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Portfolio variance = (w')(Covariance Matrix)(w)
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So we need two (2) matrices, since w' is w transposed; i.e., w is the column vector and w' is the transposed row vector
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(A)
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(B)
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(C)
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Weights:
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20%
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30%
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50%
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Covariance Matrix (M):
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(A)
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(B)
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(C)
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(A)
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0.04
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0.09
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0.16
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(B)
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0.09
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0.04
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0.01
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(C)
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0.16
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0.01
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0.04
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Here is the matrix multiplication:
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Step 1
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w'
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Covariance Matrix (M)
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w
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20%
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30%
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50%
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0.04
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0.09
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0.16
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20%
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0.09
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0.04
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0.01
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30%
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0.16
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0.01
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0.04
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50%
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Step 2
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(w')(M)
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0.115
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0.035
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0.055
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Note: I first multiplied (w') by (M), but the
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order does not matter because matrix
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multiplication is associative:
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Step 3
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(w')(M)(w)
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0.061
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[(w')(M)](w) = (w')[(M)(w)]
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