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COVID-19 is a new type of shock that is likely to produce losses on loans and financial assets higher and more correlated than historical adverse macroeconomic shocks unless policy stabilization efforts are successful. Further, the sudden economic stop caused by the need for social distancing requires bridge financing to support existing contractual arrangements for employment, debt service, and a range of other obligations. Society has resources in the form of taxation of future income that it can move to the present to provide bridge financing and absorb losses from defaulting loans and ensure that existing forms of capital (physical, human and intangible) remain available for production after the COVID-19 virus wanes. For the US this is taking the form of transfers, direct loans and equity from the US Treasury (UST), and UST “capital” used to back the Federal Reserve’s various lending facilities under its 13(3) authority. The goal of this note is to provide a simple framework to analyze how much UST capital is needed to back the Fed Facilities to achieve the stabilization goal. Simply put, what should be the aggregate capacity (leverage) of the facilities, and how much capital will be available in tail outcomes where the private banking system faces losses greater than its substantial capital buffer? We will bootstrap recent Federal Reserve stress test results to illustrate some possible answers to these questions. This is the notion of how we are stressing the stress tests.

In this chapter we describe stress testing at banks covering the major products and businesses in which banks engage. This includes commercial and retail lending, capital markets (investment banking, sales and trading), and trust and custody. We cover loss and net income modeling and thus balance sheet and P&L (income statement) evolution, including noninterest expense items in the form of operational losses.

Stress testing proved to be an effective crisis fighting tool in the Great Financial Crisis and has since become widely used by regulators and financial institutions to test resilience to financial and economic shocks. This served two objectives: (1) to identify and remediate banks with a capital shortfall, and (2) to restore confidence in the core of the banking system by requiring that banks eliminate any regulatory capital shortfall promptly either by raising capital in private markets or, if unable, from a government backstop fund. The objectives of a stress test will determine six fundamental choices in structuring the exercise: (1) the design of stress scenarios; (2) the risk exposures to be stressed; (3) the range of institutions to be tested, the length of the scenario and the intervals over which shocks are measured; (4) the development of models to map shocks into outcomes and impact on individual bank financials and on the banking system; (5) the choice of criteria to determine whether banks pass or fail the stress test; (6) the decision about what to disclose to the public. But stress tests are no panacea. We discuss a range of challenges to improving the effectiveness of stress tests, such as incorporating nonfinancial risks like cyber, taking into account second-round effects of shocks, broadening the scope beyond just banks, and resisting a tendency to disaster myopia as memories of the financial crisis recede into the past.

Identifying the relevant risk factors and their interdependence is central to understanding the risk exposures and vulnerabilities of a financial institution. It is needed for risk management, solvency assessment and stress testing. We assemble a unique dataset of risk factors relevant for insurers which are different than for banks, although they share exposure to financial asset risks such as corporate bonds and equities. We use this dataset to estimate risk factor correlations to better understand their dependence structure. We find that correlation between non-financial risk factors is very low (usually insignificant), between financial risk factors on the order of 30-50%, and a mix between the financial and non-financial risk factors. We fit marginal distributions to each of the risk factors, and using a t-copula we present simple simulation application to analyze the solvency of three types of insurers (pure life, pure property and casualty, mixed). We do so using both the point estimates of the correlations as well as the 95% upper and lower bound estimates to explore the sensitivity of stress impact on insurers’ solvency. Our analysis should help provide an empirical basis to regulators in calibrating solvency regimes and to insurers to understand their risk sensitivities and capital needs.

Stress testing served us well as a crisis management tool, and we see it applied increasingly to peacetime oversight of banks and banking systems. Stress testing is rapidly become the dominant supervisory tool on both sides of the Atlantic. Yet the objectives and certainly the conditions are quite different, and to date we see a range of practices across jurisdictions. Stress testing has proved to be enormously useful, not just for the supervisors but also for the banks. Using a simple taxonomy of stress testing – scenario design, models and projections, and disclosure – I analyze some of those different approaches with a view to examining how wartime stress testing can be adapted to peacetime concerns.

We trace the development of model risk management in U.S. banking against the backdrop of the growing importance of complex financial models in banks, the recognition of model risk, the emergence of model validation as a response to model risk, and the contribution of failures in model risk management to the Great Financial Crisis. We recognize that while substantial progress has been made in the management of model risk, the challenges have grown, including the increasing reliance by the regulators on models.

