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Quantitative Research

Image of possible yield curve and equity evolution

Fast Projection of Reserve and Capital Requirements with Proxy Functions

An emerging business requirement for North American insurers is the ability to project forward stochastic reserve and capital requirements under various planning scenarios to a specific future date. In this paper we consider applying proxy functions to this task, using function fitting techniques described in our previous research paper Fitting Proxy Functions for Conditional Tail Expectation: Comparison of Methods.

October 2018
Aubrey Clayton,  Dr. Steven Morrison

Global strategy solution concept - earth jigsaw puzzle

August 2018 U.S. Middle Market Risk Report

Private firm default rates have declined steadily during the past five years. At 1.4%, the rolling 12-month default rate is down 74% from its September 2009 peak of 5.2%. This trend has been driven primarily by a decline in the charge-off rate, now at its lowest level in ten years. In addition, the percentage of borrowers in non-accrual status has decreased 56% since September 2009. The number of borrowers rated “Substandard” has seen a steady increase since the first quarter of 2016, above pre-crisis levels, reflecting banks' cautious lending practices.

August 2018
Irina Korablev, Lin Moon, Stephanie Yu

Figure 1 illustrates the percentage of statements and defaults per year during 1998-2015 in CRD.

Features of a Lifetime PD Model: Evidence from Public, Private, and Rated Firms

With the new CECL and IFRS 9 requirements, we see an increased need for lifetime probability of default models. In this document, we formally investigate and summarize the term structure properties consistently seen across public, private, and rated firms. We observe that the default rate for “good” firms tends to increase over time, while the default rate for “bad” firms decreases over time, an indication of the mean-reversion effect seen with firms' default risk.

May 2018
Sajjad Beygiharchegani, Uliana Makarov,  Dr. Janet ZhaoDr. Douglas Dwyer

Figure 7 CCM breakdown.

A Composite Capital Measure Unifying Business Decision Rules in the Face of Regulatory Requirements Under New Accounting Standards

Prudent credit risk management ensures institutions maintain sufficient capital and limit the possibility of a capital breach. With CECL and IFRS 9, the resulting trend toward greater credit earnings volatility raises uncertainty in capital supply, ultimately causing an increase in required capital. It is ever more challenging for institutions to manage their top-of-the house capital while steering their business to achieve the desired performance level. This paper introduces an approach that quantifies the additional capital buffer an institution requires, beyond the required regulatory minimum, to limit the likelihood of a capital breach. In addition, we introduce a new measure that allocates capital and recognizes an instrument's regulatory capital requirements, loss allowance, economic concentration risks, and the instrument's contribution to the uncertainty in capital supply and demand. In-line with the Composite Capital Measure introduced in Levy and Xu (2017), this extended measure includes far-reaching implications for business decisions. Using a series of case studies, we demonstrate the limitations of alternative measures and how institutions can optimize performance by allocating capital and making business decisions according to the new measure.

May 2018
Dr. Amnon Levy, Xuan Liang, Dr. Pierre Xu

illuminated charts

Default Risk Premium in the Equity Market

This paper explores the default risk premium within the equity market. To our knowledge, this is the first study that uses the commercially-available structural model, Moody's Analytics Public Firm Model, EDF9TM, to explain the cross-section of stock returns. While distressed stocks have attracted attention in the past for their anomalously low returns, we also identify outperformance of “safe” stocks. The notions of safe and distressed are both defined in the context of Distance-to-Default within the Moody's Analytics Public Firm Model(also known as KMV). Our findings revisit the notion that value, size, and momentum price the financial distress risk. We find that safe stocks outperform the market, and risky stocks significantly anomaly, our factor is not a proxy for the low volatility factor.

