A equally weighted portfolio is formed with 4 securities A, B, C, D. Summary sta
ID: 2751801 • Letter: A
Question
A equally weighted portfolio is formed with 4 securities A, B, C, D. Summary statistics of the securities are listed below. What is the standard deviation of the portfolio?
.
Variance of A = 493.73
Variance of B = 156.25
Variance of C = 1040.06
Variance of D = 400.00
.
Covariance between A and B = 186.09
Covariance between A and C = 394.13
Covariance between A and D = 168.87
Covariance between B and C = 181.41
Covariance between B and D = 167.50
Covariance between C and D = 483.75
.
16.6
24.1
17.7
18.1
19.8
16.6
24.1
17.7
18.1
19.8
Explanation / Answer
Solution :
A
b
c
d=c^2
e=b*d
Variance
WEIGHT
WEIGHT^2
A
493.73
0.25
0.0625
30.858125
B
156.25
0.25
0.0625
9.765625
C
1040.06
0.25
0.0625
65.00375
D
400
0.25
0.0625
25
total
130.6275
F
g=f*2
h
i=g*h
COVARIANCE
COVARIANCE*2
WEIGHTS
AB
186.09
372.18
0.0625
23.26125
AC
394.13
788.26
0.0625
49.26625
AD
168.87
337.74
0.0625
21.10875
BC
181.41
362.82
0.0625
22.67625
BD
167.5
335
0.0625
20.9375
CD
483.75
967.5
0.0625
60.46875
total
197.71875
Portfolio variance (130.63+197.72)
328.3
Standard deviation (square root of 328.3)
18.1
A
b
c
d=c^2
e=b*d
Variance
WEIGHT
WEIGHT^2
A
493.73
0.25
0.0625
30.858125
B
156.25
0.25
0.0625
9.765625
C
1040.06
0.25
0.0625
65.00375
D
400
0.25
0.0625
25
total
130.6275
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