The Expensive Sixth Point: Convexity, Thresholds, and the Price of Tail Risk
Fat Tail Notes · Part 17 · V10-P5 Last week we argued that the disagreement over the Greenspan put is a measurement problem: expected welfare has no tail, and tail risk has no average. This week we price the tail properly, and the price turns out to be worse than the mean tells you. A -25% drawdown and a -31% drawdown differ by six points. Their social costs do not differ by six points. The sixth…
The debate over the Greenspan put often hinges on a measurement problem: traditional welfare calculations lack consideration for tail risk, which in turn has no average. This week's focus is on properly pricing tail risk, which reveals its true cost to be greater than what the mean suggests. A -25% drawdown and a -31% drawdown differ by six points in terms of the mean, but their social costs are not simply six points apart. The price of tail risk is the expensive sixth point.
Independent studies across multiple countries and time periods confirm that the damage caused by financial crises is not linear with the size of the crisis. Output loss from a crisis can be permanent, persisting for decades after the crisis officially ends. Present values of crisis-related losses can range from 63% to 302% of pre-crisis per-capita GDP. A seemingly minor 25% drawdown that recovers is a significant cost, while a 31% drawdown that fails to recover represents an entirely different level of cost.
Heavy-tailed severity is evident in systemic banking crises, as evidenced by Laeven and Valencia's extensive database. The insurance industry's Loss Distribution Approach, which combines frequency and severity, is applied to financial crises, providing a multi-country GDP loss distribution that confirms the heavy-tailed nature of crisis outcomes. This approach aligns with catastrophe modeling, which is the correct tool for assessing the risk and cost of financial crises.
Political aftershocks following financial crises have been studied extensively. Funke, Schularick, and Trebesch found that far-right parties tend to gain a significant share of votes after financial crises, a trend not observed in normal recessions or non-financial macroeconomic shocks. Mian, Sufi, and Trebbi documented how crises can polarize voters, weaken ruling coalitions, and reduce the likelihood of implementing financial reforms that could help mitigate the crisis's impact.
The tail event, rather than simply destroying wealth, changes the political system that ultimately determines how losses are distributed.
To examine the impact of tail risk, a Monte Carlo simulation was performed with 2,000 shocks, considering two worlds: one with exogenous leverage (λ=1.0) and another with policy-endogenous leverage (λ drawn above 1). The simulation included two additional cost measures: a convex cost function (C(L) = (−L)²) and a threshold cost that activates a fixed jump once the drawdown crosses 30%.
The results show that while the backstop policy significantly improves the mean drawdown, it only partially reduces the cost of catastrophic drawdowns. The threshold cost reveals that the policy's effectiveness is limited to the worst 1% of outcomes, as only 0.1% of paths cross the 30% threshold. This highlights the importance of properly accounting for tail risk and recognizing that the mean does not capture the full cost of extreme events.
Written by urgent.news from Dev.to's reporting — not their text. Machine-written — may contain errors; check the original before relying on it.
