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

Öz

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.

Anahtar Kelimeler

• Value at risk
• tail risk
• risk management

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

Öz

Bu çalışma, ikinci dereceden Taylor açılımının portföyler için Değer Riski (VaR) tahminini iyileştirip iyileştirmediğini incelemektedir. Analiz, Nisan 2013-Temmuz 2025 dönemini kapsayan günlük verileri ve BIST100 endeksi, Türk devlet tahvilleri ve altın olmak üzere üç varlık sınıfını kullanmaktadır. Amaç, daha doğru kuyruk riski değerlendirmesi ve dengeli bir portföy tahsisi elde etmektir. Metodoloji, VaR hesaplaması için örneklem içi tahmini örneklem dışı doğrulama ile birleştiren bootstrap yöntemlerini kullanır. Çalışma, normal olmayan getiri özelliklerini analiz etmiş, kuyruk indekslerini tahmin etmiş ve birinci ve ikinci dereceden yaklaşımları kullanarak VaR'ı hesaplamıştır. Tahmin doğruluğu, koşulsuz kapsam ve bağımsızlık testleri aracılığıyla test edilmiştir. Bulgular, ikinci dereceden yöntemin daha düzgün ve istikrarlı VaR tahminleri yanı sıra varlık ağırlıkları boyunca tutarlı Güvenlik-Önceliği (Safety-First) değerleri sağladığını göstermiştir. Ancak, geri testler bu yöntemin istenen %1'lik kuyruk kapsamını tam olarak sağlayamadığını ve aşım oranlarının kümelenmeye devam ettiğini ortaya koymuştur. Hisse senedi ve tahvil ağırlıklı portföyler yetersiz kapsam gösterirken, altın daha istikrarlı risk kontrolü sağlamıştır.

Anahtar Kelimeler

• Riske maruz değer
• kuyruk riski
• risk yönetimi.

Kaynakça

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