  A highly relevant problem of modern finance is the design of Value-at-Risk
(VaR) optimal portfolios. Due to contemporary financial regulations, banks and
other financial institutions are tied to use the risk measure to control their
credit, market and operational risks. For a portfolio with a discrete return
distribution and finitely many scenarios, a Difference of Convex (DC) functions
representation of the VaR can be derived. Wozabal (2012) showed that this
yields a solution to a VaR constrained Markowitz style portfolio selection
problem using the Difference of Convex Functions Algorithm (DCA). A recent
algorithmic extension is the so-called Boosted Difference of Convex Functions
Algorithm (BDCA) which accelerates the convergence due to an additional line
search step. It has been shown that the BDCA converges linearly for solving
non-smooth quadratic problems with linear inequality constraints. In this
paper, we prove that the linear rate of convergence is also guaranteed for a
piecewise linear objective function with linear equality and inequality
constraints using the Kurdyka-{\L}ojasiewicz property. An extended case study
under consideration of best practices for comparing optimization algorithms
demonstrates the superiority of the BDCA over the DCA for real-world financial
market data. We are able to show that the results of the BDCA are significantly
closer to the efficient frontier compared to the DCA. Due to the open
availability of all data sets and code, this paper further provides a practical
guide for transparent and easily reproducible comparisons of VaR constrained
portfolio selection problems in Python.
