Conditional Value-at-Risk-Based Portfolio Optimization for Multi-Asset Treasury Management in Nigerian Banks

Portfolio optimization remains a central problem in financial mathematics, with the classical Mean–Variance framework widely applied in asset allocation decisions. De- spite its popularity, variance as a risk measure fails to adequately capture extreme losses and tail risk, which are critical in volatile financial markets. This study extends the traditional portfolio optimization framework by incorporating Conditional Value at Risk (CVaR) as an alternative risk measure and explicitly accounting for transaction costs. Using historical asset return data of the Nigerian financial market, portfolios are constructed under both Mean–Variance and Mean–CVaR optimization frameworks, evaluated under frictionless conditions and scenarios involving proportional trans- action costs. The optimization problems are solved numerically using Python-based computational techniques, and efficient frontiers are generated for comparative analysis. Furthermore, stress testing is conducted under adverse market scenarios, including foreign exchange shocks and interest rate spikes, to assess portfolio robustness. The results indicate that Mean–CVaR optimized portfolios exhibit greater stability and lower downside risk under stressed conditions, particularly when transaction costs are present. These findings highlight the practical relevance of CVaR-based optimization in realistic portfolio management and risk control settings.