What are CoVaR, SRISK, and MES, and how do they measure systemic risk differently?

Systemic risk measures attempt to quantify how much a single institution's distress contributes to system-wide risk. Traditional risk measures (VaR, ES) focus on the institution in isolation; systemic risk measures focus on the interconnections.

The Three Key Measures

1. CoVaR (Conditional Value at Risk)

Developed by: Adrian and Brunnermeier (2016)

Question it answers: How much does the financial system's tail risk increase when institution i is in distress?

Definition:

CoVaR^{system|i} = VaR of the financial system, conditional on institution i being at its own VaR level.

DeltaCoVaR^i = CoVaR^{system|i in distress} - CoVaR^{system|i at median}

This measures the MARGINAL contribution of institution i to system-wide tail risk.

Example: When Rivermark Financial is at its 99% VaR loss, the financial system's 99% VaR increases from $50B to $65B. DeltaCoVaR for Rivermark = $15B.

2. MES (Marginal Expected Shortfall)

Developed by: Acharya et al. (2017)

Question it answers: How much does institution i lose when the SYSTEM as a whole is in its tail?

Definition:

MES_i = E[R_i | R_system < VaR_system]

This is the expected return of institution i, conditional on the system experiencing a tail event.

Example: On days when the financial sector index falls below its 5th percentile, Thornberry Capital's average return is -8.2%. That -8.2% is Thornberry's MES.

A high MES means the institution is heavily exposed to systemic downturns — it loses a lot exactly when the system is under stress.

3. SRISK (Systemic Risk Index)

Developed by: Brownlees and Engle (2017)

Question it answers: How much capital would institution i need to raise in a crisis to maintain a minimum capital ratio?

Definition:

SRISK_i = max[0, k x (D_i + MV_i) - MV_i x (1 - LRMES_i)]

Where:

• k = prudential capital ratio (e.g., 8%)
• D_i = book value of debt
• MV_i = market value of equity
• LRMES_i = long-run marginal expected shortfall (projected equity decline in a crisis)

Example: Ashworth Holdings has $200B in debt, $30B market cap, and LRMES = 45% (equity would lose 45% in a crisis).

SRISK = max[0, 8% x ($200B + $30B) - $30B x (1 - 0.45)]

SRISK = max[0, $18.4B - $16.5B] = $1.9B

Ashworth would need to raise $1.9B in fresh capital during a crisis to remain adequately capitalized.

Comparison Table

Practical Use

• Regulators use these measures to identify G-SIBs and set capital surcharges
• SRISK can be summed across all institutions to estimate the total system-wide capital gap in a crisis
• CoVaR helps regulators identify institutions whose failure would cause the most contagion
• MES helps institutions understand their own vulnerability to systemic events

FRM exam tip: Know the direction of each measure (institution-to-system vs. system-to-institution) and what each one captures that the others don't.

For more on systemic risk, explore our FRM Part II question bank.