Page 84 - DMGT207_MANAGEMENT_OF_FINANCES

Unit 4: Risk and Return Analysis

Return of portfolio (R ) Notes
p
= (0.80 × 9) + (0.20 × 8) = 7.2 + 1.6 = 8.8%
Risk of portfolio ( )
p
2
σ 2 p = (0.80 × 10.49 ) + (0.20 × 16.31 ) + (2 × 0.80 × 0.20 × 10.49 × 16.31 × 0.491)
2
2
2
= (0.64 × 110.04) + (0.04 × 266.02) + 26.88
= 70.43 + 10.64 + 26.88 = 107.95
 = 107.95 = 10.39%
p
4.7.3 Risk and Return of Portfolio (Three Assets)

Formula for calculating risk of portfolio consisting three securities

2
2
2
2
2
2
σ 2 p = W σ + W σ + W σ + 2W W ρ σ σ + W W ρ σ σ z
z
z
x
y
x
x
y
y
z
xz
x
x
yz
y
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
Illustration 13: 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

If the securities are equally weighted, how much is the risk and return of the portfolio of these
three securities?
Solution:
Expected Portfolio Return
= (25 × 1/3) + (22 × 1/3) + (20 × 1/3) = 22.33%
2
2
2
2
2
2
σ = (30) (1/3) +(26) +(24) (1/3) + 2(1/3)(-0.5)(30)(26)
p
+ 2(1/3)(1/3)(0.4)(26)(24) + 2(1/3)(1/3)(0.6)(30)(24)
σ 2 p = 100 + 75.11 + 64 – 86.67 + 55.47 + 96 = 303.91
 = 303.91 = 17.43%
P
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