I demonstrate that ratings-based capital rules, including both the current Basel Accord and its proposed revision, can be reconciled with the general class of credit value-at-risk models. Each exposure's contribution to VaR is portfolio-invariant only if (a) dependence across exposures is driven by a single systematic risk factor, and (b) no exposure accounts for more than an arbitrarily small share of total portfolio exposure. Analysis of rates of convergence to asymptotic VaR leads to a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. There is no similarly simple way to address violation of the single factor assumption.

The debate over the potential procyclicality of bank capital requirements under Basel II has focused overwhelmingly on peak-to-trough variation in minimum regulatory requirements. In this paper, we re-examine the problem from the perspective of market discipline. First, we show that the marginal impact of introducing Basel II depends strongly on the extent to which market discipline leads banks to vary lending standards procyclically in the absence of binding regulation. Second, we evaluate policy options not only by their efficacy in dampening cyclicality in capital requirements, but equally by how well the information value of Basel II market disclosures is preserved.

Auctions of government securities typically permit bidders to enter multiple price-quantity bids. Despite the widespread adoption of this institutional feature and its use by bidders, the motivations behind its use and its effects on auction outcomes are not well understood theoretically and have been little explored empirically. This paper proposes that bidders use multiple bids to adjust for winner's curse: By spreading her bids, a bidder aligns her outcome more closely to the aggregate outcome of the auction. This hypothesis is tested using bidding data from treasury bill auctions in Portugal. I find that, ceteris paribus, a bidder submits a greater number of bids and disperses prices on these bids more widely when there is a greater potential for winner's curse. In particular, both these measures of bid-spreading increase with the volatility of market interest rates and the expected number of participating well-informed bidders.

CreditRisk+ is an influential and widely implemented model of portfolio credit risk. As a close variant of models long used for insurance risk, it retains the analytical tractability for which the insurance models were designed. Value-at-risk (VaR) can be obtained via a recurrence-rule algorithm, so Monte Carlo simulation can be avoided. Little recognized, however, is that the algorithm is fragile. Under empirically realistic conditions, numerical error can accumulate in the execution of the recurrence rule and produce wildly inaccurate results for VaR. This paper provides new tools for users of CreditRisk+ based on the cumulant generating function (cgf) of the portfolio loss distribution. Direct solution for the moments of the loss distribution from the cgf is almost instantaneous and is computationally robust. Thus, the moments provide a convenient, quick and independent diagnostic on the implementation and execution of the standard solution algorithm. Better still, with the cgf in hand we have an alternative to the standard algorithm. I show how tail percentiles of the loss distribution can be calculated quickly and easily by saddlepoint approximation. On a large and varied sample of simulated test portfolios, I find a natural complementarity between the two algorithms: Saddlepoint approximation is accurate and robust in those situations for which the standard algorithm performs least well, and is less accurate in those situations for which the standard algorithm is fast and reliable.

Within the past two years, important advances have been made in modeling credit risk at the portfolio level. Practitioners and policy makers have invested in implementing and exploring a variety of new models individually. Less progress has been made, however, with comparative analyses. Direct comparison often is not straightforward, because the different models may be presented within rather different mathematical frameworks. This paper offers a comparative anatomy of two especially influential benchmarks for credit risk models, the RiskMetrics Group's CreditMetrics and Credit Suisse Financial Product's CreditRisk+. We show that, despite differences on the surface, the underlying mathematical structures are similar. The structural parallels provide intuition for the relationship between the two models and allow us to describe quite precisely where the models differ in functional form, distributional assumptions, and reliance on approximation formulae. We then design simulation exercises which evaluate the effect of each of these differences individually.

We offer a model and evidence showing that private debtholders play a key role in setting the endogenous asset value threshold below which corporations declare bankruptcy. As predicted by the model, we find that the recovery rate at emergence from bankruptcy on all of the firm’s debt taken together is increasing in the pre-bankruptcy share of private debt in all debt. We further find evidence consistent with a two-threshold model in which private debtholders force default in some cases and shareholders default strategically in others.

The impact of undiversified idiosyncratic risk on value-at-risk and expected shortfall can be approximated analytically via a methodology known as granularity adjustment (GA). In principle, the GA methodology can be applied to any risk-factor model of portfolio risk. Thus far, however, analytical results have been derived only for simple models of actuarial loss, i.e., credit loss due to default. We demonstrate that the GA is entirely tractable for single-factor versions of a large class of models that includes all the commonly used mark-to-market approaches. Our approach covers both finite ratings-based models and models with a continuum of obligor states. We apply our methodology to CreditMetrics and KMV Portfolio Manager, as these are benchmark models for the finite and continuous classes, respectively. Comparative statics of the GA reveal striking and counterintuitive patterns. We explain these relationships with a stylized model of portfolio risk.

To explain persistence of credit card interest rates at relatively high levels, Calem and Mester (AER, 1995) argued that informational barriers create switching costs for high-balance customers. As evidence, using data from the 1989 Survey of Consumer Finances, they showed that these households were more likely to be rejected when applying for new credit. In this paper, we revisit the question using the 1998 and 2001 SCF. Further, we use new information on card interest rates to test for pricing effects consistent with information-based switching costs. We find that informational barriers to competition persist, although their role may have declined.

We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a kernel measure which makes explicit the user’s priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and further propose novel variants which are easily implemented, well-sized and have good power. In an empirical application, we backtest forecast distributions for the overnight P&L of ten bank trading portfolios. For some portfolios, test results depend materially on the choice of kernel.