CONFERENCE ON LIQUIDITY, CREDIT RISK and EXTREME EVENTS | Chicago, October 30, 2009

PROGRAM

**October 30, 2009**| Gleacher Center, 6th floor
Time	Speaker	Title (click for paper)
8:30 am		Registration and Breakfast
9:15am	David Lando
10:00am	Tobias Adrian Paul Glasserman	CoVaR Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement
10:50am		Refreshment Break
11:15am	David Bates Mikhail Chernov Viktor Todorov	U.S. Stock Market Crash Risk, 1926-2006 Disasters implied by equity index options Tails, Fears and Risk Premia
12:30pm		Lunch
1:45pm	Christian Gourieroux
2:30pm	Jorg Rocholl Albert Menkveld	The Price of Liquidity: Bank Characteristics and Market Conditions Price Pressures
3:20pm		Afternoon Break
3:45pm	Bernd Schwaab Peter Christoffersen Li Xu	Macro, Industry, and Frailty effects in Defaults during the 2008 Credit Crisis: A variance decomposition, Exploring Dynamic Default Dependence A Markov Chain Monte Carlo Analysis of Credit Spread Models

David Lando and Christian Gourieroux are JFEC invited speakers.

  Chairs:
  
  Per Mykland (David Lando)
  Francis Diebold (Portfolio Choice Session)
  Roger Lee (Crash Session)
  Eric Renault (Christian Gourieroux)
  Torben Andersen (Liquidity Session)
  Pierre Collin-Dufresne (Credit Risk Session)

ABSTRACTS

CoVaR

Tobias Adrian (Federal Reserve Bank of New York)

We develop a market-wide illiquidity risk factor based on run lengths and find that it is priced using standard asset-pricing specifications. Our theoretical frame-work of equity returns derives the result that average run lengths of individual stocks proxy for liquidity, and are related to common measures of liquidity such as trading volume and trade price-impact. This relationship holds irrespective of the sampling frequency in the computation of run lengths. Thus, liquidity can be quantified by examining a stock's run length signature, providing a statistical mechanics link across illiquidity metrics. Tests using daily equity return data for all stocks over the period 1962-2005 find that run lengths are decreasing in turnover, and increasing with bid-ask spreads, and price-impact. Illiquidity is shown to be an important risk factor/characteristic in explaining equity returns.

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement

Paul Glasserman (Columbia University)

This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a ten-day value-at-risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a one-year horizon. More importantly, whereas ten-day VaR is ordinarily calculated with a portfolio’s holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio’s profit and loss distribution over a risk-measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the

discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics.

U.S. Stock Market Crash Risk, 1926-2006

David Bates (University of Iowa)

This paper applies the Bates (RFS, 2006) methodology to the problem of estimating and filtering time-changed Lévy processes, using daily data on U.S. stock market excess returns over 1926-2006. In contrast to density-based filtration approaches, the methodology recursively updates the associated conditional characteristic functions of the latent variables. The paper examines how well time-changed Lévy specifications capture stochastic volatility, the “leverage” effect, and the substantial outliers occasionally observed in stock market returns. The paper also finds that the autocorrelation of stock market excess returns varies substantially over time, necessitating an additional latent variable when analyzing historical data on stock market returns. The paper explores option pricing implications, and compares the results with observed prices of options on S&P 500 futures.

Disasters implied by equity index options

Mikhail Chernov (London Business School)

We contribute to “disaster” research by using prices of equity index options to quantify the impact of extreme events on asset returns. We define extreme events as departures from normality of the log of the pricing kernel and summarize their impact with highorder cumulants: skewness, kurtosis, and so on. We show that high-order cumulants are quantitatively important in both the representative-agent models of Barro and Rietz and in a statistical pricing model estimated from equity index options. Option prices thus provide independent confirmation of the impact of extreme events on asset returns, but they imply a somewhat different distribution of them.

Tails, Fears and Risk Premia

Viktor Todorov (Northwestern University)

We show that the compensation for rare events, or disasters, accounts for a large fraction of the equity and variance risk premia in the S&P 500 market index. The probability of rare events vary significantly over time, increasing in periods of high market volatility, but the risk premium for tail events cannot be sole explained by the level of the volatility. Our empirical investigations are essentially non-parametric and model-free, and do not resort to a peso type explanation for rare events. Instead, we estimate the expected values of the tails under the statistical probability measure from “medium” size jumps in actual high-frequency intraday prices and an extreme value theory approximation for the corresponding interdaily jump tail density. Our estimates for the risk-neutral expectations are based on actual short maturity out-of-the money options and new model-free option implied variation measures explicitly designed to separate the tail probabilities. At a general level, our results suggest that any satisfactory equilibrium based asset pricing model must be able to generate large and time-varying compensations for fears of disasters.

