Page 82 - DMGT207_MANAGEMENT_OF_FINANCES

Unit 4: Risk and Return Analysis

  = Standard deviation of returns of Security A and Security B Notes
A B
 = Correlation coefficient between returns of Security A and Security B
AB
The correlation coefficient (AB) can be calculated as follows:
Cov
AB = AB
σ σ B
A
The covariance of Security A and Security B can be presented as follows:

Cov =   
AB A B AB
The diversification of unsystematic risk, using a two-security portfolio, depends upon the
correlation that exists between the returns of those two securities. The quantification of
correlation is done through calculation of correlation coefficient of two securities ( ). The
AB
value of correlation ranges between –1 to 1; it can be interpreted as follows:
If  = 1, No unsystematic risk can be diversified.
AB
If  = –1, All unsystematic risks can be diversified.
AB
If  = 0, No correlation exists between the returns of Security A and Security B.
AB
Illustration 12: The returns of Security of Wipro and Security of Infosys for the past six years are
given below:

Year Security of Wipro Return (%) Security of Infosys Return (%)
2003 9 10
2004 5 –6
2005 3 12
2006 12 9
2007 16 15

Calculate the risk and return of portfolio consisting.
Solution:
Calculation of Mean Return and Standard Deviation of Security A:

Year Return (%) (R – R) (R – R) 2

2003 9 0 0
2004 5 –4 16
2005 3 –6 36
2006 12 3 9
2007 16 7 49
45 110

Mean Return( ) = 45/5 = 9%
R
Standard Deviation (  ) = 110 = 10.49%
A
Calculation of Mean Return and Standard Deviation of Security B

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