Suppose that John is oered a simple gamble in which a single

Suppose that John is o§ered a simple gamble in which a single die is rolled. If the die comes up 1 or 2, he wins $60, and if it comes up 3,4,5 or 6 he loses $20. Bernard is just indi§erent between taking this simple gamble and not taking it.

(a) What is the expected value of this gamble?

(b) Can you tell from this information whether Bernard is risk averse, risk neutral, or risk loving? Explain.

(c) What is the risk premium that Bernard is being paid in order to accept this gamble?

Solution

The expected value of a particular gambling scenario is worked out as follows:

[(probability of winning) x (amount won per bet) + (probability of losing) x (amount lost per bet)]

here probability for winning the bet is 2/6 and the amount won is $60. Similarly, the probability for losing the bet is 4/6 and the amount lost is $20.

Hence Expected value = ((2/6)*60)+((4/6)*(-20)) = 20-13.33 = 6.67

b) Bernard is risk averse as he is in a dilemma whether to accept the gamble or not.