Expected value and risk premium

Example numbers — the sure amount differs from person to person. This tool only works out the average and the risk premium from your inputs.

Outcome 1
Outcome 2
Certainty equivalent
Risk premium = expected value − certainty equivalent4 Risk-averse

Takes a sure amount below the average — the gap is the price paid to avoid the risk.

64144EV 104CE 100
Expected value1040.5 × 64 + 0.5 × 144
Standard deviation40√(0.5 × (64 − 104)² + 0.5 × (144 − 104)²)
Risk premium4104 − 100

Not in this calculation

  • Bets with three or more outcomes — only two are worked here
  • Anyone’s actual utility function — it differs from person to person
  • Feeling losses more than gains — loss aversion is a different theory
Reading the risk premium (RP)
RP > 0Risk-averseTakes a sure amount below the average — the gap is the price paid to avoid the risk.
RP = 0Risk-neutralTreats the bet and a sure amount equal to the average as the same.
RP < 0Risk-seekingNeeds more than the average to give up the bet — the swing itself is worth something.

Using the example values

Tool: Renuary (CC BY 4.0) · Numbers are examples. Method and limits on the original page.