EVAR

The problem with fixed-distribution risk

Most risk models use a lookback window — six months, one year — and assume the future will resemble that window. The number they produce changes slowly, even when the market has moved quickly.

In a volatility regime, the tails are fatter than the model says. In a calm regime, the model overstates risk and leaves capital idle. Either way, the sizing decisions it produces are behind the market.

A VaR model calibrated on the calm of 2023 understated the risk of 2024: for bitcoin it was breached ten times in the year, against fewer than four expected. A model calibrated on 2022 was never breached in 2023, and would not have sized back up for the recovery. The static lookback window is always fighting the last war.

What the evidence says about lookback windows

Volatility clusters. Benoit Mandelbrot observed in a 1963 study of cotton prices that large price changes, of either sign, tend to follow large changes, and small ones tend to follow small ones. Fischer Black noted in 1976 that once stocks become more volatile, they tend to stay more volatile than before. The ARCH and GARCH models, first applied to markets in the late 1980s and early 1990s, made it widely accepted that changes in volatility are highly predictable (Andersen and Bollerslev). A window that weights a quiet day from last year the same as yesterday throws that away.

Fixed windows echo old shocks. J.P. Morgan's 1996 RiskMetrics technical document warned that an equally weighted window changes abruptly when a shock drops out of the sample, often several months after the event. A fixed-window number can therefore fall on a quiet day for no market reason. RiskMetrics weighted recent days more heavily instead, with a decay factor of 0.94 that put 99% of the weight on the last 74 daily observations.

The window chooses the answer. Andrew Haldane of the Bank of England showed in 2009 that monthly UK equity returns had the same standard deviation in the decade to 2007 as over the long history. The long history's kurtosis, a measure of tail fatness, was 16 times larger, so a window can match volatility and still miss the tails. Judged by that decade's distribution, the South Sea bubble months of 1720 and Black Monday in 1987 would have been 6.5- to 12.7-sigma events. Pérignon and Smith found that historical simulation, the most popular method in bank disclosures from 1996 to 2005, carried very little information about future volatility.

Correlations rise in sell-offs. Longin and Solnik studied monthly returns in the five largest equity markets from 1959 to 1996. Large negative returns were much more correlated than a normal model predicts, while large positive returns were not. Forbes and Rigobon showed that part of the measured jump in crisis correlation is a statistical effect of higher volatility. In both readings, a book in a sell-off sees more co-movement than a calm-period correlation suggests.

A history lesson from the banks

The 1996 Basel market risk rules set capital at three times a 10-day, 99% value-at-risk, with the multiple rising when a bank's model was breached too often (Adrian and Shin; Federal Reserve). In August 2007, explaining losses at Goldman Sachs's flagship GEO fund, chief financial officer David Viniar told the Financial Times that Goldman was "seeing things that were 25-standard deviation moves, several days in a row". Haldane pointed out that, under a normal distribution, a 7.26-sigma daily loss should happen about once in 13.7 billion years, roughly the age of the universe. A single 25-sigma day should happen about once in more than 10 to the power 135 years (Dowd and co-authors). Haldane drew the simpler conclusion that the model was wrong.

Regulators responded in two steps. In July 2009 the Basel Committee added a stressed value-at-risk, computed over a one-year period of significant losses, partly to reduce the procyclicality of capital requirements. The Fundamental Review of the Trading Book, proposed in 2012, led to a final market risk standard in 2016, revised in 2019. It bases capital on a 97.5% expected shortfall, the average loss beyond the cut-off, in place of a 99% value-at-risk. Banks must calibrate it to their worst 12 months of stress in data reaching back to at least 2007, and scale it to liquidity horizons of 10 to 120 days that depend on the risk factor.

March 2020 showed how a rule tied to model breaches can raise capital in the middle of a crisis. US banks' value-at-risk models were breached at the same time, and the exceptions threatened to raise their backtesting multipliers. Regulators first let banks cap their multipliers and then excluded every exception between 6 and 27 March 2020, a decision worth about $3.3 billion of market risk capital. The Federal Reserve staff note on the episode put the exceptions down to unusual volatility, and named the multiplier as one mechanism that could make capital requirements procyclical.

What EVAR does differently

EVAR starts from the same structure as a standard loss estimate at a given confidence level — a forward-looking number that says how much the portfolio might lose in the next period, before it happens.

The difference is that EVAR conditions the distribution on the current regime, not on a fixed historical window. The regime is a continuous estimate, refreshed every day using cross-asset signals, realised volatility, and spread behaviour across the instruments in the book, and EVAR itself updates in real time as prices move.

When the regime shifts toward high volatility, the distribution widens and EVAR rises. When the regime stabilises, EVAR falls. The estimate follows the regime, rather than waiting for losses to show up in a lookback window.

How it affects strategy sizing

Each strategy in the book has an EVAR-based position limit. When the book's EVAR rises — because the regime has shifted — each limit tightens automatically. The aim is to reduce exposure as risk rises, not after losses are booked.

This is the practical difference from stop-loss management. A stop-loss is reactive: it exits after the loss. EVAR-based sizing responds to the risk environment: it reduces exposure while losses are still possible, not only once they are realised.

When EVAR falls — the regime has calmed — the limits widen again and capital is re-deployed. The cycle is continuous.

