Question

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.

Answer 1

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$=\frac{112.5+4.5}{2}=58.5$