Portfolio Modeling

We develop a model-based approach to constructing investment grade and high yield corporate bond portfolios that both outperform their respective prevalent benchmark indices and popular Exchange Traded Funds (ETFs) with better risk-return profiles, i.e., higher returns with lower or similar risk. More importantly, the outperformance is obtained after controlling for credit risk, duration risk, and downside risk. The outperformance is robust across a number of different specifications of the strategy and over time. We also achieve outperformance using relatively smaller, more realistic portfolios. These model portfolios can be potentially converted into new fixed income indices or ETFs. Our model-based approach utilizes Moody’s Analytics’ EDF™ (Expected Default Frequency) credit measures and Fair-value Spread (FVS) valuation framework as powerful tools to control for credit risk and to exploit relative value in the bond market.

Author: Zan Li, Jing Zhang, Christopher Crossen
Date: April 19, 2012

Traditional measures of Required Economic Capital are calculated over a one-year horizon. The one-year horizon is motivated by strategic planning that typically occurs annually. An institution can rebalance its portfolio at the end of each planning period and limit its risk and return analysis during subsequent periods. This argument rests on the assumption that assets in the financial institution’s portfolio are perfectly liquid. The problem becomes a different one when the portfolio contains non-traded assets that will live on the financial institution’s balance sheet beyond the time horizon. In this case, it is prudent for the organization to consider the risk over each asset’s life. In this paper, we formalize a measure that assesses RORAC for long-dated non-traded assets and propose several practical implementations. We demonstrate that by utilizing this measure, institutions can better understand the risks of non-traded assets and better align origination and strategic planning for non-traded assets. Additionally, we introduce a measure of Economic Value Added (EVA) that complements RORAC in risk management decision making.

Authors: Andrew Kaplin and Amnon Levy
Date: April 5, 2012

The recovery amount from a defaulted financial instrument can be measured by either ultimate recovery (UR) or post-default value (PDV). While these two measures have the same expected value, UR variance is usually greater than PDV variance. In most cases, the appropriate measure of variance to use in an economic capital framework is somewhere between UR and PDV variance, but is much closer to PDV variance. This paper proposes two approaches to estimating recovery variance based on UR variance and PDV variance, respectively. We find that the impact of recovery variance parameterization on economic capital can be non-trivial, especially when PD-LGD correlation (PLC) is accounted for. In this paper we demonstrate that two common parameterizations can result in capital differences of over 15% in a realistic setting.

Authors: Amnon Levy, Qiang Meng, Douglas Dwyer and Irina Korablev
Date: November 17, 2011

Sovereign exposures comprise a large part of financial institutions’ credit portfolios, and are often held due to their perceived low risk. While many sovereign exposures indeed exhibit low default probabilities when considered on a stand-alone basis, a proper risk assessment must also account for correlations. In this paper, we develop a sovereign correlation methodology which parameterizes the Moody’s Analytics Global Correlation Model (GCorr™) and uses sovereign CDS data to estimate parameters. With this methodology, we can determine correlations among sovereign exposures, as well as correlations between sovereign exposures and other asset classes within a credit portfolio. In addition, utilizing the GCorr factor structure allows us to capture the interdependencies among sovereigns due to their intertwined economies.

Authors: Amnon Levy, Nihil Patel, Libor Pospisil, Vojislav Sesum
Date: June 17, 2011

Here you can examine the latest analytical findings of our portfolio research and in particular a Gcorr update for correlations. We offer thoughts on relative risk and return, incremental risk charges (IRC) and the role that accounting for liquidity plays in pricing and risk assessment. Read on to see how Moody’s distills its findings from high quality statistical analysis.

Author: Amnon Levy
Date: June 9, 2011

This document outlines the underlying research, model characteristics, data, and validation results for Mortgage Portfolio Analyzer, which is an analytic tool to assess credit risk measures, capital levels and stress scenarios for portfolios of residential mortgages. Mortgage Portfolio Analyzer comprises loan-level econometric models for default, prepayment, and severity. These models are integrated through common dependence on local macro-economic factors, which can be either simulated at national, state, and Metropolitan Statistical Area (MSA) levels or input in the form of stress scenarios. This integration produces correlation in behaviors of loans across the portfolio.

Authors: Roger M. Stein, Ashish Das, Yufeng Ding & Shirish Chinchalkar
Date: March 1, 2011

With the help of newly-available tools, we show that using pool-level data rather than loan-level data for mortgage portfolio analysis can lead to substantially different conclusions about the credit risk of the portfolio. This finding is timely as there is an increased interest from market participants and regulators in improved credit risk models for this asset class. Further, recent advances in data accessibility as well as changes in regulatory reporting requirements have led to the increased availability of loan-level mortgage data, facilitating development of loan-level models to achieve higher accuracy in estimating portfolio credit risk.