This year, 2015, marks the six-year anniversary of US regulatory stress testing. We observe three key trends: 1) Increasingly aggressive capital management: Banks initially responded to CCAR by maintaining wide capital cushions vs. regulatory minimums. However, as CCAR processes stabilize and capital minimums increase, some institutions appear to be managing capital more and more tightly, especially investment banks, universals and custodians. 2) Drivers of enhanced financial resource management: What allows institutions to manage capital more closely? First, stress test results are beginning to stabilize and, in some cases, converge. Second, although we have just a handful of examples, the market seems to reward aggressive capital requests, even if they are, at first, rejected by the Fed. 3) Unintended consequences: As stress test results converge and institutions begin to manage capital to Fed-projected results, the Fed’s stress testing models become an increasingly important driver of the fate of the financial system.

Operational risk is fundamentally different from all other risks taken on by a bank. It is embedded in every activity and product of an institution, and in contrast to the conventional financial risks (e.g. market, credit) is harder to measure and model, and not straight forwardly eliminated through simple adjustments like selling off a position. Operational risk tends to be about 9-13% of the total risk pie, though growing rapidly since the 2008-09 crisis. It tends to be more fat-tailed than other risks, and the data are poorer. As a result, models are fragile – small changes in the data have dramatic impacts on modeled output – and thus required operational risk capital is unstable. Yet the regulatory capital regime is, surprisingly, more rigidly model focused for this risk than for any other, at least in the U.S. We are especially concerned with the absence of incentives to invest in and improve business control processes through the granting of regulatory capital relief. We make four, not mutually exclusive policy suggestions. First, address model fragility through anchoring of key model parameters, yet allow each bank to scale capital to their data using robust methodologies. Second, relax the current tight linkage between statistical model output and required regulatory capital, incentivizing prudent risk management through joint use of scenarios and control factors in addition to data-based statistical models in setting regulatory capital. Third, provide allowance for real risk transfer through an insurance credit to capital, encouraging more effective risk sharing through future product innovation. Fourth, expand upon the standard taxonomy of event type and business line to include additional explanatory variables (such as product type, flags for litigated events, etc.) that would allow more effective interbank sharing and learning from experience. Until our understanding of operational risks increases, required regulatory capital should be based on methodologies that are simpler, more standardized, more stable and more robust.

A defining difference of macro-style stress testing is the explicit consideration of profitability dynamics in the stress scenario. Traditional stress testing had focused almost exclusively on losses only, but a complete assessment of capital adequacy under stress must take into account not just the balance sheet but also the income statement. For instance, in the 2013 US stress test, reduction in projected income for the 18 mandatory bank holding companies (BHCs) covered nearly 60% of projected stress losses. We describe and discuss a framework for modeling the major components of the income statement for BHCs using the U.S. regulatory reports as an empirical illustration. We review approaches taken by the industry and trace its remarkable development in the wake of the financial crisis. We find – perhaps unsurprisingly and in line with previous literature – that successfully modeling profitability requires a tailored BHC-specific approach to revenue segmentation and modeling. We argue that failure to pursue a relatively granular income source segmentation along different business activities, far more granular than reflected in typical regulatory reports, will obscure significant underlying differences in macro risk factor sensitivities.

How much capital and liquidity does a bank need – to support its risk taking activities? During the recent (and still ongoing) financial crisis, answers to this question using standard approaches, e.g. regulatory capital ratios, were no longer credible, and thus broad-based supervisory stress testing became the new tool. Bank balance sheets are notoriously opaque and are susceptible to asset substitution (easy swapping of high risk for low risk assets), so stress tests, tailored to the situation at hand, can provide clarity by openly disclosing details of the results and approaches taken, allowing trust to be regained. With that trust re-established, the cost-benefit of stress testing disclosures may tip away from bank-specific towards more aggregated information. This paper lays out a framework for the stress testing of banks: why is it useful and why has it become such a popular tool for the regulatory community in the course of the recent financial crisis; how is stress testing done – design and execution; and finally, with stress testing results in hand, how should one handle their disclosure, and should it be different in crisis vs. “normal” times.

We examine how investor heterogeneity affects the relation between liquidity changes and yield spread changes, using newly-available trade data for more than 3,700 bonds of 635 issuers. We find that, for retail trades, liquidity is a significant determinant of yield spreads and adds substantially to the explanatory power of regressions, after accounting for issuer and market risk. Further, the impact of liquidity is inversely related to retail traders' expected holding period. In contrast, for institutional trades, liquidity and yield spreads are essentially unrelated at all holding periods. We further find, for retail traders, the return premia to holding illiquid bond portfolios is positive and concave in the expected holding period, as predicted by Amihud and Mendelson (1986). Moreover, retail traders earn greater return premia than institutions for the same holding period. Thus, the market at least partially compensates retail investors for the greater illiquidity of their bond trades. Our results point to the importance of investor heterogeneity for understanding the determinants of credit risk.

