Advanced Model
These models are the basis upon which our
demonstration is built. Model 1 relates to the case
where portfolio risk is minimized while maintaining a minimum level
of desired return, and Model 2 relates to the case
where return is maximized while maintaining not exceeding desired levels
of risk.
The NLP implementation of the first model is:
maximize sum xiRi
subject to
xiBi
<= Bd
xi >=
0
sum xi = 1
where:
- xi is the proportion of the portfolio
invested in security i
- Ri is the return on security
i
- Bi is the Beta of security
i
- Bd is the upper bound on the
portfolio's risk
The NLP implementation of the second model
is:
minimize xiBi
subject to
xiRi >=
Rd
xi >=
0
sum xi = 1
where:
- Rd is the desired rate of
return
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Last Updated November 19, 1997 by Chris Payton