Welcome to the OR-Exchange, your site for questions and answers in operations research.

2

Hello,

after stumbling upon this blog post I wonder if there is a comprehensive list of portfolio models? (If not, maybe this question could serve as community wiki?)

flag

3 Answers

0

OK, here is the classical portfolio optimization (the Markovitz model)

Var(R) = \sum_i \sum_j w_i w_j Cov(R_i, R_j) --> min!

subject to

ER = \sum_i w_i ER_i is fixed
\sum_i w_i = 1
w_i >= 0 for all i

where

R ... portfolio return
R_i ... return of position i in the portfolio
w_i ... the portion of position i in the portfolio
ER, ER_i ... the expected return
Var(R) ... the variance (or risk) of the portfolio
Cov(R_i, R_j) ... the variance/covariance of the return of two positions

Now the solution of this problem gives a composition of the portfolio with the least risk given an expected return (which characterizes the portfolio strategy).

I hope I stated it right. If you see any error, feel free to correct it. I made it a community wiki for that purpose ...

What I do not see is the equivalence to the problem formulated the blog post I cite in the question...

link|flag
The equivalence is shown by another great post of Mr Kavelagen -- tinyurl.com/35zqhrw – Karsten W. Apr 24 at 17:01
2

Some of the new developments in the field has been on using conic programming on the Markovitz model see this paper

http://linkinghub.elsevier.com/retrieve/pii/S0167637708000588

link|flag
2

R has a great list of Financial packages including a "portfolio" package. From the site... The portfolio package contains classes for equity portfolio management; the portfolioSim builds a related simulation framework and tradeCosts estimates the potential impact of trades on the prevalent market prices. The backtest offers tools to explore portfolio-based hypotheses about financial instruments. The stockPortfolio packages provides functions for single index, constant correlation and multigroup models.

http://cran.opensourceresources.org/web/views/Finance.html

link|flag
It is good to know that there readily available package. I am looking for information on what a single index model etc. is, i.e. what the underlying mathematical model is. – Karsten W. Apr 15 at 13:34
R has an implementation of CVaR. It is always very helpful. – Mark Apr 16 at 5:09

Your Answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.