Question

We have discussed in class the idea that one may measure an investor's risk tolerances to different investment scenarios and then develop a mathematical model to describe the satisfaction or utility that an investor derives from his or her investments. This mathematical function is typically called a "utility" function and greater values of utility mean greater investor satisfaction. Consider the following investor utility function U = E(r) - (A/2)o where U is the inventor's utility, E() is a portfolio's expected return, A is a parameter related to the investor's risk aversion, and o is a portfolio's standard deviation. 1A) (8 points) A portfolio has an expected return of 0.15 and a standard deviation of 0.15. The risk-free rate is 0.06. What value of A in the above utility function makes this investor indifferent between the risky portfolio and the risk-free asset? (In your calculations, use return and standard deviation in decimal form as above, i.e., use 0.15, not 15).

Answer 1

Utility=E(r)-0.5*A*standard deviation^2

Utility from risky portfolio=0.15-0.5*A*(0.15)^2
Utility from risk free asset=0.06

To be indifferent, utility from risky portfolio and risk free asset must be the same
Hence,
0.15-0.5*A*(0.15)^2=0.06
=>A=(0.15-0.06)/(0.5*(0.15)^2)
=>A=8