Market Risk Measurement - VaR and Beyond › Summary

This chapter developed the three major approaches to market risk measurement and explored their limitations and extensions.

Value-at-Risk quantifies the maximum expected loss at a given confidence level and time horizon. The parametric method assumes normally distributed returns and provides fast, closed-form calculations but underestimates tail risk. Historical simulation uses actual past returns without distributional assumptions but depends heavily on the lookback window. Monte Carlo simulation offers flexibility to incorporate complex dynamics like fat tails and time-varying volatility.

VaR limitations include silence about tail severity, potential violations of sub-additivity, and dependence on historical patterns that may not persist. The 2008 financial crisis demonstrated that VaR can provide false comfort when market dynamics shift dramatically.

Expected Shortfall addresses tail severity by measuring the average loss given that VaR is exceeded. It satisfies the coherence axioms that VaR violates and has become the primary regulatory metric under Basel III.

Stress testing complements statistical measures by examining portfolio performance under extreme but plausible scenarios. Historical stress tests use actual crisis returns, while hypothetical scenarios explore vulnerabilities not present in historical data. Together, the three methods cover dimensions of market risk that no single measure can deliver alone.