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**Unformatted text preview: **iplythe previous product by the probability of its
occurrence. Fourth, find the some of all the weighted products. The result is the
covariance.
Calculation of covariance between F and G
Probability of
Occurrence Deviation of F
from r hat Deviation of G
from r hat Product of
deviations Product *
P rob. 10%
20%
4 0%
20%
10%
100% -4 %
-2%
0%
2%
4% 4%
2%
0%
-2%
-4 % -0.1600%
-0.04 00%
0.0000%
-0.04 00%
-0.1600% -0.02%
-0.01%
0.00%
-0.01%
-0.02% Covariance =
s um = -0.04 8% Calculation of covariance between F and H
Probability of
Occurrence Deviation of F
from r hat Deviation of H
from r hat Product of
deviations Product *
P rob. 10%
20%
4 0%
20%
10%
100% -4 %
-2%
0%
2%
4% -6%
-4 %
-2%
5%
12% 0.24 00%
0.0800%
0.0000%
0.1000%
0.4 800% 0.02%
0.02%
0.00%
0.02%
0.05% Covariance =
s um = 0.108% Calculation of covariance between F and E
Probability of
Occurrence Deviation of F
from r hat Deviation of E
from r hat Product of
deviations Product *
P rob. 10%
20%
4 0%
20%
10%
100% -4 %
-2%
0%
2%
4% 0%
0%
0%
0%
0% 0.0000%
0.0000%
0.0000%
0.0000%
0.0000% 0.00%
0.00%
0.00%
0.00%
0.00% Covariance =
s um = 0.000% CORRELATION COEFFICIENT
Like covariance, the correlation coefficient also measures the tendency of two stocks to move together, but it
is standardized and it is always in the range of -1 to +1. The correlation coefficient is equal to the covariance
divided by the product of the standard deviations.
Calculation of the correlation between F and G
ρFG = Covariance FG
=
-0.04 8%
=
-0.04 8%
ρFG =
-1.0 SigmaF * SigmaG ÷
÷
÷ 2.19%
0.04 8% 2.19% Calculation of the correlation between F and H
ρFH = Covariance FH
=
0.108%
=
0.108%
ρFH =
0.935 ÷
÷
÷ SigmaF * SigmaH
2.19%
0.116% 5.27% PORTFOLIO RISK AND RETURN: THE TWO-ASSET CASE
Suppose there are two assets, A and B. wA is the percent of the portfolio invested in asset
A. Since the total percents invested in the asset must add up to 1, (1-w A) is the percent of
the portfolio invested in asset B.
The expected return on the portfolio...

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