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 33 % 38 % Fair 15 % 16 % Poor −18 % −13 % You believe that the likelihood is 18% that the economy will be good, 50% that it will be fair, and 32% that it will be poor. a. Find the expected value and the standard deviation of returns for Fund 1. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) b. Find the expected value and the standard deviation of returns for Fund 2. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) c. Which fund will you pick if you are risk averse?

Answer 1

let x and y are outcome of fund 1 and fund 2

x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)
33	38	0.18	5.94	6.84	196.02	259.92
15	16	0.5	7.5	8	112.5	128
-18	-13	0.32	-5.76	-4.16	103.68	54.08
	Total	1	7.68	10.68	412.2	442
	E(X)=ΣxP(x,y)=					7.68
	E(X2)=Σx2P(x,y)=					412.2
	E(Y)=ΣyP(x,y)=					10.68
	E(Y2)=Σy2P(x,y)=					442
	Var(X)=E(X2)-(E(X))2=					353.2176
	Var(Y)=E(Y2)-(E(Y))2=					327.9376

a)

expected value =7.68

standard deviation =sqrt(353.2176)=18.79

b)

expected value =10.68

standard deviation =sqrt(327.9376)=18.11

c)

one should pick fund 2 as it has higher expected value and lower standard deviation