Authors: Shirish Chinchalkar & Roger M. Stein
Date: November 1, 2010

Credit migration is an essential component of credit portfolio modeling. In this paper, we outline a framework for gauging the effects of credit migration on portfolio risk measurements. For a typical loan portfolio, we find credit migration can explain as much as 51% of volatility and 35% of economic capital. We compare through-the-cycle migration effects, implied by agency rating transitions, with point-in-time migration, implied by EDF™ (Expected Default Frequency) transitions, and find that migration of point-in-time credit quality accounts for a greater fraction of total portfolio risk when compared with through-the-cycle dynamics.

Authors: Yaakov Tsaig, Amnon Levy and Yashan Wang
Date: September 17, 2010

Credit migration is an essential component of credit portfolio modeling. In this paper, we outline a framework for gauging the effects of credit migration on portfolio risk measurements. For a typical loan portfolio, we find credit migration can explain as much as 51% of volatility and 35% of economic capital. We compare through-the-cycle migration effects, implied by agency rating transitions, with point-in-time migration, implied by EDF™ (Expected Default Frequency) transitions, and find that migration of point-in-time credit quality accounts for a greater fraction of total portfolio risk when compared with through-the-cycle dynamics.

Authors: Zhenya Hu, Amnon Levy, Jing Zhang
Date: April 22, 2010

This paper discusses the implications of the Moody’s Analytics PD-LGD correlation model on portfolio analysis. We provide numerical results to illustrate the impacts of PD-LGD correlation on risk and return measures of credit portfolios.  Under the PD-LGD correlation model framework, recovery is correlated with the firm’s underlying asset process via both systematic factors and idiosyncratic shocks. PD-LGD correlation introduces additional variability into instrument value and portfolio value distributions. At the instrument level, value distribution becomes more dispersed under the PD-LGD correlation model, since a good credit state is not only associated with a low default probability, but also with a high expected recovery amount. The opposite is true for a bad credit state.

Authors: Qiang Meng, Amnon Levy, Andrew Kaplin, Yashan Wang, Zhenya (Ella) Hu
Date: February 5, 2010

Asset correlation and default probability are critical drivers in modeling portfolio credit risk. It is generally assumed, as in the Basel II Accord, that average asset correlation decreases with default probability. We examine the empirical validity of this assumption in this paper. Overall, we find little empirical support for this decreasing relationship in the data for corporate, commercial real estate (CRE), and retail exposures. For corporate exposures, there is no strong decreasing relationship between average asset correlation and default probability when firm size is properly accounted for. For CRE and retail exposures, the empirical evidence suggests that the relationship is more likely to be an increasing one.

Authors: Joseph Lee, Joy Wang, Jing Zhang
Date: July 22, 2009

The Moody’s KMV approach to modeling asset correlation in measuring portfolio credit risk is to decompose a borrower’s risk into systematic and idiosyncratic components. Pairs of borrowers within a portfolio are correlated through their exposures to systematic factors. Specifically, there are two sets of inputs that determine the pair-wise correlation. The first set of inputs is the proportion of risk that is captured by the systematic factors, or R-squared values. The second set of inputs is the correlations among the respective systematic factors, or systematic factor correlations.

Authors: Qibin Cai, Amnon Levy, Nihil Patel
Date: July 17, 2009

Understanding the relationship between credit and interest rate risk is critical to many applications in finance, from valuation of credit and interest rate-sensitive instruments to risk management. This study empirically examines the relationship between interest rates and default risk using firm level corporate default data in the United States between 1982 and 2008.

Authors: Andrew Kaplin, Amnon Levy, Shisheng Qu, Danni Wang, Yashan Wang, Jing Zhang
Date: October 2, 2009

This document provides a high-level overview of the modeling methodologies implemented in RiskFrontier™ to address the challenges faced by a credit risk manager or a credit portfolio manager. RiskFrontier attempts to accurately model the value of a credit investment at the analysis date and its value distribution at some investment horizon, as well as the correlation between two instruments in a portfolio. The approach is designed to explicitly analyze a wide range of credit investments and contingencies, including term loans with prepayment options and grid pricing, dynamic utilization in revolving lines of credit, bonds with put and call options, equities, credit default swaps, and structured instruments.

Author: Amnon Levy
Date: December 29, 2008

Traditional approaches to modeling economic capital, credit-VaR, or structured instruments whose underlying collateral is comprised of structured instruments treat structured instruments as a single-name credit instrument (i.e., a loan-equivalent). While tractable, the loan-equivalent approach requires appropriate parameterization to achieve a reasonable description of the cross correlation between the structured instrument and the rest of the portfolio. This article provides an overview of how one can calibrate loan-equivalent correlation parameters. Results from taking the approach to the data suggest that structured instruments have far higher correlation parameters than single-name instruments.

