How to find the weighted deviation squared for returns and show process Covarian
ID: 2796458 • Letter: H
Question
How to find the weighted deviation squared for returns and show process Covarianceisa statistical measure of thedegree to which two or more series move together . Weighted Weighted deviation deviation Return Return Probability x Probability x squared for squared for Return on A Return on B Return on A Return on8 5.00% 0.000506 0.002162 7.20% 0.000015 0.000101 1.50% 0.000454 0.006427 on B Probability 25% 60% 15% onA Good OK Bad 15% 10% 5% 20% 12% -10% 3.75% 6.00% 0.75% -10.70% J0.000972 50.008691:-me 10.50% 3.1225 standard deviation of A= 3.1225% Standard deviation of B: 9.3226% 1110.301 ^2x 0.031225] ^20.70] ^2x [0.093226] ^2)+2(0.3)(0.7)("O·0027150"))Explanation / Answer
State
Prob-ability (a)
Rate of return on A (bA)
Rate
of return on B (bB)
(c1)= (a) x (bA)
(c2)= (a) x (bB)
Devn from expected return (dA)=
bA-E(RA)
Devn from expected return (dB)=
bB-E(RB)
Squared deviation (eA)= dA2
Squared deviation (eB)= dB2
(f)=
(a)x(eA)
(f)=
(a)x(eB)
Good
0.25
0.15
0.2
0.0375
0.05
0.045
0.093
0.002025
0.008649
0.00050625
0.00216225
OK
0.6
0.10
0.12
0.06
0.072
-0.005
0.013
0.000025
0.000169
0.000015
0.0001014
Bad
0.15
0.05
-0.1
0.0075
-0.015
-0.055
-0.207
0.003025
0.042849
0.00045375
0.00642735
E(RA)
0.105
E(RB)
0.107
Variance
0.000975
0.008691
Standard Deviation
0.031225
0.093226
Explanation:
Expected return on A, E(RA)= 0.0375 + 0.06 + 0.0075 = 0.105
Expected return on B, E(RB)= 0.05 + 0.072 + ( -0.015) = 0.105
Deviation from expected return = Rate of return – Expected return
e.g. 0.15 – 0.105 = 0.045
Squared deviation = (Deviation from expected return)2
e.g. 0.045 x 0.045 = 0.002025
Variance for A = (Squared deviation x probability)
= 0.002025 x 0.25 + 0.000025 x 0.6 + 0.003025 x 0.15 = 0.00050625 + 0.000015 +0.00045375 = 0.000975
Standard Deviation = Variance = 0.000975 = 0.031225
Variance for B = (Squared deviation x probability)
= 0.008649x 0.25 +0.000169 x 0.6 +0.042849 x 0.15 = 0.00216225 + 0.0001014 + 0.00642735= 0.008691
Standard Deviation = Variance = 0.008691= 0.093226
State
Prob-ability (a)
Rate of return on A (bA)
Rate
of return on B (bB)
(c1)= (a) x (bA)
(c2)= (a) x (bB)
Devn from expected return (dA)=
bA-E(RA)
Devn from expected return (dB)=
bB-E(RB)
Squared deviation (eA)= dA2
Squared deviation (eB)= dB2
(f)=
(a)x(eA)
(f)=
(a)x(eB)
Good
0.25
0.15
0.2
0.0375
0.05
0.045
0.093
0.002025
0.008649
0.00050625
0.00216225
OK
0.6
0.10
0.12
0.06
0.072
-0.005
0.013
0.000025
0.000169
0.000015
0.0001014
Bad
0.15
0.05
-0.1
0.0075
-0.015
-0.055
-0.207
0.003025
0.042849
0.00045375
0.00642735
E(RA)
0.105
E(RB)
0.107
Variance
0.000975
0.008691
Standard Deviation
0.031225
0.093226
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