Peter Miu

Basel requirements of downturn loss given default: modeling and estimating probability of default and loss given default correlations

Basel II requires that banks use downturn loss given default (LGD) estimates in regulatory capital calculations, citing the fact that the probability of default (PD) and LGD correlations are not captured. We show that the lack of correlation can be taken care of by incorporating a certain degree of conservatism in cyclical LGD in a point-in-time (PIT) framework. We examine a model that can capture the PD and LGD correlation in its entirety, differentiating the different components of correlations in question. Using historical LGD and default data of a loan portfolio, we calibrate our model and, through the simulation of economic capital, we show that the mean LGD needs to be increased by about 35% to 41% for a corporate portfolio and about 16% for a mid-market portfolio in order to compensate for the lack of correlations. Our hope is to provide a framework that the banks can use based on their internal data to estimate and justify their LGD choices for different portfolios. Although the paper is presented within the context of Basel II, the applications could be widened to include structured finance, credit derivatives, economic capital and portfolio modeling in general, where PD and LGD correlations need to be estimated and modeled.

Recent developments in exchange-traded fund literature: Pricing efficiency, tracking ability, and effects on underlying securities

Purpose - The purpose of this paper is to provide a brief review of three strands of the literature on exchange-traded funds. Design/methodology/approach - The paper starts with a review of the history of the growth of exchange-traded funds and their characteristics. The paper then examines the key factors and findings of the existing studies on, respectively, the pricing efficiency, the tracking ability/performance, and the impact on underlying securities of exchange-traded funds. Findings - Although there has been a substantial amount of research conducted to advance our knowledge on the trading, management, and effect of exchange-traded funds, the findings are still far from conclusive in addressing a number of research questions. Practical implications - Investors and other market participants will find this review informative in enhancing the understanding of exchange-traded funds. Originality/value - By highlighting the general theme of the related research findings, the paper provides a systematic review of the existing literature that future researchers can utilize in developing their research agenda.

Practical and Theoretical Challenges in Validating Basel Parameters: Key Learnings from the Experience of a Canadian Bank

This paper, inspired by the efforts of a Canadian bank, discusses Basel preparation and validation issues. A comprehensive outcomes analysis (eg, back-testing) framework is presented, including a simulation-based calibration test. A consistent risk rating philosophy - point-in-time (PIT) or through-the-cycle (TTC) - encompasses both the probability of default (PD) and the default correlations, and the validation needs to be consistent with both. Related arguments are made that not only PD itself, but the correlation of PD used in economic capital models should be rating system specific. We need to use a larger PD correlation under a TTC rating system than under a PIT rating system. Furthermore, Basel loss given default may not be appropriate for commonly used internal models, and accordingly adjustments are proposed.

Estimating and Validating Long-Run Probability of Default With Respect to Basel II Requirements

Basel II adopting banks estimate and validate Long-Run Probability of Default (LRPD) for each of their Internal Risk Ratings (IRRs). In this study, we examine alternative methodologies in estimating and validating LRPD. We propose the maximum likelihood estimators incorporating both cross-sectional and serial asset correlations while being consistent with the economic model underlying the Basel II capital requirement formulation. We first adopt Basels infinitely granular portfolio assumption and propose a LRPD estimation methodology for regulatory capital estimation. We then relax this assumption to examine alternative estimation methodologies and their performances for finite number of borrowers. Simulation-based performance studies show that the proposed estimators outperform the alternatives in terms of their accuracies even under a number of small sample settings. Using the simple average of default rates as an estimator is found to be prone to underestimation of LRPD. For the purpose of validating the assigned LRPDs, we also examine alternative ways of establishing confidence intervals (CIs). For most of the cases, the use of the CIs constructed based on the proposed maximum likelihood estimators results in fewer errors in hypothesis tests. We show that the proposed method enables the use of external default rate data to supplement internal default rate data in attaining a more accurate and representative estimate of LRPD.

