Method guide · Uncertainty

Decision tree and EMV: calculate expected monetary value

Structure decisions, uncertain events, probabilities and payoffs, then calculate expected monetary value without treating it as a forecast.

Key points

What to remember

  1. 01

    Separate decision, chance and outcome nodes.

  2. 02

    Make probabilities total 100% at each chance node.

  3. 03

    Fold the tree back from right to left.

  4. 04

    Test EMV against risk, liquidity and reversibility.

01

Build an unambiguous structure

A decision node contains controllable options. A chance node contains mutually exclusive uncertain events. A leaf holds a payoff in a common unit and horizon.

Assign, date and justify probabilities. A missing branch or a total other than 100% makes the calculation incomplete.

02

Fold back expected value

For an option, EMV = Σ(probability × payoff). In the illustrative example, A gives 40% × €5m + 60% × −€1m = €1.4m. B gives 40% × €2m + 60% × €0.5m = €1.1m.

A decision node selects the maximum when EMV is the sole objective. This does not automatically represent risk aversion.

OptionHigh outcomeLow outcomeEMV
A40% × €5m60% × −€1m€1.4m
B40% × €2m60% × €0.5m€1.1m
03

Test assumptions that change the choice

Find the probability or payoff threshold that reverses the preference. Sensitivity turns an average into an evidence question.

Similar EMVs may hide different maximum losses, funding needs, timing and exit options.

04

Retain the calculation and accountability

The proposed journey associates Plot with the tree and Atlas with the decision file. Probabilities and payoffs remain sourced, discussed and validated; expected monetary value does not choose on the decision-maker’s behalf.

Retain structure, probabilities, payoffs, sources, sensitivities and the human rationale.

FAQ

Frequently asked questions

Does EMV predict the outcome?

No. It is a probability-weighted average under assumptions.

Should the highest EMV always be chosen?

No. Liquidity, maximum loss, constraints, utility and reversibility may change the choice.

What if probabilities are uncertain?

Use ranges and calculate the threshold at which the choice changes.

SRC

Full sources