The Risk Modeling Evaluation Handbook: Rethinking Financial Risk Management Methodologies in the Global Capital Markets - Rilegato

Gregoriou, Greg N.; Hoppe, Christian; Wehn, Carsten S.

Rilegato

ISBN 10: 0071663703 ISBN 13: 9780071663700

Casa editrice: McGraw Hill, 2010

Riassunto

The first in-depth analysis ofinherent deficiencies in present practices

“A book like this helps reduce the chance of a future breakdown in risk management.”
Professor Campbell R. Harvey, the Fuqua School of Business, Duke University

“A very timely and extremely useful guide to the subtle and often difficultissues involved in model risk—a subject which is only now gaining theprominence it should always have had.”
Professor Kevin Dowd, Nottingham University Business School, the University of Nottingham

“This book collects authoritative papers on a timely and important topic . . .and should lead to many new insights.”
Professor Philip Hans Franses, Erasmus School of Economics, Erasmus University

“Inadequate valuation and risk management models have played their part intriggering the recent economic turmoil felt around the world. This timely book,written by experts in the field of model risk, will surely help risk managers andfinancial engineers measure and manage risk effectively.”
Dr. Fabrice Douglas Rouah, Vice President, State Street Corporation

“This invaluable handbook has been edited by experts . . . and should prove to beof great value to investment finance and credit risk modelers in a wide range ofdisciplines related to portfolio risk, risk modeling in finance, international moneyand finance, country risk, and macroeconomics.”
Professor Michael McAleer, Erasmus School of Economics, Erasmus University

About the Book:

If we have learned anything from the globalfinancial collapse of 2008, it is this: themathematical risk models currently used byfinancial institutions are no longer adequatequantitative measures of risk exposure.

In The Risk Modeling Evaluation Handbook,an international team of 48 experts evaluatesthe problematic risk-modeling methodsused by large financial institutions and breaksdown how these models contributed to thedecline of the global capital markets. Theirconclusions enable you to identify the shortcomingsof the most widely used risk modelsand create sophisticated strategies for properlyimplementing these models into your investingportfolio.

Chapters include:

• Model Risk: Lessons from Past Catastrophes(Scott Mixon)
• Effect of Benchmark Misspecification on RiskadjustedPerformance Measures (Laurent Bodsonand George Hübner)
• Carry Trade Strategies and the Information Content ofCredit Default Swaps (Raphael W. Lam andMarco Rossi)
• Concepts to Validate Valuation Models(Peter Whitehead)
• Beyond VaR: Expected Shortfall and Other CoherentRisk Measures (Andreas Krause)
• Model Risk in Credit Portfolio Modeling(Matthias Gehrke and Jeffrey Heidemann)
• Asset Allocation under Model Risk (Pauline M. Barrieuand Sandrine Tobolem)

This dream team of the masters of riskmodeling provides expansive explanations ofthe types of model risk that appear in riskmeasurement, risk management, and pricing,as well as market-tested techniques formitigating risk in loan, equity, and derivativeportfolios.

The Risk Modeling Evaluation Handbook is thego-to guide for improving or adjusting yourapproach to modeling financial risk.

Su questo libro

Informazioni sull?autore

Greg N. Gregoriou is professor of finance in theSchool of Business and Economics at StateUniversity of New York (Plattsburgh). He isthe author of numerous financial books andcoeditor for the Journal of Derivatives andHedge Funds.
Christian Hoppe is group head of credit solutionsin the corporate banking division of CommerzbankAG Frankfurt. He is cofounder andCEO of the Anleihen Finder GmbH.
Carsten S. Wehn is head of market risk control atDekaBank, Frankfurt, where he is responsiblefor measuring market and liquidity risk,developing risk methods and models, andvalidating the adequacy of the respective riskmodels.

Estratto. © Ristampato con autorizzazione. Tutti i diritti riservati.

THE RISK MODELING EVALUATION HANDBOOK

Rethinking Financial Risk Management Methodologies in the Global Capital Markets

The McGraw-Hill Companies, Inc.

