[R-SIG-Finance] mean-(scalar) portfolio optimization
Brian G. Peterson
brian at braverock.com
Wed Aug 23 15:03:18 CEST 2006
The R function solve.QP is used by several authors to solve classic
Markowitz mean-variance optimization using solve.QP and a covariance
matrix.
Many other classes of portfolio optimization solve for the weighting
vector w using a scalar measure of risk, such as VaR, Sortino, Omega,
etc.
Basically, this class of problems could be expressed as:
let w' be the desired portfolio weights
let R be a set of returns for various instruments
solve for a weighting vector w such that risk is minimized
w' = min(risk(R))
solve for a weighting vector w such that return is maximized over risk
budget y
w'=max(mean(R)) such that risk(R)<.05
and other similar formulations.
solve.QP does not appear to be appropriate for these kinds of
optimization. The functions 'optim' and 'optimize' seem to return scalar
values, solving only for a single minima or maxima, and not for the
vector (although I may be misunderstanding them).
Does anyone have any pointers on how you might go about solving these
kinds of optimization problems in R? I apologize if this is a simple
problem that I haven't been able to find a reference for online. I will
happily post the optimizer code once it's working.
Thank you,
- Brian
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