Risk and performance optimization for portfolios of bonds and stocks

Tom Fischer
Darmstadt University of Technology¹

Armin Roehrl
Approximity GmbH²

Date: October 24, 2003

Abstract:

We explain how to optimize portfolios of bonds and stocks with respect to the Expected Shortfall (ES), respectively RORC or RORAC based on ES. In a pragmatic approach we combine and correlate a stock market model with geometric brownian motions with a two-factor Cox-Ingersoll-Ross (CIR-2) model for the interest rates/bonds. We use recent results from the theory of risk capital allocation, performance measurement and Swarm Intelligence for optimization. Examples for German market data as well as an analysis of the scalability of the solution to assure fast run-times on clusters of computers for large real-life portfolios are given.

JEL:	G11, G31
Keywords:	Cox-Ingersoll-Ross model; Expected Shortfall;
	Parallel computing; Portfolio optimization; RORAC;
	Swarm Intelligence