### Risk (management) shocks

The risk management rules of most institutional investors follow commonly accepted standards. Alas, similar rules often coerce similar flows. And one-sided flows in markets with limited liquidity can push prices far from fundamental values. In this way, conventional risk management rules can be a cause of distortions and even set in motion self-reinforcing feedback loops.

Prominent risk metrics are **value-at-risk** **(VaR)**, a statistical measure of expected maximum loss at a specific horizon within a specific range of probability, and **expected shortfall**, a measure of expected drawdown in a distress case. These statistical assessments of risk rely on historical variances and covariances, and can be subject to sudden major revisions.

- The calculation of risk metrics depends on the lookback window, i.e. the history of the price return experiences used for its calculation and the weighting of recent versus distant observations. Lookback windows that rely on multi-year experience adapt poorly to a changing risk environment. Therefore,
__many risk metrics are short, with a half-time of lookbacks of no more than 11 days. This makes them susceptible to drastic reassessments based on market volatility alone__. Such “statistical” reassessment would occur without any consideration of the underlying causes of changes in volatility.
__Even with many years of data history, risk estimates are still vulnerable to event shocks__. Small variations in assumptions can cause large changes in forecasts. Some research claims that it would take half a century of daily price data for VaR and expected shortfall models to reach their theoretical asymptotic properties. Intuitively, even long historical samples have only limited data on actual crises and hence are subject to revision with each new crisis experiences (view post here).
__Risk models are prone to compounding uncertainty when they matter most: in financial crises__. Research shows that different types of statistical risk models tend to diverge during market turmoil and hence become themselves a source of fears and confusion (view post here). Acceptable performance and convergence of risk models in normal times can lull the financial system into a false sense of reliability

Reliance on statistical metrics can give rise to so-called **‘VaR shocks’**: __If estimated risk metrics surge, VaR-sensitive institutions recalibrate the risk of their existing positions and subsequently reduce their positions __(view post here). For example, if an institution has a fixed “statistical” risk budget a doubling of the estimated value-at-risk or expected shortfall requires it to liquidate half of its nominal positions. Importantly, this type of selling pressure typically arises *after* the initial price decline.

Analogously, many trading desks or asset management companies set “drawdown limits” for their managers. These are loss thresholds for a portfolio’s net asset value beyond which traders must liquidate part of all of their positions. Managers are typically under obligation to cut risk regardless of asset value and return prospects. Hence, __once the common drawdown limits are broken additional flows ensue in the same direction of the original loss, accentuating price movements__ for no fundamental reason.