Can you help me to solve this problem step by step please. 20. Given the followi
ID: 2713299 • Letter: C
Question
Can you help me to solve this problem step by step please.
20. Given the following information, what is the standard deviation of the returns on this stock?
State of Economy Probability of State of Economy Rate of Return
Boom .04 .26
Normal .74 .17
Recession .22 -.44
A. 19.90 percent
B. 20.52 percent
C. 22.41 percent
D. 23.79 percent
E. 25.52 percent
Explanation / Answer
Solution :
option 'E' is correct i.e 25.52%
a
b
c
D
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.0394)^2
b x e
Boom
0.04
0.26
0.0104
0.04866436
0.001946574
Normal
0.74
0.17
0.1258
0.01705636
0.012621706
recession
0.22
-0.44
-0.0968
0.22982436
0.050561359
0.0394
0.29554508
0.06512964
Mean = 0.0394
25.52%
Variance = p [(r - mean)^2]
Standard deviation = square root of variance
a
b
c
D
e
f
state of economy
Probability (p)
return (r)
P xr (i.e mean)
(c-0.0394)^2
b x e
Boom
0.04
0.26
0.0104
0.04866436
0.001946574
Normal
0.74
0.17
0.1258
0.01705636
0.012621706
recession
0.22
-0.44
-0.0968
0.22982436
0.050561359
0.0394
0.29554508
0.06512964
Mean = 0.0394
25.52%