The Application of VAR and TCE in Solving a Portfolio Risk Management Problem in Financial Institutions

Risk management is central to the stability and profitability of financial institutions, particularly in the face of market volatility and uncertain loss distributions. Among the most widely applied risk measures are Value at Risk (VaR) and Tail Conditional Expectation (TCE). VaR provides a probabilistic threshold for potential losses at a given confidence level, making it attractive for regulatory coverage and capital requirement resolve. However, its inability to capture the magnitude of losses beyond this threshold limits its effectiveness in managing extreme risk. TCE addresses this limitation by quantifying the expected loss given that the VaR boundary has been breached, thereby offering a more all-inclusive view of tail risk. This paper investigates the application of VaR and TCE in portfolio risk management when asset returns follow a Pareto distribution, a heavy-tailed model frequently used to capture extreme events in financial markets. Analytical formulations of VaR and TCE under the Pareto framework are derived, and their effectiveness in capturing tail risk is compared through a simulated portfolio problem. The results suggest that financial institutions relying solely on VaR may miscalculate losses, whereas incorporating TCE into risk management frameworks enhances robustness against disastrous market downturns.