Discount Rate for Workout Recovery: An Empirical Study

In order to comply with the Advanced Internal Rating-Based (IRB) approach of Basel II, financial institutions need to estimate the economic loss given default (LGD) of their instruments in order to compute the minimum regulatory capital requirement under Pillar I of the accord. One of the key parameters in the estimation of LGD is the appropriate discount rate (and thus risk premium) to be applied to the workout recovery values. By matching the recovery cash flows received post-default with the market prices of defaulted debts, we conduct an empirical analysis to study the determinants of the implicit risk premium by using a comprehensive database comprising both distressed bonds and loans. We find that investor uncertainty concerning the recovery value of defaulted debt is the primary driver of risk premiums. Risk premiums vary significantly by initial issuer ratings, whether or not the industry is in stress at the time of default, relative seniority to other debt and instrument type. The conclusions are found to be robust to potentially confounding determinants of required risk premium.

Can Basel III Work? Examining the New Capital Stability Rules by the Basel Committee: A Theoretical and Empirical Study of Capital Buffers

In the aftermath of the financial crisis, to reinforce the stability of the financial system, policy makers and the Basel Committee have developed proposals to ensure that financial institutions maintain sufficient capital buffers. The December proposal by the Basel Committee outlines fundamental changes and is already being called “Basel III” by the practitioners. It includes a more restrictive definition of Tier 1 Capital, use of leverage ratios, restrictions on discretionary distributions of earnings, and a “bottom-of-the-cycle” calibration for the Pillar I regulatory capital requirements. In this paper we study these proposals first from a theoretical standpoint and then conduct a quantitative impact study. Recent studies and observations support increasing the quality of capital, although a recalibration of minimum Tier 1 ratio will be required. Leverage ratios appear redundant and implementation of them would further complicate the risk optimization problem faced by financial institutions (FIs). Constraining the discretionary distributions of earnings can keep agency costs under control but needs be carefully thought through to make sure that value transfer simply does not take another form and it does not overly interfere with the FI’s dividend policies. The “bottom-of-the-cycle” calibration does not look defendable. Among other problems, it could adversely affect the FI’s profitability, decelerating the capital built up by reducing the income generation per unit of capital base. Addressing the capital buffer problem within the Pillar II Internal Capital Adequacy Assessment Process (ICAAP) framework supplemented by conditional and forward looking stress testing is clearly the preferred approach.

Adapting the Basel II Advanced Internal-Ratings-Based Models for International Financial Reporting Standard 9

Banks around the globe are implementing International Financial Reporting Standard 9 (IFRS 9), which is a considerable effort. A key element of IFRS 9 is a forward-looking “expected loss” impairment model, which is a significant shift from the incurred-loss model. We examine how we may use advanced internal-ratings-based (A-IRB) models in the estimation of expected credit losses for IFRS 9 purposes. We highlight the necessary model adaptations required to satisfy the new accounting standard. By leveraging on the A-IRB models, banks can lessen their modeling efforts in fulfilling IFRS 9 and capture the synergy between different modeling endeavors within institutions. In outlining the proposed probability of default, loss given default and exposure at default models, we provide detailed examples of how they may be implemented on secured lending. Moreover, in discussing the issues related to the estimation of the expected credit loss for IFRS 9, we highlight the challenges involved and propose practical solutions to deal with them. For instance, we propose the use of a convexity adjustment approach to circumvent the need for assigning probabilities in multiple-scenario analysis.

Performance and Tracking Errors

The performance of ETFs is measured by tracking error, commonly defined as the deviation of the returns on net asset values (NAVs) of ETFs from the corresponding returns on the underlying benchmark indices. The deviation tells us how effective and efficient is the fund management in tracking the performance of the benchmark index and delivering the promised return. Unlike price deviations (as discussed in chapter 5), which are typically expected to be within the arbitrage bounds given the creation/redemption process of ETFs, any deviations of the returns on NAV from those of their underlying benchmarks can accumulate over time and thus significantly affect the long-term performance of the ETFs.

Return Dynamics and Compounding Effects

In this chapter, we will take a look at the dynamics of LETFs’ returns over different time horizons. In the process, we will discuss in detail how compounding affects LETFs’ returns.

Regulations and Taxations

In this chapter, we will discuss the regulations governing the issuance and trading of LETFs. We will then look at the tax treatments of LETFs and how they are different from those of traditional ETFs.