ACE 446 - Class 5-6 Outline (w/extra materials)
April 3-5, 2017
Administrivia
:
Midterm likely 4/19.
Also need a date for a quiz to prep for midterm.
Handouts
: (i) Notes
Class Goals
:
i). Any Qs on Duration?
Hedging applications?
Use of Solver vs. Goal Seek?
Other?
ii).
Begin "Modern Portfolio Theory" concepts by building own portfolio assessment utility.
(
See example
sheets. Starting settings in Excel. Copy file to
own folder
– don’t open from class folder)
I
.
Portfolio Problem:
"how to allocate wealth across a set of available investments".
You typically
first encounter the concepts from a perspective of stock selection, but the principles apply to most
facets of constrained financial decision making.
An example could be how much to spend on clothes,
housing, cars, savings, insurance, retirement items and how to allocate within each category.
Or more
generally, these items represent an approach for
general constrained optimization
– a useful thing to
know how to attack and solve regardless of the context.
In any case, modern
portfolio
theory begins by developing
multiple investment asset
versions of
mean return or
µ
, standard deviation or
σ
, and introducing a measure of the association between the
outcomes of two variables at a time, or correlation.
The correlation between
x
and
y
is often
represented by
ρ
x,y
.
The covariance or
σ
2
xy
is the analogue of the variance, but instead of the
probability weighted squared deviations is found by multiplying the deviations from the means of two
variables at a time – and thus can be negative unlike variance.
Common notations for covariance
includes
cov(x,y),
and sometimes without the power as
σ
x,y
.
Our motivating examples will involve combining various investments with different individual
returns distributions and correlations or covariances among returns.
In practice, you then add
the complication of different risk aversions and the resulting implication for choosing “most
preferred” mixture of assets. Financing is nearly always treated as separable.