Ralph Vince - Portfolio Mathematics

Classical Portfolio Construction 257

Now we pull out row three and column one, the ones that pertain to
Toxico, and also pull row six and column four, the ones that pertain to the
savings account:

Starting Augmented Matrix

X 2 X 3 L 1 L 2 | Answer Pertains to

0.13 0.21 0 0 | 0.1965 Incubeast

1100 | 1 LA Garb

0.25 0.079 0.13 1 | 0L 1

0.079 0.4 0.21 1 | 0L 2

So we will be working with the following matrix:

Starting Augmented Matrix

X 2 X 3 L 1 L 2 | Answer Pertains to

0.13 0.21 0 0 | 0.1965 Incubeast

1100 | 1 LA Garb

0.25 0.079 0.13 1 | 0L 1

0.079 0.4 0.21 1 | 0L 2

Through the use of row operations...the identity matrix is obtained:

1000 | .169 Incubeast

1100 | .831 LA Garb

0010 |−2.97/.5 =−5.94 L 1

0001 | .2779695/.5 = .555939 L 2

Another method we can use to solve for the matrix is to use theinverse
of the coefficients matrix. An inverse matrix is a matrix that, when multiplied
by the original matrix, yields the identity matrix. This technique will be
explained without discussing the details of matrix multiplication.
In matrix algebra, a matrix is often denoted with a boldface capital letter.
For example, we can denote our coefficients matrix asC. The inverse to a
matrix is denoted as superscripting−1 to it. The inverse matrix toCthen
isC−^1.