THE EMPIRICAL FRONTIER FOR VALUE-AT-RISK: A USEFUL TOOL OF MARKET RISK MANAGING.

In addition to measuring and monitoring financial risk, it is important for risk managers to understand how financial risky portfolios can be restructured effectively to reduce risk and maximize expected return. The aim of this work is to construct efficient frontiers for relevant market risk measures, like Value-at-Risk (VaR), Conditional VaR (CVaR) and Expected Regret (ER). Unfortunately, VaR is an "untractable" measure in an optimization sense. For this reason, we show how to derive an approximate, or empirical, frontier for VaR from two risk measures both relevant and tractable, like CVaR and ER. Our final goal is to choose as a proxy of VaR the tractable and relevant risk measure better performing with refer to the intractable measure (VaR). Successively, we construct an empirical frontier for VaR that acts as a useful approximation to the "true" efficient frontier. This positive result may provide a precious guide for risk manager who need to rebalance trading book in order to improve its risk-return profile.