Question

expected return and standard deviation. use the following information to answer the questions.

state Econ, probability. AssetsA, AssetB, AssetsC
Boom.              0.31.           0.05.       0.23.         0.33
Normal.           0.46.           0.05.       0.06.          0.19
Recession.      0.23.           0.05.       -0.03.       -0.24

A) what is the expected return of each asset?

B) what is the variance of each asset?

C) what is the standard deviation of each asset?

hint: make sure to round all intermediate calculations to at least seven decimal places. the input instructions, phases in parenthesis after each answer box, only apply for the answers you will type.

Answer 1

a) Expected Return of Asset A = 0.31*0.05+0.46*0.05+0.23*0.05 = 5%
Expected Return of Asset B = 0.31*0.23+0.46*0.06-0.23*0.03 = 9.2%
Expected Return of Asset C = 0.31*0.33+0.46*0.19+0.23*-0.24 =13.45%

b) variance of Asset A =0.31*(0.05-5%)^2+0.46*(0.05-5%)^2+0.23*(0.05-5%)^2 = 0%
variance of Asset B =0.31*(0.23-9.2%)^2+0.46*(0.06-9.2%)^2+0.23*(-0.03-9.2%)^2 = 0.9798%
variance of Asset C =0.31*(0.33-13.45%)^2+0.46*(0.19-13.45%)^2+0.23*(-0.24-13.45%)^2 = 4.5523%

c) Standard Deviation of Asset A = (Variance)^0.5 = 0%
Standard Deviation of Asset B = (Variance)^0.5 = 0.9798%^0.5 =9.90%
Standard Deviation of Asset A = (Variance)^0.5 = 4.5523%^0.5 = 21.34%

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