### Calibrating tail risk

Standard __risk management relies on past volatility of price changes, historical correlation, and assumptions regarding outliers__ of price changes beyond normal ranges. On this basis, the majority of portfolios of liquid financial instruments is managed based on some form of Value-at-Risk (VaR) model, a statistical estimate of a loss threshold that will only be exceeded with a low probability.

Unfortunately, past __volatility is not always a helpful gauge for financial markets risk__. Volatility is merely the magnitude of historic price fluctuations, while risk is the probability and scope of future permanent losses (view post here). The two are not equivalent and may even become opposites. In particular, reliance on historic volatility can create an illusion of predictability that gives rise to carelessness in specific markets. Indeed, low volatility itself is often a cause of excessive leverage and crowded positioning and hence conducive to subsequent outsized market movements.

Therefore, it is helpful to go beyond conventional risk metrics when assessing and calibrating the risk of large outlier events (“tail risk”):

__Risk estimation should include expert assessment with subjective and non-quantifiable elements__. For example, the risks and consequences of political upheavals, monetary policy regime breaks, or first-time sovereign defaults are not typically quantifiable through price history. A broad assessment of risk always requires a broad perspective, common sense, and an open mind.
- Portfolio risk estimates can explicitly consider extreme market regimes. For example, the basic idea behind
**extreme value theory** is to fit an appropriate limiting distribution over returns that exceed a specific threshold. In particular, **extreme value mixture models** simultaneously estimate the threshold for extreme distributions and the extreme distribution itself (view post here). An alternative statistical approach is Bayesian risk forecasting, which accounts for the considerable distributional parameter uncertainty of Value-at-Risk and Expected shortfall estimates (forthcoming post).
- There are also
__quantitative warning signs of increased “tail risk” other than volatility__. The simplest are valuation metrics for detecting bubbles (view post here), i.e. asset prices that are unusually high relative to the present value of estimated future cash flows. Academic papers have argued that equity markets with low dividend yields relative to local government bond yields are prone to large corrections (view post here). Similarly, countries with overvalued exchange rates and high short-term interest rates are prone to currency crises (view post here).
__Volatility-based risk management metrics can be adapted for “tail events” and “gap risk”. __Historically, diversification and downside risk analyses have assumed normal (“Gaussian”) probability distributions. Those are convenient for calculation but give little weight to large outliers. By now this “normality assumption” has been widely refuted and better gauges of tail risk are available (view post here), such as conditional Value-at-Risk. The distribution assumption is crucial for setting risk management parameters realistically and for assessing the potential upside of long-volatility and short-risk strategies.