Lottery and risk aversion

Text

A lottery pays $50$ EUR with probability $0,4$ and makes you lose $20$ EUR with probability $0,6$. What is the expected value $\bar V$? Would you rather accept a certain amount of $10$ EUR? Compare the expected value and risk aversion.

Solution

The expected value of the lottery is the average of the payoffs weighted by the probabilities: $\bar V_L = 0,4\cdot 50 + 0,6\cdot(-20) = 20 - 12 = \boxed{8\ \text{EUR}}$ The certain amount is worth $\bar V_S = 10$ EUR, so it is greater than the expected value of the lottery. A rational individual, even merely risk-neutral, prefers the certain one. Only a risk lover would accept the lottery (expected value $8$ EUR) giving up the guaranteed $10$ EUR: this behaviour illustrates risk aversion, whereby at equal or nearly equal expected value one prefers the less uncertain outcome.

Links

Topics: Probabilita
Concepts: Avversione al rischio · Valore atteso
Methods: Valore atteso
Skills: Calcolo probabilita · Modellizzare
Exercise type: Problema probabilita