Use of Beta to Partition Risk
The total risk or variability in earnings can be attributed to two classes of factors:

Marketwide factors which create variability in all securities.

Company specific factors which cause variability in the returns of that company's shares only.
The marketwide factors contribute to the systematic risk and the companyspecific factors contribute to the unsystematic risk. While the systematic risk cannot be diversified away (since all shares purchased to widen the portfolio would be affected by market factors), the unsystematic risk can be diversified away.

The investor would like to know the exact proportions of the systematic and unsystematic risks in the total risk. To determine the systematic risk of a share, the beta (or b) of the share must be ascertained.
Systematic Risk of a Security = ^{b2 }x Variance of the Market Returns
The variance of the market returns is the variance of the returns from the market index.
Unsystematic Risk of a Security = Variance of Returns of Security  Systematic Risk
It must be noted that though the standard deviation is commonly used to denote the risk. However, while partitioning the risk, it is the variance of returns that is partitioned into systematic and unsystematic components.
The coefficient of determination may also be employed to partition the risk.
PERIOD

RETURN ON MARKET INDEX (%) (X)

RETURN ON SECURITY INDEX (%) (Y)








1

24

20

4

16

8.00

22.48

6.1504

2.5

2

10

12

256

144

192.00

11.84

0.0256

148

3

36

26

100

4

20.00

31.6

31.36

58

4

16

8

1764

1024

1344.00

7.92

0.0064

1019

5

20

26

36

4

12.00

19.44

43.0336

21

6

32

28

36

16

24.00

28.56

0.3136

21

7

14

8

144

256

192.00

14.88

47.3344

83

8

30

36

16

144

48.00

27.04

80.2816

9.20

9

60

48

1156

576

816.00

49.84

3.3856

670

10

50

44

576

400

480.00

42.24

3.0976

335


Total

260

240

4088

2584

3112.00

240

214.9888

2362.70


Mean

26

24








Covariance





345.78





S.D

21.3125

16.9443








Variance

454.22

287.11








The coefficient of determination gives us the percentage of the variation of the security's return that is explained by the characteristic line. This time the variance of the security's return gives us the systematic risk.
In our example, let us compute the systematic risk by employing both R^{2} and b
Total return of security = V(Y) = 287.11
R^{2} = = 0.914
Partition of risk of security by employing β
Systematic risk=b^{2} x Variance of the market returns
=(0.761)^{2} x 454.22 = 263.05
Unsystematic risk =Variance of returns of security  Systematic risk
=287.11  263.05 = 24.06
Partition of risk of security by employing R^{2}
Systematic risk =R^{2} x Variance of the security's return
=0.914 x 287.11
=262.42 ≈ 263.00
Unsystematic risk =Variance of returns of security  Systematic risk
=287.11  263.00 = 24.11