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MES, LRMES, and SRISK

A family of market-based systemic measures. MES (marginal expected shortfall) is the expected loss on a firm’s equity conditional on the market experiencing a tail event (its returns falling into the bad tail). LRMES (long-run MES) extends this to a prolonged crisis, the expected equity decline if the market drops sharply over roughly six months (a common calibration uses a market fall of about 40%). SRISK (Brownlees & Engle, 2017; Acharya et al., 2012) is the expected capital shortfall of a firm in a systemic crisis: the capital it would need to restore a prudential equity-to-assets ratio kk after an LRMES-sized loss, given its debt and equity. Summing SRISK across firms gives a market-based estimate of aggregate capital shortfall.

Try it yourself

SRISK — expected capital shortfall

How big a capital hole would open in a systemic crisis? SRISK = k·D − (1 − k)(1 − LRMES)·W compares the equity a prudential ratio k requires against debt to the equity expected to survive a crash. Positive SRISK is a shortfall; it climbs with leverage D/W and with LRMES.

SRISK (expected capital shortfall)+US$39.8bn
-47048961440.2×6.8×13.4×20.1×26.7×33.3×Leverage D/W (×)SRISK (US$bn)SRISK = 0+US$39.8bnSRISK vs leverage (this MES)This bank
MES (1-day) 3.0%LRMES (crisis) 42%Leverage D/W 15.0×
SRISK = required cushion k·D − surviving equity (1 − k)(1 − LRMES)·W
k·D = US$72.0bnsurviving equity = US$32.2bn
Market equity W (US$bn)US$60bn
Book debt D (US$bn)US$900bn
Prudential capital ratio k8.0%
MES, 1-day (%)3.0%
MES — expected 1-day equity loss given a market tail.
LRMES — long-run MES, the expected equity drop in a six-month crisis: 1 − exp(−18·MES).
SRISK — expected capital shortfall built from LRMES, debt, equity, and k.
A crisis would leave only US$32.2bn of surviving equity against a required cushion of US$72.0bn, a shortfall of US$39.8bn. Large size, heavy leverage, and high LRMES together make a firm systemically risky.
A sibling measure, ΔCoVaR, takes the other view: the system's VaR when this bank is in distress minus its VaR when the bank is at its median state — the firm's marginal contribution to system risk.

Why it matters

MES asks: when the market has a bad day, how much does this firm’s stock fall on average? It is the firm’s sensitivity to market tail events. LRMES scales that up to a full-blown crisis. SRISK then turns the loss into a capital question: after such a crash, given how much debt the firm carries, how big a hole would open in its balance sheet relative to the capital regulators want it to hold? A firm is systemically dangerous when it is large, highly leveraged, and falls hard in a crisis, exactly the combination SRISK is built to flag.

Formulas

MES (marginal expected shortfall)
MESi=− E ⁣[ Ri  |  Rm≤−C ]\text{MES}_{i} = -\,E\!\left[\,R_i \;\middle|\; R_m \le -C\,\right]
Expected return on firm ii’s equity conditional on the market return RmR_m being in its lower tail (below threshold CC). Reported as a positive loss. MES is the marginal contribution of firm ii to the market’s expected shortfall.
LRMES (long-run MES, crisis approximation)
LRMESi≈1−exp⁡ ⁣(−18×MESi)\text{LRMES}_{i} \approx 1 - \exp\!\left(-18 \times \text{MES}_{i}\right)
Standard Brownlees-Engle approximation of the expected fractional equity decline of firm ii in a six-month crisis with the market down about 40%. It maps a short-horizon MES into a long-run crisis loss.
SRISK (expected capital shortfall in a crisis)
SRISKi=E ⁣[ Capital Shortfalli∣crisis ]=k Di−(1−k) (1−LRMESi) Wi\text{SRISK}_{i} = E\!\left[\,\text{Capital Shortfall}_i \mid \text{crisis}\,\right] = k\,D_i - (1-k)\,(1-\text{LRMES}_i)\,W_i
kk = prudential capital ratio (e.g. 8%), DiD_i = book debt, WiW_i = market equity. Positive SRISK = a firm expected to be undercapitalized in a crisis. Aggregate systemic risk is ∑imax⁡(SRISKi,0)\sum_i \max(\text{SRISK}_i, 0).

