Question

Phillip offers Kenny a choice of a gamble that pays $1 with probability 0.7 and $2 with probability 0.1 and $4 with probability 0.2 . He then also offers Kenny that instead of taking the gamble he will give him $2.10 with certainty. Kenny says he would prefer to take the $2.10. What does this tell you about Kenny's risk aversion? What if instead he was offered the same gamble or $1.70 with certainty and Kenny prefers the gamble? Explain

Answer 1

The expected value of the gamble is 1x0.7+2x0.1+4x0.2=0.7+0.2+0.8=1.70

It actually does not tell anything about Kenny since in this case, the expected return and variance both are high for the gamble. It is actually a rational choice to go for the certain option.

If Kenny prefers to gamble in the second option, it means he is risk loving because even though both are having same expected return, Kenny is choosing the high risk option, so he must be risk loving.