Copyright © 2010 The McGraw-Hill Companies, Inc.
All right reserved.
ISBN: 978-0-07-166370-0

Contents

Chapter One

MODEL RISK Lessons from Past Catastrophes

Scott Mixon

ABSTRACT

Financial engineers should study past crises and model breakdowns rather than simply extrapolate from recent successes. The first part of this chapter reviews the 2008 disaster in convertible bonds and convertible arbitrage. Next, activity in nineteenth-century option markets is examined to explore the importance of modern theory in pricing derivatives. The final section reviews the linkage between theory and practice in bridge building. The particularly interesting analogy is the constructive direction taken by engineers after the highly visible, catastrophic failure of the Tacoma Narrows Bridge in Washington in 1940. Engineers were reminded that highly realistic models may increase the likelihood of failure if they reduce the buffer against factors ignored by the model. Afterward, they focused efforts on making bridges robust enough to withstand eventualities they did not fully understand and could not forecast with accuracy.

MODEL RISK: LESSONS FROM PAST CATASTROPHES

The holddown cables stabilizing the bridge began to vibrate in the wind around 3:30 in the morning, as the storm increased. The bridge was oscillating by 8 a.m., allowing a driver to watch the car up ahead disappear into a trough. Yet this was nothing new for the bridge nicknamed "Galloping Gertie." An hour later, the tiedown cables cracked like whips as they alternately tightened and slackened.

The twisting began around 10 a.m. Winds were only 45 miles per hour, but the bridge was pivoting around the center line of the two-lane roadway. One lane would lift up 45 degrees, and the other would twist down by the same amount. The bridge was twisting itself to pieces. A major section of roadway, hundreds of feet long, fell into Gig Harbor at 11 a.m. Ten more minutes and the remainder of the bridge (plus two abandoned cars and a dog) was gone. Leon Moisseiff, prominent engineering theorist and designer of the bridge, was completely at a loss to explain the disaster.

The collapse of the Tacoma Narrows Bridge took with it the entire trajectory and hubris of the suspension bridge building industry. The bridge lasted just four months, and it failed in winds less than half the 100 miles per hour for which it was designed to withstand. The dramatic collapse was captured on film, so the world saw the images repeated over and over in newsreels.

Suspension bridges had become longer and thinner in the decades before the Tacoma Narrows collapse in 1940. The George Washington Bridge, spanning the Hudson River into New York City, epitomized this trend. Built according to the most advanced theories, it had doubled the length of the longest suspension span extant before its 1931 completion. Engineers were under pressure from the economic realities of the Great Depression to reduce costs, while theoretical advances showed that conventional bridge designs were considerably overengineered. Suspension bridges had moved from designs in which the suspending cables were superfluous to ones in which cables were the dominant element.

Moisseiff and Lienhard's (1933) extension of existing theory meant that wind loads carried by the suspended structure of the George Washington Bridge, for example, were 80 percent lower than previously thought. The cables carried the weight. It was only natural that Moisseiff's Tacoma Narrows design would incorporate this economically appealing feature. The bridge had a width to span ratio of 1:72, even though a more traditional ratio was 1:30. It was a narrow, two-lane highway suspended in the sky, and it was theoretically justified to carry its loads adequately. For four months, it did.

Engineers had built little margin of safety into the Tacoma Narrows Bridge. It was elegant, economical, and theoretically justified. Moving to more realistic theories of load bearing ironically led to catastrophic failure, since the theories provided little buffer against risk factors not considered in the models. Henry Petroski (1994) has noted that the reliance on theory, with little first-hand experience of the failures from decades before, led to a design climate in which elements of recent successes were extended beyond their limits. Petroski therefore recommended that engineers carefully study past design failures in order to improve their current design process. This chapter adopts Petroski's logic to model risk evaluation for financial engineers.

INTRODUCTION

First, we discuss the disaster in the convertible bond market during 2008 and pay particular attention to the difficulties faced by the model-intensive convertible arbitrage strategy. Next, we review the activity in option markets in the nineteenth century to explore the importance of modern theory in pricing derivatives. This is followed by a section reviewing the linkage between theory and practice in bridge building. It highlights the direction taken by the engineering profession after the highly visible, catastrophic failure of the Tacoma Narrows Bridge in 1940. The final section provides concluding thoughts.

