Risk perception and decision

What is Expected Value (EV)?

It is the average result you expect from a risky decision.

What is the formula for EV?

EV = ∑(xᵢ × pᵢ)

How do you calculate EV?

Multiply each outcome by its probability, then sum all the results.

What is EV used for?

To estimate the long-run average return from repeating the decision.

How do you interpret EV?

It shows the expected average payoff, but it does not show risk.

What is variance?

It measures how much the outcomes differ from the expected value.

What is the formula for variance?

Variance = ∑[pᵢ × (xᵢ − EV)²]

How do you calculate variance?

1. Compute EV
2. Subtract EV from each outcome
3. Square the result
4. Multiply by probability
5. Add all values

How do you interpret variance?

Higher variance means more spread and more risk.

What is standard deviation?

It is the square root of the variance and shows the average distance from the EV.

What is the formula for standard deviation?

Standard deviation (σ) = √Variance

How do you interpret standard deviation?

It shows how far results typically vary from the average, in real units like CHF or €.

What is semi-variance?

It measures how much only the outcomes below the EV deviate from it.

What is the formula for semi-variance?

Semi-variance = ∑[pᵢ × (xᵢ − EV)²] for xᵢ < EV

What is semi-variance used for?

To measure downside risk, especially in the Safety-First model.

What is the Mean-Variance (MV) principle?

It balances expected return and risk using a penalty for risk.

What is the formula for MV?

MV = EV − k × Variance

What does "k" represent?

k is the risk aversion coefficient: the higher it is, the more you dislike risk.

How do you calculate MV?

1. Calculate EV
2. Compute variance
3. Multiply variance by k
4. Subtract the result from EV

How do you interpret MV?

It shows the value of a risky option after accounting for how much you dislike the risk.

What is the Safety-First principle?

It focuses on avoiding outcomes below a minimum acceptable level (called a safety threshold).

What is the formula for Safety-First?

SF = (EV − S) / σ
Where S is the safety threshold, and σ is standard deviation

How do you calculate SF?

1. Subtract the safety level S from the expected value EV
2. Divide the result by the standard deviation σ

How do you interpret SF?

Higher SF means a lower chance of falling below your safety threshold — so it’s safer.

What is the Maximin principle?

It chooses the option with the best of the worst-case outcomes.

When is Maximin used?

When you want to avoid disasters and don’t trust probabilities.

How do you apply Maximin?

1. List the worst outcome for each option
2. Choose the one with the highest minimum

How do you interpret Maximin?

It’s a very conservative method that protects against worst-case scenarios.

What is Expected Utility (EU)?

It measures the average satisfaction (utility) you expect from a risky decision.

EU = ∑(pᵢ × u(xᵢ))