Scenario analysis replaces a single price target with a range of outcomes, usually a bull, base and bear case, each carrying a probability. Multiplying every outcome by its probability and adding the results gives an expected value: one figure that respects the whole range of what might happen instead of pretending the future is settled.

This module shows how to build the three cases, how to assign and justify probabilities, how to fold them into an expected value, and how to avoid the error that quietly ruins most scenario work, which is internal inconsistency.

Why one number isn’t enough

A single price target has a quiet dishonesty built into it. It states one figure for a future that has not happened, and by stating only one it implies a confidence nobody actually has.

Scenario analysis makes that uncertainty visible by modelling three distinct futures instead of one: a bull case in which things go well, a base case that is the most likely path, and a bear case in which they go badly.

The most useful thing on the page is then not the middle figure. It is the distance between the outer two. A narrow spread says the analyst can see the shape of this business clearly and the outcomes do not diverge much. A wide spread says the future genuinely forks, and that the same company could reasonably be worth twice as much or half as much depending on things not yet known. Two companies with an identical base case target are not comparable investments if one has a £5 spread and the other has a £40 spread.

The expected value formula

Having three separate futures is honest but awkward, since you eventually have to decide something. Probability is what collapses them back into one number without discarding the information.

One thing about expected value confuses almost everyone the first time, so it is worth stating plainly. The expected value is not a prediction. In the worked example below the expected value is £45.75, and £45.75 is not one of the possible outcomes. The share ends up near £60, near £45 or near £30. The expected value is the average result you would get if this same situation were repeated many times, which is exactly what makes it the right basis for deciding, and exactly what makes it a poor description of what will happen once.

Setting probabilities

This is where judgement enters, and where scenario work is most often done badly. Two rules govern it. The probabilities must sum to 100%, and each one must be justified rather than plucked from the air. The base case, being the most likely, carries the highest weight.

Here is a worked example, with illustrative figures.

The probabilities sum to 100% and the expected value comes to £45.75, which sits just above the base case of £45. That small gap is worth pausing on, because it shows you exactly what the machinery is doing.

Notice that the bull case is £15 above the base and the bear case is £15 below it. The distances are identical, so they cannot be what pushed the answer upward. What pushed it upward is the weighting: 25% on the upside against 20% on the downside. With equal distances, the probabilities alone decide which way the expected value leans. Change those two weights to 20% and 25% and the expected value falls to £44.25, without a single target moving.

That is why unjustified probabilities matter so much. They look like the soft part of the analysis next to all those pounds and pence, and they are in fact the lever that moves the conclusion.

Set that expected value against a current price of, say, £40 and you have framed the decision properly: a modest expected gain, with the size of the possible loss stated openly rather than left to the imagination.

Internal consistency: the most common error

Now the mistake that ruins more scenario work than any other, and it is not an arithmetic mistake.

Every variable inside a scenario must follow from the same story. A scenario is not a slot machine where you set each dial to whatever level suits the case. It is a description of one coherent future, and the numbers in it have to be the numbers that future would actually produce.

So a bull case cannot pair record revenue growth with recession level margins, because the conditions that deliver record growth are not the conditions that crush margins. A bear case cannot assume demand collapses while pricing stays premium, because a company losing its customers does not usually keep its prices. Each of those pairings is internally at war, and the target that comes out of it describes a world that cannot exist.

The test to apply is simple and it is a narrative test rather than a numerical one. Read the assumptions of one case aloud as a short story about the company’s year. If the story contradicts itself halfway through, the case is broken, no matter how neat the arithmetic looks afterwards.

Catalysts and timing

A scenario without a catalyst is a wish. Strong scenario analysis ties each case to specific catalysts: the events that would actually push the company towards that outcome, and roughly when they would land.

A bull case might rest on a product launch landing well, or a margin target being reached by a particular quarter. A bear case might rest on losing a major contract, or a regulatory ruling going the wrong way.

This does two things for you as a reader. It makes the range something you can watch rather than merely believe, because you now know which announcements to pay attention to and roughly when they are due. And it forces the analyst to commit to a mechanism. Anyone can assert that a share might reach £60. Saying it reaches £60 if the second half launch converts at the rate management has guided is a claim you can check against reality in six months, which brings you straight back to the falsifiability test from module 1.

Reading scenario analysis critically

When you meet scenario work in a note, four checks will tell you most of what you need to know about its quality.

• Do the probabilities sum to 100%? If they do not, the expected value is arithmetically wrong, and it is worth checking because it happens more often than you would expect.
• Is the bull case one coherent story, or is it every good thing that could possibly happen, stacked on top of one another? The second is not a scenario. It is a fantasy with a number attached, and its probability should be far lower than whatever has been assigned to it.
• Is the bear case realistic? Look at where the bear target sits relative to today’s price. If a bear case still sits above the current price, no genuine downside has been modelled at all. The analyst has described three versions of winning.
• Are the probabilities justified or merely asserted? As the worked example showed, the weights move the answer. Weights offered without reasoning are guesses wearing the clothes of analysis.

One final caution about expected value itself. It tells you the average outcome, but it says nothing about whether you could survive the bad one. Two investments can share an identical expected value while one risks a 20% loss and the other risks losing everything. Expected value informs the decision of whether to buy. It does not answer the separate question of how much, which is where position sizing comes in.