Answer to Question #228233 in Finance for benson

Question #228233

Below are the returns for two assets;




State of nature

r1

r2

probability

Weak growth

15%

15%

1/3

Strong growth

30%

12

1/3

Very strong growth

45%

9

1/3

Expected returns

30%

12

total    1.0


Calculate the two variances and Cov (r1, r2). If assets 1 and 2 are combined 50-50 into a portfolio, what is the variance of this portfolio? Show your calculations.


1
Expert's answer
2021-08-24T17:01:57-0400

Variance tells us the degree of spread in

data set.

"Variance=\\frac{\\sum( x_1-\\bar{x})}{n-1}"

S2=sample variance

"x_1" =the value of the one observationn

"\\bar{x}" =the mean value of all observations

n=the number of observations

r1

"Mean=\\frac{15+30+45+30}{4}=30"

Squared deviation

"=(15-30)^2+(30-30)^2+(45-30)^2+(30-30)^2=450"

Variance"=\\frac{450}{4}=112.5"


r2

"Mean=\\frac{15+12+9+15}{4}=12"

Squared deviation

"=(15-12)^2+(12-12)^2+(9-12)^2+(12-12)^2=18"

Variance"=\\frac{18}{4}=4.5"


Average variance"=\\frac{112.5+4.5}{2}=58.5"



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