VaR That Understated a Rate Shock
A regional bank runs a 99%, one-day historical VaR on its EUR 900m bond portfolio using 250 days of data. The model reports EUR 4.1m. The portfolio has shifted over the past year from short government bonds to long-dated, lower-rated corporate paper with an average duration of 9.2 years, but the historical window still contains mostly the old, calm regime. A new treasurer notices that on the three worst days in the sample, losses were EUR 6.8m, EUR 7.2m and EUR 5.9m, yet the reported VaR is lower because the positions changed. Separately, the bank's liquidity coverage ratio is 108%, just above the 100% minimum, and 22% of high-quality liquid assets are Level 2B equities. The board asks whether VaR is adequate for the interest-rate risk it now carries.
1. Explain why the reported VaR understates current risk and what adjustments are needed.
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Historical VaR revalues today's portfolio against past market moves. If the portfolio now has duration 9.2 years and lower credit quality, applying a historical window dominated by a short-duration, high-quality regime produces shocks that are too small for the current book. The model is not wrong arithmetic; it is mismatched inputs.
Three problems compound:
- Regime mismatch. The 250-day window mostly reflects the old portfolio's environment. A 1bp yield move on EUR 900m at 9.2 years duration is roughly EUR 0.83m, so a 10bp move is ~EUR 8.3m - larger than the reported EUR 4.1m VaR. Small historical yield changes therefore understate plausible shocks.
- Tail evidence ignored. The EUR 6.8m–7.2m losses in the sample show the tail is fatter than the VaR number implies, and those losses occurred on a smaller-duration book.
- VaR is not coherent. It says nothing about the size of losses beyond the 99% threshold, which is exactly what a rate shock delivers.
Adjustments: extend or reweight the window to include stress periods; apply volatility scaling or a shorter, regime-aware window; complement VaR with expected shortfall and duration-based sensitivity limits (e.g., a maximum loss per 25bp move); and run scenario stress tests (parallel +200bp, steepener, credit spread widening). Report all three to the board, not VaR alone.
2. The treasurer argues that because VaR is only EUR 4.1m against EUR 900m of assets, interest-rate risk is immaterial. Critique this and link it to the liquidity position.
Read the worked answer
Comparing a one-day 99% VaR to total assets is a category error. VaR is a threshold loss over a single day at a stated confidence; it is not a measure of economic value sensitivity or of the loss the bank could suffer over a holding period. A 9.2-year duration book loses roughly 8.4% of value for a 100bp parallel rise - about EUR 75m - which is orders of magnitude above the VaR figure. Materiality should be judged on economic value of equity and net interest income sensitivity, plus earnings volatility, not on a one-day tail statistic.
Liquidity linkage: an LCR of 108% is a thin buffer, and 22% of HQLA in Level 2B equities is fragile - equities fall and haircuts widen exactly when rates shock markets. A rate shock that triggers collateral calls or deposit outflow would force asset sales at depressed prices, converting a market-risk event into a liquidity and solvency event. The correct conclusion is the opposite of the treasurer's: the combination of long duration, thin LCR and illiquid HQLA makes interest-rate risk highly material. Recommend a duration cap, HQLA composition limits, and integrated IRRBB/liquidity stress reporting.