Nine VaR Exceptions in 250 Days
A Karachi asset manager runs a PKR 65bn Shariah-compliant equity fund. Risk uses a 1-day 99% variance-covariance VaR calibrated on 250 days of returns; current VaR is 2.1% of NAV, about PKR 1.37bn. Backtesting over the last 250 days shows nine exceptions; five fell in one week in October. Returns are fat-tailed and negatively skewed. The portfolio has 31% in banks, 18% in a single stock, and 12% in small caps that would take about eight days to liquidate at 10% of average daily volume. The investment committee treats VaR as a hard limit and cuts exposure whenever it is approached. The regulator's stress-testing guidance expects scenario analysis and liquidity considerations. The CRO wants to keep the model because it passed validation two years ago.
1. Test the backtesting result. Is nine exceptions in 250 days consistent with a 99% model? What does the clustering tell you?
Read the worked answer
Expected exceptions = 250 x 1% = 2.5. Nine is far outside that. A binomial or Poisson approximation gives a probability of about 0.1% of observing nine or more exceptions if the model were correct, so the null is rejected: the model understates risk at the 99% level.
Clustering is a second, independent failure. Five exceptions in one week means the exceptions are not independent; the model assumes stable volatility and normal innovations, but the fund experienced a regime shift. A 250-day equal-weighted window adapts slowly, and the normal 2.33 multiplier is too thin for fat, negatively skewed returns. The October event likely combined a market-wide move with a sector move in banks, which the variance-covariance correlation matrix would have treated as diversifying if correlations were estimated over a calm period.
Diagnostics to run: compare each exception's P&L with the VaR forecast and with the volatility forecast; test whether volatility rose before the exceptions; check whether the single stock or the bank sector drove the losses; and re-estimate with a shorter window or exponentially weighted volatility. Passing validation two years ago is not evidence about today's model, and model validation is an annual, ongoing control.
2. Recommend two concrete model changes and quantify the liquidity adjustment for the small-cap sleeve.
Read the worked answer
First, replace or supplement variance-covariance with filtered historical simulation over at least 500 days, using an exponentially weighted volatility update so the model responds to regime shifts. Report expected shortfall at 97.5% alongside VaR; ES captures the size of tail losses that VaR ignores and is less sensitive to the exact exception count.
Second, apply a liquidity horizon to the illiquid sleeve rather than scaling the whole portfolio. The small-cap sleeve is 12% of PKR 65bn = PKR 7.8bn. Its 1-day 99% VaR at 2.1% is about PKR 164m. Scaling by the square root of the eight-day liquidation period (sqrt(8) = 2.83) gives roughly PKR 463m, an incremental add-on of about PKR 299m. That is a defensible first approximation; a more careful approach uses the actual bid-ask spread and market impact at 10% of ADV, and applies a shorter horizon to the liquid large caps.
Also add a single-name concentration limit review - 18% in one stock is high for a fund with daily redemption rights - and a bank-sector stress. These changes should be documented, independently validated and approved by the risk committee before use in limits.
3. The investment committee uses VaR as a hard limit that forces selling into falling markets. Advise on limit design and communication.
Read the worked answer
A hard VaR limit tied to automatic deleveraging is procyclical: volatility rises, VaR rises, the fund sells, and it locks in losses and transfers value to redeeming investors at the wrong price. VaR is also a short-horizon statistical estimate, not a liquidation instruction, and with 12% of the portfolio taking eight days to sell, the trigger cannot be executed at the assumed one-day horizon.
Design: a green, amber and red framework. Green is normal operation. Amber triggers a documented review - reduce risk, hedge, or prepare a communication - with escalation to the CRO and the risk committee. Red requires action within a stated period but permits a temporary breach with formal approval. Pair the VaR zone with hard limits that are genuinely non-negotiable: expected shortfall, a stress-loss limit (for example a 2008-style 40% market fall plus a bank-sector shock), a single-name cap, and a days-to-liquidate limit. Measure liquidity-adjusted VaR monthly.
Communication: present the IC with a one-page statement of what VaR does and does not measure, the current stress results, and the pre-agreed playbook. Report the nine exceptions and the model change transparently. Model risk should sit on the risk register with an owner, annual validation and a limit on how much reliance the IC places on any single number.