins a big contract (worth ₹340) or does not (worth ₹120) with nothing in between, the "expected value" of ₹230 is a value the company will never actually be worth. The average of two futures is not a third future.

1. Anchoring the base case to the price. The lazy way to build a base case is to reverse-engineer whatever value justifies today's price, then add a bear below and a bull above. Now your "independent" valuation is just the market's opinion with error bars. Build the base case from the business, not from the quote.

2. A bear case that isn't bearish. Most people's bear case is a good outcome with the enthusiasm turned down slightly. A real bear case imagines genuine trouble — the margin halving, growth stalling, a key customer lost — because that is the case that should be restraining what you pay.

3. Weights that always favour the story you like. If your probabilities happen to make the stock you already wanted to buy look cheap, the weights are conclusions in disguise. Set the values first, then the probabilities, and check whether you would defend those same weights for a stock you disliked.

4. Reporting the expected value and hiding the range. Quoting "₹215" without "₹120 to ₹340" throws away the single most useful thing the exercise produced. The width is the honesty; deleting it restores the false confidence you started with.

5. Building scenarios on reported profit, not owner earnings. If the cash the owner can actually take out is well below accounting profit, every scenario is inflated by the same optimistic denominator, and the whole fan of values floats too high.