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 Fund Fund Economy 1 2 Good 42% 43% Fair 16% 22% Poor -18% -12% You believe that the likelihood is 13% that the economy will be good, 55% 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.) Fund 1 Expected value Standard deviation 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.) Fund 2 Expected value Standard deviation

Answer 1

Solution:-

(A). Find the expected value and the standard deviation of returns for Fund 1

X	P(X)	xP(x)	X^2P(X)
42	0.13	5.46	229.32
16	0.55	8.8	140.8
-18	0.32	-5.76	103.68
		Σ xP(x) = 8.5	Σ X^2P(X) = 473.8

Expected value of return for fund 1 is:-

μ = Σ xP(x)

     = 8.5 %

Standard value of return for fund 1 is:-

σ = √ Σ X^2P(X)

   = √ 473.8 – 8.5^2

   = √ 473.8 – 72.25

= √ 401.55

   = 20.04

(B). Find the expected value and the standard deviation of returns for Fund 2

X	P(X)	xP(x)	X^2P(X)
43	0.13	5.59	240.37
22	0.55	12.1	266.2
-12	0.32	-3.84	46.08
		Σ xP(x) = 13.85	Σ X^2P(X) = 552.65

Expected value of return for fund 2 is:-

μ = Σ xP(x)

     = 13.85 %

Standard value of return for fund 2 is:-

σ = √ Σ X^2P(X)

   = √ 552.65 – 13.85^2

   = √ 552.65 – 191.8225

= √ 360.83

   = 18.995 or 19