Expected return and standard deviation. Use the following information to answer
ID: 2448912 • Letter: E
Question
Expected return and standard deviation. Use the following information to answer the questions.
State of
Economy
Probability
of State
Return on
Asset D in
State
Return on
Asset E in
State
Return on
Asset F in
State
Boom
0.36
0.06
0.32
0.15
Normal
0.48
0.06
0.19
0.08
Recession
0.16
0.06
0.24
0.05
a.What is the expected return of each asset?
b.What is the variance of each asset?
State of
Economy
Probability
of State
Return on
Asset D in
State
Return on
Asset E in
State
Return on
Asset F in
State
Boom
0.36
0.06
0.32
0.15
Normal
0.48
0.06
0.19
0.08
Recession
0.16
0.06
0.24
0.05
Explanation / Answer
Expected Return on Asset D = (0.36 x .06) + (0.48 x .06) + ( 0.16 x .06) = .06
Expected Return on Asset E = (0.36 x .32) + (0.48 x .19) + (0.16 x - 0.24) =.168
Expected Return on Asset F = (0.36 x .15) + (0.48 x .08) + (0.16 x -.05) = .0844
Variance of Asset D = no variance because expected return matches with actual return.
Variance of Asset E:
Boom = 0.32 - .168 = .152
Recession = .19 - .168 = .022
Normal = -.24 - .168 = -.408
Variance of Asset F
Boom = 0.15 - .0844 = .0656
Recession = .08 - .0844 = -.0044
Normal = -.05 - .0844 = -.1344
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