### Systemic Risk Analysis (Dynamic MES with simulation) of U.S. Financials

The Systemic Risk Analysis presents a variety of risk measures for major Global 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. If this capital shortage occurs at a time when the financial sector is already financially constrained, then the government faces the question of whether to rescue the firm with taxpayer money as other avenues are no longer available. 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 analysis presented here seeks to measure these concepts for U.S. financials. The program calculates the expected capital shortage 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. For U.S. Financials, 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 two steps. First it estimates the expected fractional loss of the firm equity in a crisis when the aggregate market declines significantly in a six-month period. This is called Long-Run Marginal Expected Shortfall or LRMES and is calculated from simulation. Specifically, we first estimate an asymmetric volatility (GJR-GARCH) and correlation (DCC) model for each firm's daily return and the S&P 500 daily return, then simulate many times into the next six months using the bootstrapped residuals. LRMES is then the empirical average of firm returns conditional on the market index falling by 40% in the simulation. Secondly, equity losses expected in a crisis are combined with current equity market value and outstanding measures of debt to determine how much capital would be needed in such a crisis. By default, the prudential capital requirement used in calculating such capital shortfalls is set to be 8% for U.S. firms.

#### 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.

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

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

where $k$ is the capital requirement, $\mathrm{LRMES}$ is the Long-Run Marginal Expected Shortfall, $\mathrm{EQUITY}$ 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. 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 $\Delta \left(\mathrm{RISK}\right)$.