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	41	%	36	%
Fair	18	%	23	%
Poor	−14	%	−12	%

You believe that the likelihood is 23% that the economy will be good, 47% 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 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.)

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)	xy*f(x,y)
41	36	0.23	9.43	8.28	386.63	298.08	339.48
18	23	0.47	8.46	10.81	152.28	248.63	194.58
-14	-12	0.3	-4.2	-3.6	58.8	43.2	50.4
	Total	1	13.69	15.49	597.71	589.91	584.46
	E(X)=ΣxP(x,y)=					13.69
	E(X2)=Σx2P(x,y)=					597.71
	E(Y)=ΣyP(x,y)=					15.49
	E(Y2)=Σy2P(x,y)=					589.91
	Var(X)=E(X2)-(E(X))2=					410.2939
	Var(Y)=E(Y2)-(E(Y))2=					349.9699

a)

expected value for fund 1=13.69%

standard deviation for fund 1 =sqrt(410.2939)=20.26%

b)

expected value for fund 2=15.49%

standard deviation for fund 1 =sqrt(349.9699)=18.71%