This paper seeks to put forward a framework, from the perspective of practitioners and policymakers, for how the known, unknown, and unknowable vary by risk type within banking. We define total bank risk in terms of earnings volatility, which can be broken down into five major classes of risk: market, credit, asset/liability, operational, and business risks. For our purposes, risk is known (K) if it can be enumerated, in the sense of being identified, and quantified; it is unknown (U1) if the set of risks can be identified and enumerated but not meaningfully quantified; and it is unknowable (U2) if the existence of the risk or set of risks is not predictable ex ante, let alone quantifiable. Based on these definitions, we position the five sources of bank risk within the K, U1, U2 space based on evidence from industry practice and suggest that K decreases, and U1 and U2 increase, along a spectrum from market risk to credit risk, asset/liability risk, operational risk, and business risk. Using bank-level data we attempt to quantify or size both total bank risk and the contribution from each risk type based on a large sample of earnings volatility data for US bank holding companies over the 1986-2005 period. We find that a) total earnings volatility is protected by minimum regulatory capital requirements at implied credit rating levels ranging from about A- to BBB, depending on the sample; b) when allocating among the different risk types, market risk accounts for only about 5%, credit for almost half, structural interest rate risk for about 18%, and non-financial risks, including both operational and business risk, for about 30% of total risk; c) the diversification benefit, i.e., the difference between the whole and the sum of the parts, is about one-third. Not surprisingly, large banks also seem to experience fewer extreme adverse outcomes.

This paper examines the common factors that drive the returns of U.S. bank holding companies from 1997 to 2005. We compare a range of market models from a basic one-factor model to a nine-factor model that includes the standard Fama-French factors and additional factors thought to be particularly relevant for banks such as interest and credit variables. We show that the market factor clearly dominates in explaining bank returns, followed by the Fama-French factors. The bank-specific factors are not informative, particularly for the largest banks, which take advantage of protection in the form of interest rate and credit derivatives. Even in our broadest model, however, considerable residual variation remains with the mean pair-wise correlation of residuals for the largest banks near 0.25. This suggests that important hidden factors remain. A principal component analysis shows that this residual variance is relatively diffuse, although the largest banks do tend to load in the same direction on the first component. Relative to large firms in other sectors, bank returns are relatively well explained with standard risk factors and both the residual correlation and degree of factor loading agreement are not particularly large. These results have clear implications for public policy in terms of quantifying the sources of the common exposures across banks necessary for certain types of systemic risk and for portfolio management in terms of optimal diversification strategies.

Unused loan commitments expose banks to systematic liquidity risk, but this exposure can be reduced by combining loan commitments with transactions deposits. We show that bank equity volatility increases with unused loan commitments, but this increase is reduced for banks with high levels of transaction deposits. This deposit-lending synergy becomes even more powerful during periods of tight liquidity, when nervous investors move funds into their banks. Thus, the simultaneous taking of deposits and lending may be thought of as a liquidity hedge.

The potential for portfolio diversification is driven broadly by two characteristics: the degree to which systematic risk factors are correlated with each other and the degree of dependence individual firms have to the different types of risk factors. Using a global vector autoregressive macroeconometric model accounting for about 80% of world output, we propose a model for exploring credit risk diversification across industry sectors and across different countries or regions. We find that full firm-level parameter heterogeneity along with credit rating information matters a great deal for capturing differences in simulated credit loss distributions. Imposing homogeneity results in overly skewed and fat-tailed loss distributions. These differences become more pronounced in the presence of systematic risk factor shocks: increased parameter heterogeneity reduces shock sensitivity. Allowing for regional parameter heterogeneity seems to better approximate the loss distributions generated by the fully heterogeneous model than allowing just for industry heterogeneity. The regional model also exhibits less shock sensitivity.

In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation methods, cohort and duration (intensity), with 22 years of credit ratings data. We find that the bootstrapped intervals for the duration-based estimates are relatively tight when compared to either analytic or bootstrapped intervals around the less efficient cohort estimator. We show how the large differences between the point estimates and confidence intervals of these two estimators are consistent with non-Markovian migration behavior. Surprisingly, even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PDAA− from a PDA+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated PDs. Conditioning on the state of the business cycle helps: it is easier to distinguish adjacent PDs in recessions than in expansions.

