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Statistics for finance · level 1

Expected value of a payoff

Decision trees, options and scenario cases all reduce to the same sum: each outcome weighted by its probability. Check the probabilities add to one before you start.

Theory: Risk Management

Worked example: Payoffs: 30% → 80, 50% → 80, 20% → -60. Expected value?

30%80
50%80
20%-60
E[x]52

Step by step

  1. 1

    Weight each payoff by its probability

    E[x] = Σ pᵢ xᵢ

  2. 2

    Terms

    24 + 40 + -12

  3. 3

    Total

    52

Payoffs: 30% → 80, 50% → 80, 20% → -60. Expected value? = 52

The theory behind it

Intuition

Expected value is the probability-weighted payoff — the fair price of a gamble before risk preferences.

Common pitfalls

  • ×Forgetting a branch, so the probabilities do not sum to one.
  • ×Treating expected value as the likely outcome when the distribution is bimodal.

In the interview

Decision-tree rounds: launch, delay or abandon.