April 2018
Houman Dehghan, Pooya Nazeran

Average projected LGD from LossCalc 4.0, by industry, North America Firms

Measuring and Managing the Impact of IFRS 9 and CECL Requirements on Dynamics in Allowance, Earnings, and Bank Capital

Reserving for loan loss is one of the most important accounting aspects for banks. Its objective is to cover estimated losses on impaired financial instruments due to defaults and non-payment. Reserve measurement affects both the balance sheet and income statement. It impacts earnings, capital, dividends and bonuses, and attracts the attention of bank stakeholders ranging from the board of directors and regulators to equity investors. In response to the so-called “too-little, too-late” problem experienced with loan loss reserve during the Great Financial Crisis, accounting standard setters now require that banks provision against loan loss based on expected credit losses (ECL). Arguably, calculating the Expected Credit Loss Model under IFRS 9 and CECL presents a momentous accounting change for banks, with the new standards coming into effect sometime between 2018 and 2021, depending on the jurisdiction.

March 2018

Proxy and Validation vs. yield curve change risk factor

Fitting Proxy Functions for Conditional Tail Expectation: Comparison of Methods

This paper details alternative methods for fitting proxy functions to CTE, employing quantile regression in combination with OLS among other techniques. We compare methods according to quality of fit for an example portfolio of variable annuities.

March 2018
Aubrey Clayton,  Dr. Steven Morrison

Tail Risk contribution

Uncertainty in Asset Correlation Estimates and Its Impact on Credit Portfolio Risk Measures

Credit portfolio models rely on estimated and calibrated parameters, such as default and rating migration probabilities, recovery rates, and asset correlations. Users of these models must understand how various errors in the parameter estimates impact model outputs, for example Unexpected Loss (UL) or Economic Capital (EC). Asset correlations estimated using asset return time series are subject to inherent uncertainty — statistical errors — arising due to a limited length of the time series. The main question this paper addresses is how these errors translate into statistical errors in the estimated UL and EC. We illustrate several properties of the errors using an analytical method. As expected, longer time series lead to lower errors in UL and EC. Increasing the number of exposures in a portfolio, however, can reduce the errors in UL and EC only to a certain degree.

March 2018
Jimmy Huang, Libor Pospisil

charts on transparent display

Economic Capital Model Validation: A Comparative Study

Using a long history of public firm defaults from Moody's Investor Services and Moody's Analytics, this study illustrates a validation approach for jointly testing the impact of PD and correlation upon model performance. We construct predicted default distributions using a variety of PD and correlation inputs and examine how the predicted distribution compares with the realized distribution. The comparison is done by looking at the percentile of realized defaults with respect to the predicted default distribution. We compare the performance of two typical portfolio parameterizations: (1) a through-the-cycle style parameterization using agency ratings-based long-term average default rates and Basel II correlations; and (2) a point-in-time style parameterization using public EDF credit measure, and Moody's Analytics Global Correlation Model (GCorr™). Results demonstrate that a through-the-cycle style parameterization results in a less conservative view of economic capital and substantial serial correlation in capital estimates. Results also show that when point-in-time measures are used, the tested economic capital model produces consistent and conservative economic capital estimates over time. A version of this paper appears in the Journal of Risk Model Validation, March 2013.

February 2018
Zhenya Hu,  Dr. Amnon LevyDr. Jing Zhang

One-Year CCA Median EDF Values by State as of June 2017

November 2017 U.S. Middle Market Risk Report

Private firm default rates have declined steadily during the past five years. At 1.5%, the rolling 12-month default rate is down 73% from its September 2009 peak of 5.3%. This trend has been driven primarily by a decline in the charge-off rate, now at its lowest level in the past ten years. In addition, the rate of borrowers in non-accrual status has decreased 53% since September 2009. Banks downgraded 17% of borrowers on their internal rating scales during the past year, compared to 15% in 2016.

November 2017
Lin Moon, Stephanie Yu,  Irina Korablev

Solvency Ratio under various asset allocations, in scenario where credit spreads rise

Solvency In Sight - New Tools for Understanding the Impact of Investment Decisions on Capital

In this paper, we have considered the use of proxy models as a way of overcoming some of the operational and computational challenges associated with measuring future solvency under different market conditions and ALM assumptions.

October 2017

chart from article

Toys R Us Exposure in CLOs

This report shows the CLO exposure to Toys R Us as of the latest available monthly surveillance report on September 8, 2017.

September 2017
Tess Likens