The Price of Liquidity: Bank Characteristics and Market Conditions
Jorg Rocholl (European School of Management)

This paper examines prices in the market for liquidity and how they are affected by bank specific and market wide factors. We have price data at the individual bank level and unique to this paper, data on individual banks reserve requirements and actual reserve holdings, thus allowing us to gauge the extent to which a bank is short or long liquidity. We find that the price a bank pays for liquidity depends on the liquidity positions of other banks, as well as its own. There is evidence that liquidity squeezes occasionally occur and short banks pay more the larger is the potential for a squeeze. The price paid for liquidity is decreasing in bank size and small banks are more adversely affected by an increased potential for a squeeze. Contrary to what one might expect, banks in formal liquidity networks do not pay less.

Price Pressures

Albert Menkveld (VU University of Amsterdam)

We study price pressures—price deviations from fundamental values due to a risk-averse intermediary supplying liquidity to asynchronously arriving investors with idiosyncratic hedging values. In our model, the intermediary uses price pressure to mean-revert costly inventory by trading off the size of the price pressure against the cost of remaining in a risky inventory state. Price pressure is associated with the social cost of lower realization of investor hedging value because the intermediary’s efforts to mean revert inventory substitutes low-hedge-value investors on the side of the market that reduces the risk of the intermediary’s position for high-hedge-value investors on the risk-increasing side. Empirically, twelve years of daily New York Stock Exchange (NYSE) intermediary data reveal economically large price pressures and associated social costs. A $100,000 inventory shock causes price pressure of 1.01% for the small-capitalization stocks and 0.02% for the large-cap stocks. However, the price pressure conditional on inventory reduces inventory positions leading to the smaller differences in transitory volatility in daily stock returns (average price pressure): 1.20% vs. 0.17% for small and large stocks, respectively. The intermediary’s larger volatility of inventory positions in large stocks results in a greater model-based estimate of social cost due lower unrealized hedge gains for large stocks of $9.68 million per year vs. $0.67 million for small stocks. The aggregate lost hedging gains are estimated to be greater than $50 billion for all NYSE common stocks for our sample period.

Macro, Industry, and Frailty effects in Defaults during the 2008 Credit Crisis: A variance decomposition

Bernd Schwaab (VU University of Amsterdam & Timbergen Institute)

We introduce a new joint modeling framework for systematic default risk and macroeconomic developments. The new approach captures three sources of default clustering: the systematic variation of defaults with (i) a large number of observed macroeconomic and financial time series, (ii) latent frailty risk to capture unobserved default dynamics, and (iii) industry dynamics due to for example default contagion at the sectoral level. The mixed modeling framework with both Gaussian and non-Gaussian time series requires the derivation of new results for estimation and inference in a mixed measurement panel data setting. We decompose the systematic risk into each of its three constituents and find that both macro, frailty, and industry effects are important. When applying these results, we show that model-implied capital buffers would have protected a stylized US financial institution in every quarter of the years 1981 to 2008. This result no longer obtains if we neglect latent risk factors.

Exploring Dynamic Default Dependence

Peter Christoffersen (McGill University and CREATES)

Characterizing the dependence between companies’ defaults is a central problem in the credit risk literature, and the dependence structure is a first order determinant of the value of credit portfolios and structured credit products such as collateralized debt obligations (CDO), as well as the relative values of CDO tranches. We compare correlation measures implied by CDO prices with time-varying correlations implied by equity returns and CDS spreads. We use flexible dynamic equicorrelation techniques introduced by Engle and Kelly (2008) to capture time variation in CDS-implied and equity return-implied correlations. We perform this analysis using North American firms from the CDX index, as well as European firms from the iTraxx index. All correlation time series are highly time-varying and persistent, and correlations extracted from CDSs and CDOs increased significantly in European and North American markets during the turbulent second half of 2007. Interestingly, we find that the correlation time-series implied by CDO prices co-moves very strongly with the correlation time-series extracted from CDS spreads, but somewhat less strongly with the correlations between equity returns. These findings suggest that the cross-sectional dependence in these complex structured products is fairly well measured. However, changes in CDO prices may be due to changes in correlation, and more sophisticated models with time-varying correlations are thus needed to value CDOs.

A Markov Chain Monte Carlo Analysis of Credit Spread Models

Li Xu (Stanford University)

We analyze various specifications of stochastic volatility models for credit spread index returns. Specifically, we consider specifications that incorporate the following four features: correlations between the return and return volatility (the so-called leverage effect), a heavy-tailed student component in the return process, and a jump component in the return process and/or in the volatility process. In particular, we examine the standard stochastic volatility model without leverage effect (the base model) and its 11 extensions.

We estimate the 12 model specifications using the Markov Chain Monte Carlo (MCMC) method with option-adjusted spreads (OAS) of Merrill Lynch (ML) corporate bond indices for three rating/maturity categories over January, 1997 through April, 2005. We do model selections based on the Deviance Information Criterion. Our empirical results show that there is no “leverage effect” in credit spread indices returns and jumps in return process are important and that the SVIJJ (the SV model with independent jumps in both returns and volatility) model is the best model for capturing the dynamic behavior of investment-grade indices returns and SVTJ (the SV model with both a student-t component and a jump component in returns) model is the best model for high-yield indices returns over the sample period considered in this study.