Authors: Tomer Yahalom, Amnon Levy, Andrew S. Kaplin
Date: November 13, 2008

The first commercial EDF™ credit measure model was released by KMV in 1990, although its foundations in extending the Merton model date from the early 1980s. The EDF model is now in use at hundreds of institutions worldwide, and Moody’s KMV EDF credit measures are produced daily on more than 30,500 listed firms in 58 countries.

Author: Brian Dvorak
Date: March 25, 2008

Asset correlation is a critical driver in modeling portfolio credit risk. Despite its importance, there have been few studies on the empirical relationship between asset correlation and subsequently realized default correlation, and portfolio credit risk. This three three-way relationship is the focus of our study using U.S. public firm default data from 1981 to 2006.

Authors: Jing Zhang, Fanlin Zhu, Joseph Lee
Date: March 3, 2008

In the Moody’s KMV Vasicek-Kealhofer (VK) model, asset values and asset returns are calculated separately. Moody’s KMV GCorr™ uses weekly asset returns directly from the VK model to calculate asset correlations. As an alternative, asset returns estimated from monthly asset values from Credit Monitor? can be used to estimate asset correlations. This study shows that the asset returns backed out from asset values are vulnerable to capital structure changes and other corporate activities, especially for financial firms.

Authors: Fanlin Zhu, Brian Dvorak, Amnon Levy, Jing Zhang
Date: September 12, 2007

This paper proposes a theoretical framework to account for systematic risk in recovery and to address the correlation between the firm’s underlying asset process and recovery. Under the proposed framework, the expected value in default under the risk neutral measure can be expressed as a linear function of the expected value under the physical measure. This allows for a simple mapping between expected recovery observed in the data and a measure that can be applied when using risk neutral valuation methods.

Authors: Amnon Levy, Zhenya Hu
Date: April 20, 2007

Collateralized Debt Obligations (CDOs) are sophisticated financial products that offer a range of investments, known as tranches, at varying risk levels backed by a collateral pool typically consisting of corporate debt (bonds, loans, default swaps, etc.). The analysis of the risk-return properties of CDO tranches is complicated by the highly non-linear and time dependent relationship between the cash flows to the tranche and the underlying collateral performance. This paper describes a multiple time step simulation approach that tracks cash flows over the life of a CDO deal to determine the risk characteristics of CDO tranches.

Author: William J. Morokoff
Date: August 26, 2003

Over the last thirty years there has been considerable research on the use of forecasting models to estimate correlation structure of security returns in the areas of asset management and risk management. In the area of credit risk management, portfolio models such as CreditMetrics, CreditRisk+, KMV’s Portfolio Manager and McKinsey’s Portfolio View have gained various degrees of acceptance and application by financial industry. In general, these models do not measure credit correlations directly because credit events such as defaults and credit migrations are rare.

Authors: Bin Zeng, Jing Zhang
Date: April 11, 2001

The measurement of default risk has been one of the major advances in finance in the last decade. Anyone managing a portfolio of obligations subject to default risk is interested in the average or expected loss associated with the portfolio, and the range of possible losses surrounding that expectation. It is this latter quantity that constitutes the true credit risk of the portfolio.

Authors: Stephen Kealhofer, Sherry Kwok, Wenlong Weng
Date: March 3, 1998

An infinite series expansion is given for the bivariate normal cumulative distribution function. This expansion converges as a series of powers of d1 − ρ 2 i , where ρ is the correlation coefficient, and thus represents a good alternative to the tetrachoric series when ρ is large in absolute value.

Author: Oldrich Alfons Vasicek
Date: 1996

Corporate liabilities have default risk. There is always a chance that a corporate borrower will not meet its obligations to pay principal and interest. For the typical high-grade borrower, this risk is small, perhaps 1/10 of 1% per year. For the typical bank borrower this risk is about 1/2 of 1%.

Authors: Stephen Kealhofer, Jeffrey R. Bohn
Date: November 15, 1993

This note gives the limiting form of the probability distribution of the percentage gross loss L on a very large portfolio. It is assumed that the probability of default on any one loan is p, and that the values of the borrowing companies' assets are correlated with a coefficient r for any two companies. Attached to this file is a related note, Probability of Loss on Loan Portfolio, Oldrich Vasicek, February 12, 1987.

Author: Oldrich Alfons Vasicek
Date: September 8, 1991

Consider a portfolio consisting of n loans in equal dollar amounts. Let the probability of default on any one loan be p, and assume that the values of the borrowing companies’ assets are correlated with a coefficient ρ for any two companies. We wish to calculate the probability distribution of the percentage gross loss L on the portfolio.

Author: Oldrich Alfons Vasicek
Date: February 12, 1987