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Equation (37) follows also from
predicting from by a linear regression model.
Specifically, assume data pairs
.
In the case of the CAPM these data will be pairs
,
sampled for example at times .
Out aim is to find an optimal prediction of the
based on the (i.e.,, for CAPM, prediction of
the based on the ).
To determine an optimal predicting function
we define a quadratic error measure
|
(40) |
In the particular situation of linear regression
the function is linear, =
.
(A more flexible would for example be a neural network.)
The optimal parameters , are now found as usual by setting
= 0 and
= 0.
Thus,
or
from which follows
|
(45) |
The definition of
being thus the same,
Eq. (43)
can now be identified with
Eq. (37) with
corresponding to ,
to ,
and to .
Next: Nonlinear constraints and spin
Up: Capital Asset Pricing Model
Previous: Capital Asset Pricing Model
Joerg_Lemm
2000-02-25