Page 284 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 11: Capital Market Theory

and so indicates the degree to which the individual security’s risk premium reacts to changes in Notes
the market portfolio’s risk premium. The greater the beta coefficient value the greater the slope
of the characteristic line, greater the systematic risk for an individual security. The slope of the
characteristic line (regression line) is obtained statistically and it shows the relationship of an
individual security with the market.
It is observed from the graph that greater the expected return for the market, the greater the
expected excess for the stock. The characteristic line equation for the individual security is given
below:
R – R = (R – R )
i f 1 1 m f

Example: The rates of return on the security of Company Wipro and market portfolio
for 10 periods are given below:

Period Return of Security Wipro (%) Return on market portfolio (%)
(x) (y)
1 20 22
2 22 20
3 25 18
4 21 16
5 18 20
6 -5 8
7 17 -6
8 19 5
9 -7 6
10 20 11

1. What is the beta of Security Wipro?
2. What is the characteristic line for Security Wipro?
Solution:

1. Let us assume that Market is y and Security Wipro is x

Period R R (R – R ) (R – R ) (R – R )(R – R ) (R – R ) 2
x m x x m m x x m m m m
1 20 22 5 10 50 100
2 22 20 7 8 56 64
3 25 18 10 6 60 36
4 21 16 6 4 24 16
5 18 20 3 8 24 64
6 –5 8 –20 –4 80 16
7 17 -6 2 –18 –36 324
8 19 5 4 -7 –28 49
9 –7 6 –22 –6 132 36
10 20 11 5 –1 –5 1
150 120 120 357 706

R R (R – R )(R – R ) (R – R )
x m x x m m m m

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