### SYSTEMIC RISK RANKINGS WITH SIMULATION

The RISK page of the Volatility Laboratory presents a variety of risk measures for major US financial firms. These measures are updated weekly and reveal several dimensions of risk. Historical estimates of each of these risk measures can be plotted to see the changing performance of individual firms.

A financial firm will be unable to function when the value of its equity falls to a sufficiently small fraction of its outstanding liabilities. In good times, such a firm will likely be acquired, may be able to raise new capital or may face an orderly bankruptcy. In bad times, the firm will be unlikely to be able to raise capital, leaving the government with the question of whether to rescue the firm with taxpayer money. In the theoretical analysis of Acharya, Pederson, Phillipon and Richardson (2010), such a capital shortage is damaging to the real economy as the failure of this firm will have repercussions throughout the financial and real sectors. Consequently a firm is systemically risky if it is likely to face a capital shortage just when the financial sector itself is weak.

The analyses presented on this web site seek to measure these concepts for US financial firms. The program calculates the expected capital shortfall faced by a firm in a potential future financial crisis. Conceptually this calculation is like the stress tests that are regularly applied to financial firms; however, here it is done with only publicly available information and is quick and inexpensive to compute. There are two methods used to compute the Long-Run Marginal Expected Shortfall (LRMES) of a firm -- one method which uses simulation and another that does not.

#### Systemic Risk Analysis with Simulation

This calculation takes three steps. First it estimates on a daily basis, the relation between equity returns on a particular firm and the broad market. These are estimated using asymmetric volatility, correlation and copula methods similar to those in other sections of V-Lab. Then it simulates this process in order to calculate the drop in equity value of this firm that would be expected if the aggregate market falls more than 40% in a six-month window. This is called Long Run Marginal Expected Shortfall or LRMES. Finally, equity losses expected in a crisis are combined with current market value of equity and book value of debt to determine how much capital would be needed in a crisis in order to maintain an 8% capital ratio to asset value.

#### Systemic Risk (SRISK)

SRISK is the expected capital shortfall of this firm if there is another crisis. The NYU Stern Systemic Risk Ranking, SRISK%, is the firm’s percentage of financial sector capital shortfall. Firms with a high percentage of capital shortfall in a crisis are not only the biggest losers in a crisis but also are the biggest contributors to the crisis.

Systemic Risk Rankings are based on estimates of the capital shortfall that a financial institution would face if the US equity market collapsed. This measure is constructed for almost 1200 financial institutions around the world using daily equity market data and low frequency accounting data. The Long Run Marginal Expected Shortfall ($\mathrm{LRMES}$) is estimated by calcuating the loss an equity investor would expect if US equity markets fall by at least 40% in six months. The capital shortfall in a crisis is calculated assuming a minimum capital ratio ($k$), which can vary by region, country, or even by firm. Because this is a crisis scenario, firms will be unlikely to be able to raise this capital privately and will come to government officials who may or may not provide taxpayer funds to keep the institution viable. Because a financial bankruptcy in the middle of a crisis is likely to have severe economic consequences, there will be many who will argue for a bailout.

The first step estimates the volatility and correlation between daily firm returns and daily market equity returns. The market returns are measured with the S&P 500 Composite Index. To estimate these models, the market volatility is treated as a univariate GJR-GARCH model while the model of a firm is treated as a GJR-GARCH with DCC correlation that is adjusting between the firm and idiosyncratic shock.

Capital shortfall ($\mathrm{SRISK}$) is computed as

$(22) SRISK = k ⋅ DEBT - 1-k ⋅ EQUITY ⋅ 1-LRMES$

In this equation, $\mathrm{EQUITY}$ is the current market capitalization of this firm and $\mathrm{DEBT}$ is the book value of debt which is calculated as the book value of assets minus the book value of equity.

To sort the firms by any of these categories, simply click on the heading. To plot any of the series, click on the firm name and select the series to be plotted. You can select the time horizon of the plot. To see help, click on the "?s" in the page.

#### Systemic Risk Decomposition

On the V-Lab Systemic Risk Pages, you can see estimates of the amount of capital that firms will need in the event of a crisis, SRISK, and you can view the components and changes in SRISK over time. But what causes SRISK to change? If we look at the SRISK equation, we can get a better idea of the underlying aspects behind these changes:

$(1) SRISK = k ⋅ DEBT - 1-k ⋅ EQUITY ⋅ 1-LRMES$

Where $k$ is the capital requirement and $\mathrm{LRMES}$ is the Long-Run Marginal Expected Shortfall. From equation (1) we can see that the total differential of $\mathrm{SRISK}$ is given by:

$(2) Δ SRISK = k ⋅ d DEBT - 1-k ⋅ 1-LRMES ⋅ d EQUITY + 1-k ⋅ EQUITY ⋅ d LRMES$

Thus, the change in SRISK for any given firm ($\Delta \mathrm{SRISK}$) can be decomposed into three parts:

• $\Delta \left(\mathrm{DEBT}\right)=k\cdot d\mathrm{DEBT}$ — This is the contribution to SRISK of the firm's debt. As a firm takes on more debt, the contribution to SRISK will be positive. Since this data is reported no more frequently than on a quarterly basis, month-to-month values can show no change in $\Delta \left(\mathrm{DEBT}\right)$.

• $\Delta \left(\mathrm{EQUITY}\right)=-\left(1-k\right)\cdot \left(1-\mathrm{LRMES}\right)\cdot d\mathrm{EQUITY}$ — This measure shows how changes in a firm's equity position affects SRISK. A decline in the market capitalization of a company will increase SRISK.

• $\Delta \left(\mathrm{RISK}\right)=\left(1-k\right)\cdot \mathrm{EQUITY}\cdot d\mathrm{LRMES}$ — An increase in the risk attributes of a firm, such as the correlation or volatility, also contributes to SRISK.

To view the changes in SRISK over a period of time in the Systemic Risk Analysis pages on V-Lab, click the 'View Changes' checkbox at the top of the SRISK table. A drop-down will appear which will allow you to select a time period and the SRISK table format will change to the SRISK Decomposition format, which will display the SRISK values for both time periods, $\Delta \mathrm{SRISK}$, $\Delta \left(\mathrm{DEBT}\right)$, $\Delta \left(\mathrm{EQUITY}\right)$, and $\Delta \left(\mathrm{RISK}\right)$.