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Portfolio Design, Optimization, and Stability Analysis


Diethelm Würtz, Rmetrics Association
Mahendra Mehta, Rmetrics Association

This webinar reviews some content available in the eBook Portfolio Optimization with R/Rmetrics, and part of the open source software can be found in the R/Rmetrics package fPortfolio. The most recent developments presented in this webinar will become part in a forthcoming second edition of the eBook and in updates of the Rmetrics software packages. In-depth coverage of these materials is available in courses, tutorials and workshops on portfolio analytics provided by the Rmetrics Association.

In Part I we introduce Rmetrics and summarize the business requirements of portfolio managers from the recent EDHEC Report. [Felix Goltz, A long Road Ahead for Portfolio Construction: Practicioners’ Views of an EDHEC Survey, EDHEC 2009]

In Part II we present the implementation of methods and algorithms as part of the Rmetrics software environment and discuss the supported portfolio objectives, the general quanti¬fication of risk, the interface to the solver factory, and possible constraints settings. A few examples are presented including Markowitz portfolio optimization, factor models, robust covariance estimation, shortfall risk optimization, and covariance and Copulae tail risk budget constraints.

Part III is dedicated to new directions. This includes recent developed concepts like portfolio risk surfaces and portfolio ridge profile lines, rastered risk surfaces and motion charts. They are used for new investment strategies along ridge profiles as an alternative to investments along the efficient frontier.

Part IV investigates stability issues of portfolios. We discuss different stability measures creating selective views on structural breaks and changes, jumps, outliers, and extreme dynamical dependencies. These are based on statistical concepts from structural changes, breakpoint detection, volatility and extreme value clustering, stress scenarios, multireso¬lution views from time/frequency and wavelet analysis, and robust phase space embedding of financial time series.

In Part V we show how to valuate and compare correlations and dependency structures in portfolios, in peer groups, and in trading strategies. A new approach is introduced based on geometric factorization. We explore the time dependence of portfolio instabilities looking on the evolution of shape pictograms and cycles characterizing the feasible set of a portfolio. This allows to define portfolio optimization stability objectives.

At the end of the webinar we add references and links for further studies.

This webinar is a joint presentation from Revolution Analytics, Finance Online and NeuralTechSoft.