FROM FIRST- TO SECOND-ORDER VALUE-AT-RISK: IMPLICATIONS FOR TAIL RISK MANAGEMENT AND DIVERSIFICATION

This study examines whether the second-order Taylor expansion improves Value-at-Risk (VaR) estimation for portfolios. The analysis uses daily data for three asset classes, namely the BIST100 index, Turkish government bonds, and gold, spanning from April 2013 to July 2025. The goal is to achieve more accurate tail risk assessment and a balanced portfolio allocation. The methodology uses bootstrap methods for VaR calculation, combining in-sample estimation with out-of-sample validation. It analyzed non-normal return features, estimated tail indices, and computed VaR using first- and second-order approximations. Predictive accuracy was tested via unconditional coverage and independence tests. Findings show that the second-order method yielded smoother and more stable VaR estimates, as well as consistent Safety-First values across asset weights. However, backtesting revealed it did not fully achieve the desired 1% tail coverage, with exceedances still clustering. Equity- and bond-heavy portfolios showed under-coverage, while gold provided more stable risk control.