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Graduate-Level Modeling · Systemic Risk & Macroprudential Finance

Systemic Risk Contribution Model: CoVaR & SRISK

Size alone was never the right way to spot the next institution that could bring the system down. This is the math that actually ranks them.

How To Use This Model

Reading This Tool

Set beta, volatility, equity and debt for four institutions, and this tool computes the three systemic risk measures the post-2008 academic literature actually uses to rank institutions by how dangerous their distress would be to everyone else.

CoVaR asks how much worse the system's own tail gets when one institution is in trouble. Marginal Expected Shortfall asks the reverse, how much a single institution loses precisely when the whole system is already in its tail. SRISK converts that into an actual expected capital shortfall in dollars, the number regulators eventually care about most.

Institution A

Beta To System 1.60

Idiosyncratic Vol (Daily) 1.2%

Market Cap (Equity, $B) $45B

Book Debt ($B) $520B

Institution B

Beta To System 1.10

Idiosyncratic Vol (Daily) 0.9%

Market Cap (Equity, $B) $28B

Book Debt ($B) $260B

Institution C

Beta To System 0.75

Idiosyncratic Vol (Daily) 0.7%

Market Cap (Equity, $B) $15B

Book Debt ($B) $95B

Institution D

Beta To System 2.10

Idiosyncratic Vol (Daily) 1.8%

Market Cap (Equity, $B) $8B

Book Debt ($B) $140B

System & Method

System (Market) Daily Volatility 1.5%

Tail Quantile Threshold 5%

Prudential Capital Ratio k 8%

Simulated Observations 30000

Focus Institution (For Detail Tab)

A B C D

Aggregate Systemic Risk

Aggregate SRISK (Positive Contributors)

Largest Systemic Contributor

Institutions Requiring Capital

System VaR At Threshold

SRISK By Institution ($B Expected Capital Shortfall)

ΔCoVaR By Institution (Contribution To System Tail Risk)

Systemic Risk & Macroprudential Finance

The Core Formulas

ΔCoVaR_i = β·(VaR_q(i) − Median(i)), from regressing System Return on Institution Return
MES_i = −E[R_i | R_system ≤ VaR_q(system)]
LRMES_i = 1 − exp(−18·MES_i) (NYU Stern V-Lab long-run scaling)
SRISK_i = k·Debt_i − (1−k)·(1−LRMES_i)·Equity_i

When To Actually Use This Model

Teaching post-2008 systemic risk measurement and macroprudential regulation in a financial stability or banking regulation course.
Building intuition for why regulators designate certain institutions as systemically important (D-SIBs, G-SIBs) based on more than just balance sheet size.
Comparing how leverage, market beta and idiosyncratic risk each separately feed into an institution's true systemic footprint.

Key Assumptions & Limitations

This tool uses a single-factor return model to generate institution-system return pairs, real-world SRISK estimation (e.g., NYU Stern's V-Lab) uses a full GARCH-DCC model estimated on actual historical return data.
The 18-day LRMES scaling constant reflects a specific horizon convention from the original SRISK literature, other implementations use different horizon assumptions.
Real systemic risk also depends on network interconnectedness (direct counterparty exposures), which none of CoVaR, MES or SRISK directly captures, they're all return-based, not network-based, measures.

Foundational References

Adrian, T., & Brunnermeier, M. K. (2016). CoVaR. American Economic Review, 106(7), 1705-1741.

Acharya, V. V., Pedersen, L. H., Philippon, T., & Richardson, M. (2017). Measuring Systemic Risk. The Review of Financial Studies, 30(1), 2-47.

Brownlees, C., & Engle, R. F. (2017). SRISK: A Conditional Capital Shortfall Measure of Systemic Risk. The Review of Financial Studies, 30(1), 48-79.

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