In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches from large sample theory as well as bootstrapped small-sample confidence intervals. We do so for two different PD estimation methods, cohort and duration (intensity), using 22 years of credit ratings data. We find that the bootstrapped intervals for the duration based estimates are surprisingly tight when compared to the more commonly used (asymptotic) Wald interval. We find that even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PD(AA-) from a PD(A+). However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated default probabilities. Conditioning on the state of the business cycle helps: It is easier to distinguish adjacent PDs in recessions than in expansions.

The goal of integrated risk management in a financial institution is to measure and manage risk and capital across a range of diverse business activities. This requires an approach for aggregating risk types (market, credit, and operational) whose distributional shapes vary considerably. In this paper, we construct the joint risk distribution for a typical large, internationally active bank using the method of copulas. This technique allows us to incorporate realistic marginal distributions that capture some of the essential empirical features of these risks like skewness and fat-tails while allowing for a rich dependence structure. We explore the impact of business mix and inter-risk correlations on total risk, whether measured by value-at-risk or expected shortfall. We find that given a risk type, total risk is more sensitive to differences in business mix or risk weights than to differences in inter-risk correlations. There is a complex relationship between volatility and fat-tails in determining the total risk: depending on the setting, they either offset or reinforce each other. The choice of copula (normal versus Student-t), which determines the level of tail dependence, has a more modest effect on risk. We then compare the copula-based method with several conventional approaches to computing risk, each of which may be thought of as an approximation. One easily implemented approximation, which uses empirical correlations and quantile estimates, tracks the copula approach surprisingly well. In contrast, the additive approximation, which assumes no diversification benefit, typically overestimates risk by about 30-40%.

Credit migration matrices are cardinal inputs to many risk management applications; their accurate estimation is therefore critical. We explore two approaches: cohort and two variants of duration - one imposing, the other relaxing time homogeneity - and the resulting differences, both statistically through matrix norms and economically using a credit portfolio model. We propose a new metric for comparing these matrices based on singular values and apply it to credit rating histories of S&P rated U.S. firms from 1981-2002. We show that the migration matrices have been increasing in "size" since the mid-1990s, with 2002 being the "largest" in the sense of being the most dynamic. We develop a testing procedure using bootstrap techniques to assess statistically the differences between migration matrices as represented by our metric. We demonstrate that it can matter substantially which estimation method is chosen: economic credit risk capital differences implied by different estimation techniques can be as large as differences between economic regimes, recession vs. expansion. Ignoring the efficiency gain inherent in the duration methods by using the cohort method instead is more damaging than imposing a (possibly false) assumption of time homogeneity.

The New Basel Accord will allow internationally active banking organizations to calculate their credit risk capital requirements using an internal ratings based (IRB) approach, subject to supervisory review. One of the modeling components is loss given default (LGD), the credit loss incurred if an obligor of the bank defaults. The flexibility to determine LGD values tailored to a bank's portfolio will likely be a motivation for a bank to want to move from the foundation to the advanced IRB approach. The appropriate degree of flexibility depends, of course, on what a bank knows about LGD broadly and about differentiated LGDs in particular; consequently supervisors must be able to evaluate "what a bank knows." The key issues around LGD are: 1) What does LGD mean and what is its role in IRB? 2) How is LGD defined and measured? 3) What drives differences in LGD? 4) What approaches can be taken to model or estimate LGD? By surveying the academic and practitioner literature, with supportive examples and illustrations from public data sources, this paper is designed to provides basic answers to these questions. The factors which drive significant differences in LGD include place in the capital structure, presence and quality of collateral, industry and timing of the business cycle.

We examine why these regulatory differences exist and what they imply for differences in minimum capital requirements for position risk. We consider differences in the definition and measurement of regulatory capital and we quantify differences in the capital charges for position risk by reference to a model portfolio that contains a variety of financial instruments including equity, fixed income instruments, swaps, foreign exchange positions, and options - instruments that may appear in the portfolios of securities firms, banks or insurance companies. For most leading firms in the financial services industry, however, market forces, not minimum regulatory capital requirements, appear to play the dominant role in firms' capital decisions. Thus we conclude by considering measures to enhance market discipline.

