U State of the Economy Good Fair Poor . 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. Fund 1 (in %) 20 10 -10 Fund 2 (in %) 40 20 -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. b. Find the expected value and the standard deviation of returns for Fund 2.
Question
U
State of the Economy
Good
Fair
Poor
. 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.
Fund 1 (in %)
20
10
-10
Fund 2 (in %)
40
20
-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.
b. Find the expected value and the standard deviation of returns for Fund 2.
Solution
a. To find the expected value for Fund 1, we multiply each possible outcome by its probability and sum these products.
Expected Value (Fund 1) = (0.2 * 20) + (0.5 * 10) + (0.3 * -10) = 4 + 5 - 3 = 6%
To find the standard deviation, we first need to calculate the variance. The variance is the average of the squared differences from the mean.
Variance (Fund 1) = [(0.2 * (20-6)^2) + (0.5 * (10-6)^2) + (0.3 * (-10-6)^2)] = 1.6 + 8 + 76.8 = 86.4
The standard deviation is the square root of the variance.
Standard Deviation (Fund 1) = sqrt(86.4) = 9.3%
b. We use the same process for Fund 2.
Expected Value (Fund 2) = (0.2 * 40) + (0.5 * 20) + (0.3 * -40) = 8 + 10 - 12 = 6%
Variance (Fund 2) = [(0.2 * (40-6)^2) + (0.5 * (20-6)^2) + (0.3 * (-40-6)^2)] = 23.2 + 39.2 + 331.2 = 393.6
Standard Deviation (Fund 2) = sqrt(393.6) = 19.8%
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