Page 83 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes
2
Year Return (%) (R –R) (R – R)
2003 10 2 4
2004 –6 14 196
2005 12 4 16
2006 9 1 1
2007 15 7 49
40 266

R
Mean Return( ) = 40/5 = 8%
Standard Deviation ( ) = = 16.31%
B
Analysis – Security A has a higher historic level of return and lower risk as compared to Security B.
Correlation Coefficient ( ).
AB
NΣXY – (ΣX)(ΣY)
=
2
2
NΣX – (ΣX) 2 NΣY – ΣY 2
A’s return (%) B’s return (%)
2
X X 2 Y Y XY
9 81 10 100 90
5 25 –6 36 –30
3 9 12 144 36
12 144 9 81 108
16 256 15 225 240
2
X= 45 X = 515 Y = 40 Y = 586 XY = 444
2

(5×5) – (45) 2 5×586 – (40) 2
=
(5×515) – (45) 2 5×586 – (40) 2
2,220 – 1800 420
= 2575 – 2025 2930 – 1600 = 550 1330

420 420
= = = 0.491
23.452×36.469 855.271
Verification:
Calculation of Covariance of Returns of Securities A and B

Year Returns (%)
(R –R ) (R –R B) (R A – R ) × (R B – R )
A B A A B A B
2003 9 10 0 2 0
2004 5 –6 –4 –14 56
2005 3 12 –6 4 –24
2006 12 9 3 1 3
2007 16 15 7 7 49
CovAB = 84

Cov 84
 = AB = = 0.491
AB σ σ 10.49×16.31
A B
Cov =    = 10.49 × 16.31 × 0.491 = 84
AB A B AB

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