What is different in crypto

A weekend market on weekday plumbing. Silicon Valley Bank failed on Friday 10 March 2023, and at 10pm that night Circle disclosed that it could not withdraw $3.3 billion of USDC reserves held there. USDC redemptions ran on US banking hours, so they dropped to minimal levels over the weekend while trading carried on, and USDC traded as low as 86 cents. Its price rose sharply after a joint backstop announcement by US authorities on Sunday evening and fully recovered once redemptions restarted on Monday (Federal Reserve).

Stress can arrive when other markets are shut. On Friday 10 October 2025 a US announcement of an extra 100% tariff on Chinese imports landed just after the US equity close, leaving crypto the only major market open for price discovery into the weekend. About $19 billion of leveraged positions were liquidated, nearly 90% of them longs, and bitcoin fell about 12.5% intraday (21Shares). FTI Consulting reported that top-of-book bitcoin depth fell by more than 90% on key venues that day. The same pattern appeared in May 2021, when the IMF judged that heavy leverage, offered at up to 125 times on some exchanges, and the automatic liquidations it triggered likely deepened a 40% fall in crypto market value.

The venue sets the price. The same day USDe, a dollar-linked token, fell as low as $0.65 on Binance's order book while staying close to $1 on-chain, and the gap took about 40 minutes to close. Margin systems on the exchange marked positions against that local price, liquidations followed, and Binance later compensated affected users (21Shares). Separately, FTI Consulting reported that auto-deleveraging, which closes profitable positions to cover losses that liquidations leave behind, reduced or closed some of the best-hedged shorts that day and left hedged books exposed. A loss estimate that assumes every hedge holds misses this risk.

The link to equities changes by regime. The IMF found that the correlation between bitcoin and S&P 500 returns rose from 0.01 in 2017 to 2019 to 0.36 in 2020 to 2021. A window that straddles a change like that averages two different markets.

Traps that are easy to miss

Regimes are clearest in hindsight. A real-time regime estimate updates its beliefs as each new observation arrives, so it can miss a regime change or raise a false alarm (Ang and Timmermann). The more persistent the regimes are assumed to be, the more weight the estimate puts on past data. Published regime charts can show smoothed probabilities instead, as one of Ang and Timmermann's does, and these use the whole sample, including data from after the date plotted. Judge any regime signal by what it knew on the day.

Everyone reads the same signal. Jon Danielsson and Hyun Song Shin explained endogenous risk with London's Millennium Bridge, which wobbled on its opening day in June 2000 because pedestrians adjusted their stance in step and made it sway more. Markets behave the same way when many firms cut risk as measured volatility rises. Adrian and Shin found that broker-dealer leverage was strongly procyclical and traced it to firms managing their balance sheets against measured risk. A rule that cuts one book's exposure adds to the selling when many books share it.

Models disagree most in a crisis. Danielsson, James, Valenzuela and Zer found that standard risk models give similar readings in calm periods and disagree much more in market distress. The same number therefore carries more model risk in a crisis than in a quiet month.

Low volatility can be imposed. A price held by a central bank floor or a redemption promise shows little volatility until the support goes. The Swiss National Bank enforced a minimum exchange rate of 1.20 francs per euro until 15 January 2015, when it dropped the floor with immediate effect and the franc appreciated sharply against all currencies. An estimate built from recent volatility sees little danger in a pegged price, and stablecoins carry the same shape of risk.

What EVAR does not do

It does not predict direction. EVAR says nothing about whether the market goes up or down. It says how much risk is appropriate given the current environment.

It is not a guarantee. Markets can move faster than any risk update can respond. A single session can move beyond any reasonable EVAR estimate. That residual risk cannot be eliminated, only managed and disclosed.

It is not a replacement for judgment. The CIO report that goes out each day includes the EVAR reading alongside a qualitative read on what is driving it. The numbers and the narrative run together.

How to read a risk number

Count the breaches, then check when they came. A 99% one-day estimate should be exceeded on about one day in a hundred. Peter Christoffersen showed in 1998 that the count can look right while breaches arrive in clusters, the mark of an estimate that does not track changes in volatility. In March 2020 US banks' breaches bunched together, and a Federal Reserve staff comparison found that even the best GARCH benchmarks, refitted on fresh data, breached about as often as the banks did. Versions run on week-old data or never refitted after 2019 breached more, so faster updating helps without removing the problem.

Match the horizon to the exit. A one-day figure fits only a position that can be closed in a day. Scaling it up with the square root of time understates risk when prices jump, and the error grows with the horizon, the jump intensity and the confidence level (Danielsson and Zigrand). Basel sets liquidity horizons of 10 to 120 days by risk factor for the same reason, and requires the 10-day base figure to be measured directly over 10 days, without scaling from a shorter horizon. It still scales that base figure up to reach the longer horizons.

Keep a stressed figure beside it. Regulators added a stressed figure to bank capital partly to make requirements less procyclical. Basel even requires the observations in its 12-month stress window to be equally weighted. A regime-conditioned estimate has a different job. The gap between the two shows how much of today's sizing depends on today's conditions lasting.

Know what the number leaves out. A loss estimate built from prices does not see a venue failing, a redemption window closing or an exchange closing a hedge. The IMF records that major exchanges reported outages on 19 May 2021, when liquidations of leveraged positions peaked. After FTX collapsed, the SEC alleged in December 2022 that FTX customers' funds had been diverted to Alameda Research, a privately held crypto firm owned by FTX's founder. Venue, custody and exchange-rule risks need their own limits.