Chapter 12
Problem 1
From the information listed in the text, compute the average annual return, the
variance, standard deviation, and coefficient of variation for each asset.
ASSET ANNUAL
RETURNS
A) 5%, 10%, 15%, 4%
B) -6%, 20%, 2%, -5%, 10%
C) 12%, 15%, 17%
D) 10%, -10%, 20%, -15%, 8%, -7%
A) 5,10,15,4=34/4=8.5
Average annual return =
8.5
5-8.5=-3.5
3.5*3.5=12.25
10-8.5=1.5
1.5*1.5=2.25
15-8.5=6.5
6.5*6.5=42.25
4-8.5=-4.5
4.5*4.5=20.25
77 / (4-1) =
25.66 Variance
Standard Deviation square root of 25.66 =
5.065
CV= 5.065 / 8.5 =
.60
B) -6, 20,2,-5,10=20.59
21/5=4.2
Average annual return =
4.2
-6
-4.2= -10.2
10.2*10.2=104.04
20-4.2= 15.8
15.8*15.8=249.64
2-4.2= -2.2
2.2*2.2=4.84
-5 – 4.2= -9.2
9.2*9.2=84.64
10-4.2= 5.8
5.8*5.8=33.64
476.8
476 / (5-1) =
119 Variance

Standard Deviation is the square root of 119 =
10.908
10.908 / 4.2 = 2.597
CV = 2.60
C) 12, 15 ,17=44/3=14.67
Average Annual Return=14.67
12-14.67= -2.67
2.67*2.67= 7.13
15-14.67= .33
.33*.33= .11 (.1089)
17-14.67= 2.33
2.33*2.33= 5.43
12.67
12.67 / (3-1) =
6.34 Variance
(6.335)
Standard Deviation is the square root of 6.34 = 2.52
(2.517)
2.52/14.67=.17 (.1717)
CV= .17
D) 10, -10, 20, -15, 8, -7 = 8/6=1.33
Average Annual return=1.33
10 – 1.33=8.67
8.67*8.67=75.17
-10 – 1.33= -11.33
11.33*11.33=128.37
20-1.33= 18.67
18.67*18.67=348.57
-15 – 1.33= -16.33
16.33*16.33=266.67
8-1.33=6.67
6.67*6.67=44.49
-7 – 1.33= -8.33
8.33*8.33=69.39
932.66
932.66 / (6-1)=
186.53 Variance

Standard Deviation is the square root of 186.53 = 13.66
(13.657)
CV 13.66 / 1.33 = 10.27
Problem 2

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