This paper presents a new approach to modeling conditional credit loss distributions. Asset value changes of firms in a credit portfolio are linked to a dynamic global macroeconometric model, allowing macro effects to be isolated from idiosyncratic shocks from the perspective of default (and hence loss). Default probabilities are driven primarily by how firms are tied to business cycles, both domestic and foreign, and how business cycles are linked across countries. We allow for firm-specific business cycle effects and the heterogeneity of firm default thresholds using credit ratings. The model can be used, for example, to compute the effects of a hypothetical negative equity price shock in South East Asia on the loss distribution of a credit portfolio with global exposures over one or more quarters. We show that the effects of such shocks on losses are asymmetric and non-proportional, reflecting the highly non-linear nature of the credit risk model.

The New Basel Accord for bank capital regulation is designed to better align regulatory capital to the underlying risks by encouraging better and more systematic risk management practices, especially in the area of credit risk. We provide an overview of the objectives, analytical foundations and main features of the Accord and then open the door to some research questions provoked by the Accord. We see these questions falling into three groups: What is the impact of the proposal on the global banking system through possible changes in bank behavior; a set of issues around risk analytics such as model validation, correlations and portfolio aggregation, operational risk metrics and relevant summary statistics of a bank's risk profile; issues brought about by Pillar 2 (supervisory review) and Pillar 3 (public disclosure).

We examine the question of deposit insurance through the lens of risk management by addressing three key issues: 1) how big should the fund be; 2) how should coverage be priced; and 3) who pays in the event of loss. We propose a risk-based premium system that is explicitly based on the loss distribution faced by the FDIC. The loss distribution can be used to determine the appropriate level of fund adequacy and reserving in terms of a stated confidence interval and to identify risk-based pricing options. We explicitly estimate that distribution using two different approaches and find that reserves are sufficient to cover roughly 99.85% of the loss distribution corresponding to about a BBB+ rating. We then identify three risk-sharing alternatives addressing who is responsible for funding losses in different parts of the loss distribution. We show in an example that expected loss based pricing, while appropriately penalizing riskier banks, also penalizes smaller banks. By contrast, unexpected loss contribution based pricing significantly penalizes very large banks because large exposures contribute disproportionately to overall (FDIC) portfolio risk.

The turmoil in the capital markets in 1997 and 1998 has highlighted the need for systematic stress testing of banks' portfolios, including both their trading and lending books. We propose that underlying macroeconomic volatility is a key part of a useful conceptual framework for stress testing credit portfolios, and that credit migration matrices provide the specific linkages between underlying macroeconomic conditions and asset quality. Credit migration matrices, which characterize the expected changes in credit quality of obligors, are cardinal inputs to many applications, including portfolio risk assessment, modeling the term structure of credit risk premia, and pricing of credit derivatives. They are also an integral part of many of the credit portfolio models used by financial institutions. By separating the economy into two states or regimes, expansion and contraction, and conditioning the migration matrix on these states, we show that the loss distribution of credit portfolios can differ greatly, as can the concomitant level of economic capital to be assigned.

A financial institution such as a bank is ultimately exposed to macroeconomic fluctuations in the countries to which it has exposure, the most acute example being commercial lending to companies whose fortunes fluctuate with aggregate demand. It was this risk management need for financial institutions which motivated us to build a compact global macroeconometric model capable of generating (point as well as density) forecasts for a core set of macroeconomic factors for a set of regions and countries which explicitly allows for interconnections and dependencies that exist between national and international factors in a coherent and consistent manner. This paper provides such a global modeling framework by making use of recent advances in the analysis of cointegrating systems. In an unrestricted VAR model covering N countries/regions, the number of unknown parameters will be unfeasibly large (around p(4N-1)+1, where p is the order of the VAR), requiring a more parsimonious solution. We first estimate individual country (or region) specific vector error correcting models, where the domestic macroeconomic variables are related to corresponding foreign variables constructed exclusively to match the international trade pattern of the country under consideration. The individual country models are then combined in a consistent and cohesive manner to generate forecasts for all the variables in the world economy simultaneously. We estimate the model using quarterly data from 1979Q1 to 1999Q1 and perform contagion analysis by investigating the transmission of shocks of one variable to the rest of the world.

Is volatility forecastability important for long-horizon risk management, or is a traditional constant-volatility assumption adequate? In this paper, the authors address this question, exploring the interface between long-horizon financial risk management and long-horizon volatility forecastability and, in particular, whether long-horizon volatility is forecastable enough such that volatility models are useful for long-horizon risk management.