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 major Global Financial Firms. 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.

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**. The measure incorporates the volatility of the firm and its correlation with the market, as well as its performance in extremes. These are estimated using asymmetric volatility, correlation and copula methods similar to those in other sections of V-Lab. We either use simulation or extrapolation to determine LRMES. 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 firms in Africa, Asia and Americas and 5.5% for firms in Europe due to differences in accounting standards.

**The Systemic Risk Contribution, SRISK%, is the percentage of financial sector capital shortfall that would be experienced by this firm in the event of a crisis**. Firms with a high percentage of capital shortfall in a crisis are not only the biggest losers in a crisis but also are the firms that create or extend the crisis. This SRISK% is the NYU Stern Systemic Risk Ranking of the US Financial sector. Some of the firms on this list are already under government protection. Their risk status is a reflection of the costs to the system if the government guarantees were suddenly withdrawn.

$$\phantom{\rule{0ex}{7ex}}\begin{array}{c}\mathrm{SRISK}=k\cdot \mathrm{DEBT}-\left(1-k\right)\cdot \mathrm{EQUITY}\cdot \left(1-\mathrm{LRMES}\right)\end{array}$$

$$\phantom{\rule{0ex}{5ex}}\mathrm{MES}=-\left({\gamma}_{\mathrm{i,t+1}}+{\beta}_{\mathrm{i,t}}\right){E}_{\mathrm{t-1}}\left({r}_{\mathrm{m,t}}|{r}_{\mathrm{m,t}}<c\right)$$$$\begin{array}{c}\mathrm{SRISK}=k\cdot \mathrm{DEBT}-\left(1-k\right)\cdot \mathrm{EQUITY}\cdot \left(1-\mathrm{LRMES}\right)\end{array}$$

$$\phantom{\rule{0ex}{7ex}}\begin{array}{c}\mathrm{SRISK}=k\cdot \mathrm{DEBT}-\left(1-k\right)\cdot \mathrm{EQUITY}\cdot \left(1-\mathrm{LRMES}\right)\end{array}$$

$$\phantom{\rule{0ex}{5ex}}\begin{array}{}\text{(2)}& {r}_{\mathrm{i,t}}=\left({\Phi}_{1}+{\Phi}_{2}{\beta}_{\mathrm{i,t}}\right){r}_{\mathrm{m,t}}+\sqrt{{h}_{\mathrm{i,t}}}{\xi}_{\mathrm{i,t}}\end{array}$$$$\begin{array}{c}\mathrm{SRISK}=k\cdot \mathrm{DEBT}-\left(1-k\right)\cdot \mathrm{EQUITY}\cdot \left(1-\mathrm{LRMES}\right)\end{array}$$