Chapter 13
1
• Co-efficient of Variation: (V) = σ/Đ
• Co-efficient of Variation(A) = 1400/2200= 0.64
• Co-efficient of Variation(B) = 1960/2730 = 0.72
• Co-efficient of Variation(C) = 1490/2250 = 0.66
6
• Co-efficient of Variation: (V) = σ/Đ
• Alternative 1
Outcomes(D)
Failure
50
Acceptable
90
Successful
135
Đ = ∑DP = 100
Probability(P)
0.2
0.4
0.4
DP
10
36
54
• Risk / Standard deviation: σ = √∑ (D – Đ)^2*P
• Outcomes(D)
Đ
(D-Đ)
(D-Đ)^2 P
50
100 -50
2500 0.2
90
100
-10
100 0.4
135
100
35
1225 0.4
Standard Deviation = √∑(D-Đ)^2*P
= √1030
=32.09
Coefficient of Variation = 32.09/100 = 0.3209=.32
(D-Đ)^2*P
500
40
490
Alternative 2
• Outcomes(D)
• 90
• 190
• 225
•
Probability (P)
DP
0.3
27
0.3
57
0.4
90
Expected Value , Đ = ∑DP = (27+57+90)= 174
•D
• 90
• 190
• 225
Đ
174
174
174
( D-Đ)
(-84)
16
51
(D-Đ)^2
7056
256
2601
P
0.3
0.3
0.4
(D-Đ)^2*P
2116.8
76.8
1040.4
• Standard Deviation = √∑(D−Đ)^2∗P
• SD= √(2116.8+76.8+1040.4) = 3234 = 56.87
• Co-Efficient of variation = SD/ Expected Value = 56.87/174= 0.33
Alternative 3
•D
P
• 95
0.2
• 215
0.6
• 380
0.2
• Expected Value = (19+129+76)= 224
•
DP
19
129
76
•D
Đ
( D-Đ) (D-Đ)^2
P
(D-Đ)^2*P
• 95
224
(-129) 16641
0.2
3328.2
• 215 224
(-9)
81
0.6
48.6
• 380 224
156
24336
0.2
4867.2
• SD = √ ( 3328.2+ 48.6+ 4867.2) = √8244 =90.80
• Coefficient of variation = SD/Expected Value = 90.80/224= .41
• Alternative 1, .32, Lowest Risk
• Alternation 2, 0.33
• Alternative 3 , 0.41 highest risk
10
• Co-efficient of Variation (Stock) = SD/Expected Value
• COV(S) = 6140/9140= 0.67
• COV (B) = 2560/7680= 0.33
• COV(CF)= 26700/19100= 1.40
• COV(O)= 18200/17700= 1.03
• As Tim is risk averse . Tim will chose bonds as COV(B) is lowest
• B) Mike likes taking risk. Mike will chose Commodity future as
COV(CF) is highest.
18
•A
• Expected Cash Flow ( Palmar Heights) = ( 70*0.2+
75*0.2+90*0.2+105*0.2+110*0.2) = 90
• Expected Cash Flow ( Crenshaw Village) = (75*0.2+
80*0.3+90*.4+100*0.1) = 85
B(Palmer Heights )
•D
Đ
( D-Đ) (D-Đ)^2
P
(D-Đ)^2*P
• 70
90
(-20)
400
0.2
80
• 75
90
(-15)
225
0.2
45
• 90
90
0
0
0.2
0
• 105
90
15
225
0.2
45
• 110
90
20
400
0.2
80
• Standard Deviation = √∑(D-Đ)^2*P
• SD ( Palmer Heights) = √(80+45+0+45+80) = √250= 15.81
• COV(PH) = SD/ Đ= 15.81/90=0.18
Crenshaw Village (SD)
•D
Đ
( D-Đ) (D-Đ)^2
P
(D-Đ)^2*P
• 75
85
-10
100
0.2
20
• 80
85
-5
25
0.3
7.5
• 90
85
5
25
0.4
10
• 100
85
15
225
0.1
22.5
• SD ( Crenshaw Village) = √∑(D-Đ)^2*P
• SD (CV) = √(20+7.5+10+22.5)= 60 = 7.75
• COV ( CV) =SD/Đ= 7.75/85= .09
• C. Palmer heights has more risk as its’ COV is higher.