Worked examples

Scenario

During 2008, large, highly leveraged financial firms showed high MES and very high SRISK. Why did SRISK rank them as the biggest systemic threats?

Solution

These firms fell sharply when the market fell (high MES and LRMES) and carried large debt relative to thin equity. SRISK combines both: a big crisis equity loss on top of heavy leverage produces a large expected capital shortfall, the hole regulators would have to fill to restore prudential capital. SRISK therefore flagged precisely the firms whose undercapitalization most threatened the system.

Scenario

Two firms have the same MES. Firm X is small with little debt; Firm Y is large and highly leveraged. Which has higher SRISK, and what does that teach about MES alone?

Solution

Firm Y. SRISK scales the crisis loss by firm size and leverage, so the large, debt-heavy firm has a far larger expected capital shortfall despite identical MES. The lesson: MES measures crisis sensitivity, but systemic damage also depends on size and leverage, which is why SRISK, not MES alone, ranks systemic importance.

Common mistakes

  • ✗MES, LRMES, and SRISK are the same measure. They are distinct: MES is the firm’s expected equity loss given a market tail; LRMES is its long-run crisis version; SRISK is the expected capital shortfall built from LRMES, debt, equity, and the prudential ratio kk.
  • ✗MES measures the firm’s loss when the firm itself is in distress. MES conditions on the market being in its tail, not on the firm; it is the firm’s sensitivity to a market crash.
  • ✗A high MES alone makes a firm the top systemic threat. Systemic damage also depends on size and leverage; SRISK can rank a large, leveraged firm above a small one with the same MES.
  • ✗SRISK requires confidential supervisory data. SRISK is computed from public market and balance-sheet data, which is part of its appeal for external monitoring.

Revision bullets

  • •MES: expected equity loss of a firm given a market tail event
  • •LRMES: long-run MES, the crisis-scale (about six-month, market down ~40%) version
  • •SRISK: expected capital shortfall in a crisis, from LRMES, debt, equity, and ratio k
  • •SRISK rises with crisis sensitivity, size, and leverage together
  • •Aggregate SRISK estimates system-wide capital shortfall from public data

Quick check

Marginal expected shortfall (MES) for firm ii is the expected

SRISK differs from MES because SRISK also incorporates

Connected topics

Systemic RiskCoVaRStress TestingEfficiency & Systemic

Sources

  1. Acharya, Engle & Richardson (2012)
    Acharya, V. V., Engle, R., and Richardson, M. "Capital Shortfall: A New Approach to Ranking and Regulating Systemic Risk." American Economic Review: Papers & Proceedings 102 (3), 2012, 59-64.
    Introduces the capital-shortfall (SRISK) approach and the role of leverage and size.
  2. Brownlees & Engle (2017)
    Brownlees, C., and Engle, R. F. "SRISK: A Conditional Capital Shortfall Measure of Systemic Risk." Review of Financial Studies 30 (1), 2017, 48-79.
    Formal definition and estimation of MES, LRMES, and SRISK from public market data.
  3. Nguyen, V. P. (Thesis, Ch. 3)
    Nguyen, V. P. Bank Efficiency and Systemic Risk. Doctoral thesis, Chapter 3. (Author’s own research; the authoritative source for the MES/LRMES/SRISK estimation used in this atlas.)
    Dr. Nguyen’s thesis estimates MES/LRMES/SRISK to relate bank cost efficiency to systemic-risk contribution.
How to cite this page
Dr. Phil's Quant Lab. (2026). MES, LRMES, and SRISK. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-mes-srisk
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