Question

4. Risk aversion Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment costs $1,000 today and provides a payoff, also described below, one year from now. Option Payoff One Year from Now 100% chance of receiving $1,100 50% chance of receiving $1,000 50% chance of receiving $1,200 50% chance of receiving $200 50% chance of receiving $2,000

Answer 1

Let us evaluate "Expected Values" of all the 3 options

Expected Value of Option I: 100% of $1,100 = $1,100

Expected Value of Option II: ( 50% of $1,000) + ( 50% of $1,200) = $(500+600) = $1,100

Expected Value of Option III: ( 50% of $200) + ( 50% of $ 2,000) = $ 1,100

Hence, Expected Values from all 3 options are equal.

A "risk neutral" person, wishes to maximize his expected value. If Expected Value of all options are equal, then the person will be indifferent between the 3 options.

If Erik is a risk-neutral investor, then he will be indifferent between these options, as Expected Value of all options are equal.

Risk-averse refers to investors who, when faced with investments having a similar expected return, prefer the lower-risk option. Since, Expected Value of all options are equal and risk associated with Option 1 is the least, Devin will prefer Option 1, assuming everything else remains constant.