Question

You are considering two mutual funds as an investment. The possible returns for the funds are dependent on the state of the economy and are given in the accompanying table. State of the Economy Fund 1 Fund 2 Good 20 % 40 % Fair 10 % 20 % Poor −10 % −40 % You believe that the likelihood is 20% that the economy will be good, 50% that it will be fair, and 30% that it will be poor. a. Find the expected value and the standard deviation of returns for Fund 1. (Round your final answers to 2 decimal places.) b. Find the expected value and the standard deviation of returns for Fund 2. (Round your final answers to 2 decimal places.) c. Which fund will you pick if you are risk averse? Fund 1 Fund 2

Answer 1

Give

Economy condition. Fund 1 return fund 2 return

Good 20 % 40%

Fair. 10% . 20%

Poor. -10% . -40%

Also given P(good)=0.2. P(fair)=0.5 . P(poor)=0.3

Var(fund 1 return)=E(fund 1 return ²) -(E(fund 1 return))²

=160-36 =124

Standard deviation (fund 1 return)=sqrt(var)=sqrt(124)=11.14

Var(fund 2 return)=E(fund 2 return ²)-(E(return of fund 2))²

=1000-36 =964

Standard deviation(fund 2)=sqrt(var)=sqrt(964)=31.05

Since the both funds have same expected return while fund 2 have high standard deviation compared to fund 1 and we know that the if standard deviation is high then there is more deviation in the data so fund 2 is more risky than fund 1 hence being a risk averse I will pick fund 1 as it less risky.