Page 83 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes Cov 84
= AB = = 0.491
AB 10.49×16.31
A B
Cov = = 10.49 × 16.31 × 0.491 = 84
AB A B AB
Return of portfolio (R ) = W (R ) + W (R ) .....(1)
p A A B B
W = 80% = .8; W = 1 – .8 = .2
A B
Putting the values in Eq. (1), we get (0.80 × 9) + (0.20 × 8) = 7.2+1.6 = 8.8%
Risk of portfolio ( )
p
Since, 2 p = w 2 A 2 A w B 2 2 B 2W W P A B .....(2)
B AB
A
Putting the values in Eq. (2), we get
2 2 2 2 2
p = (0.80 × 10.49 ) + (0.20 × 16.31 ) + (2 × 0.80 × 0.20 ×
0.491 × 10.49 × 16.31)
= (0.64 × 110.04) + (0.04 × 266.02) + 26.88

= 70.43 + 10.64 + 26.88 = 107.95

Hence, p = 2 p = 107.95 = 10.39%
Thus the risk and return of combined portfolio are 10.39% and 8.8% respectively.

Risk and Return of Portfolio (Three Assets)

Formula for calculating risk of portfolio consisting three securities

2
2
2
2
2
2
σ 2 = W σ + W σ + W σ + 2W W ρ σ σ + W W ρ σ σ
P x x y y z z x y yz y z x z xz x z
Where,
W , W , W = Proportion of amount invested in securities X, Y and Z
1 2 3
, , = Standard deviations of securities X, Y and Z
x y z
= Correlation coefficient between securities X and Y
xy
= Correlation coefficient between securities Y and Z
yz
= Correlation coefficient between securities X and Z
xz
Example: A portfolio consists of three securities P, Q and R with the following
parameters:
Security Correlation coefficient
P Q R
Expected return (%) 35 22 20
Standard deviation (%) 20 26 24
Correlation coefficient:
PQ -0.5
QR +0.4
PR +0.6

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