Financial risk estimation in Ethiopia is crucial for effective financial management and policy-making. Traditional methods often lack precision and robustness, necessitating advanced analytical techniques. We employ a combination of spectral decomposition and condition number analysis on historical Ethiopian financial data. Theoretical assumptions include the validity of linear models for financial transactions, while key properties focus on the stability and convergence of our analytical approach under various market conditions. Our analysis revealed that the eigenvalues derived from the spectral methods exhibit a clear proportionality to risk levels across different sectors in Ethiopia's economy, with significant deviations observed during periods of economic instability. The study underscores the importance of advanced mathematical tools in enhancing financial risk prediction and management frameworks. The empirical results provide a concrete example of how these techniques can be applied to real-world data. Financial regulators and policymakers should consider integrating spectral methods and condition-number analysis into their risk assessment methodologies, particularly during periods of economic volatility. Functional Analysis, Financial Risk Estimation, Spectral Methods, Condition Number, Ethiopia The analytical core is $\hat{y}_t=\mathcal{F}(x_t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.