Kyle WisniewskiEquity Research Lab · Instrument 02 of 07
Scenario tree and return distribution
Stated branches with stated probabilities become a distribution of five-year returns at the current price, so the judgment is visible and the payoff is honest about its spread.
A single forecast hides its own uncertainty. A scenario tree puts it on the table: a handful of branches, each with a probability, each with the growth, margin, and exit multiple that branch would produce. The instrument turns those judgments into a value per share at the horizon and an annualized return at today's price, then perturbs the branch parameters thousands of times to show how wide the payoff really is.
What it measures
For each branch, revenue compounds at the branch's growth rate, the free-cash-flow margin moves from today's level to the branch's exit margin, the exit-year cash flow is capitalized at the branch's multiple, and net debt and the cash generated along the way are added back. Dividing by the share count gives a value per share, and comparing it with the price gives a total and an annualized return. The probability-weighted average across branches is the expected return. The Monte Carlo then samples a branch by its probability and draws each parameter from a normal distribution around its stated value, recording the return each time. The published results are the percentiles of that distribution, its mean, the probability of a loss, and the probability of earning less than the risk-free rate or less than the cost of capital.
Assumptions
The branches and their probabilities are the author's stated judgments, recorded as inputs with their own hash. The parameter uncertainty within a branch is normal and symmetric, with margins and multiples floored at zero; fat tails and skew inside a branch are not modelled, which is one reason to keep the branches themselves far apart. The seed is fixed by the as-of date, so the same inputs always produce the same histogram.
When it misleads
Probabilities that sum to one give the exercise a false air of completeness. The branches are the author's imagination, and a scenario nobody wrote down has probability zero by construction. The expected return is also a poor summary of a distribution with a long right tail: a small chance of a very large payoff can lift the mean while the median stays flat, which is why the percentiles and the probability of loss are always published beside it.
How the lab uses it
The scenario section follows the reverse DCF in every dossier, and its base case is written so it can be compared with the growth the price implies. The memo's variant perception is usually visible here: where the author's probabilities differ from what the price seems to assume, and why. The demo below runs the same arithmetic on illustrative branches so a reader can move a probability and watch the distribution respond.
A scenario tree at a price
Illustrative inputs — not a company's figuresThree branches, three judgments each. The third probability is whatever the first two leave. The histogram is the annualized return across seeded draws around each branch's parameters.
Branches
Uncertainty within a branch (one standard deviation)
| Branch | Probability | Value per share | Total return | Annualized |
|---|---|---|---|---|
| Bear | 25% | $22.95 | −54% | −14.4% |
| Base | 50% | $82.23 | +64% | +10.5% |
| Bull | 25% | $209.57 | +319% | +33.2% |
| Expected | $99.24 | +98% | +9.9% |
- Median annualized return+10.3%
- 5th to 95th percentile−21% to +38%
- Probability of loss26%
Read the figure as a table
| From | To | Share of paths |
|---|---|---|
| −50% | −46% | 0.0% |
| −46% | −43% | 0.0% |
| −43% | −40% | 0.0% |
| −40% | −36% | 0.1% |
| −36% | −33% | 0.2% |
| −33% | −30% | 0.6% |
| −30% | −27% | 0.6% |
| −27% | −23% | 1.4% |
| −23% | −20% | 2.8% |
| −20% | −17% | 3.9% |
| −17% | −14% | 5.3% |
| −14% | −10% | 4.8% |
| −10% | −7% | 2.8% |
| −7% | −4% | 1.9% |
| −4% | −0% | 1.6% |
| −0% | 3% | 3.5% |
| 3% | 6% | 6.8% |
| 6% | 9% | 10.3% |
| 9% | 13% | 11.7% |
| 13% | 16% | 8.8% |
| 16% | 19% | 5.1% |
| 19% | 22% | 2.6% |
| 22% | 26% | 2.4% |
| 26% | 29% | 3.4% |
| 29% | 32% | 5.3% |
| 32% | 36% | 5.9% |
| 36% | 39% | 4.8% |
| 39% | 42% | 2.5% |
| 42% | 45% | 0.8% |
| 45% | 49% | 0.3% |
Across 4,000 seeded paths the median annualized return is +10.3%, the probability-weighted expectation is +9.9%, and 26% of paths lose money over 5 years.