Question

1. Suppose you can take a bet that pays you based on a coin flip.  If the coin ends on heads you receive nothing, if the coin ends on tales you win $500.  Assume that you are risk averse.  First, describe the concept of Certainty Equivalent Wealth (CEW).  Next, describe how and why your CEW changes if your level of risk aversion were to increase.  Finally, describe how and why your CEW changes if the likelihood of ending on tales is greater than 50%.

Answer 1

Here , if coin land ends on head you lose and if ends on tail you win

Chance coin can land on Head = 50%

Chance coin can land on tail = 50%

Concept:

If You are a risk averse person , you are not willing to take risk for more profit when there is much profit at the time. So the Certainty equivalent wealth may be explained as the guaranteed profit or return that you accept now , rather than taking risk for more or higher but uncertain return in the future . It is not sure you will get the profit , you can even lose your profit that you have now. A risk averse person can't take risk in this condition .

If the person is risk averse ,in all cases the certainty equivalent wealth should be less than the expected outcome of the event . If the level of risk averse increase then the person has a tendency to withdraw amount suddenly from the bet.It will decrease the amount of certainty equivalent because as the risk averse increase the difference between the average output and the certainty equivalent will also increase , here the average output is constant so to increase the difference between average output and CEW , the CEW should decrease .

Here the chance of getting tails is increased from 50% initial chance , hence the winning chance is also greater than before. It decreases the risk of bet . Because now winning chance is much more than failing chance. As risk is reduced player can get an additional courage to be part of the bet for more time . It will change the certainty equivalent. The CEW can be increased.