The goal of bringing together such disparate topics is to provide a broad perspective on model risk. Some of the key issues addressed are: (1) How can we best frame themes regarding model breakdowns during market crises? (2) What can the careful study of the evolution of derivatives markets and no-arbitrage pricing models suggest for robustifying market practice against traumatic shocks? (3) What can be learned from the experiences of other disciplines that have suffered catastrophic failures when moving from theory to reality?

There are some straightforward conclusions for this chapter. First, financial engineers should study past crises and model breakdowns rather than simply extrapolate from recent successes. Second, theoretical advances have had a profound impact on the pricing of derivative securities and the mindset for financial engineering, but the real world is tricky. Highly realistic models may increase the likelihood of failure if they reduce the buffer against factors glossed over by the model. For example, highly complex no-arbitrage models may fail miserably when trading is not continuous and arbitrage opportunities exist for a period of time (i.e., when liquidity disappears).

Financial engineers can look to the experience of the civil engineering profession after the traumatic failure of the Tacoma Narrows suspension bridge in 1940. Bridge builders could have concluded that their theories were too naïve to build economical bridges as long as the ones proposed. They did not throw out the models or abandon the practice of bridge construction. Rather, they focused efforts at making bridges robust enough to withstand eventualities they did not fully understand and could not forecast with accuracy.

Faced with calamities such as the recent one in the financial markets, one could take the position that highly quantitative models are dangerous and should be thrown out. This idea is completely unjustified. A key idea running through this chapter is that some of the assumptions behind derivatives modeling, such as continuous, frictionless trading at a single market price (i.e., the absence of arbitrage) can fail at critical moments. Engineers (and drafters of legal documentation) should seek ways to robustify the structures so that these disruptions do not lead to catastrophic failures.

For example, some of the hedge fund industry might move to longer lock-ups and increased acceptance of a secondary market in ownership interests (a cross between ETFs and closed-end funds). During extreme liquidity crunches, as in the fall of 2008, investors requiring liquidity could have raised cash by selling their hedge fund interests, yet the underlying funds would not have been forced to sell assets to fulfill redemption requests. Is this not, in fact, a substantial part of the logic behind having a liquid secondary market for corporate ownership of companies?

CONVERTIBLE CATASTROPHE, 2008

The bottom line is that everything went wrong for convertibles in the last part of 2008, and the convertible arbitrage strategy gave back about six years of gains in a few months. There was tremendous selling pressure on convertibles, about 70 percent of which were held by hedge funds. Convertible arbitrageurs typically were long convertibles and hedged various risks to profit from perceived mispricing of the convertible. In extremely volatile and thin markets, the ability to hedge was disrupted: the ability to short many stocks was eliminated (partially by government fiat), synthetic credit hedges were not following the same trajectory as cash bonds, and the implicit call options in convertible bonds were priced completely out of sync with listed options. Margin requirements increased massively. Redemptions loomed for hedge funds of all stripes, and raising liquidity became the overriding goal. Convertible arbitrage was hit hardest among the hedge fund strategies during 2008, with some indexes showing the strategy down more than 50 percent.

This section puts a finer point on these issues. The conceptual framework of the model risk in mind for a crisis of this type is p_it = E^m [p_it] + e_it, e_it = c_t + d_it, where p_it is the market price of asset i at time t, E^m [p_it] is the expected value of the asset at time t under the model m, and there is an error term e_it that causes the observed price to deviate from the model price ("fair value"). We can divide the error term into two components: the idiosyncratic disturbance d_it and the market-wide term c_t. Roughly speaking, a crisis is when c_t, on rare occasions, dominates price movements. Evaluating model risk and figuring out ways to work around model failure during a crisis means understanding when c_t is the driving force behind market prices.

What Happened?

Table 1.1 displays convertible arbitrage index performance in 2008, along with performance for the S&P 500 and Vanguard's Intermediate Corporate Bond Fund. Returns are standardized by subtracting the average and dividing by the unconditional standard deviation. Averages and standard deviations are computed using data through December 2007. The Center for International Securities and Derivatives Markets (CISDM) index data begin in January 1992, the Credit Suisse/Tremont data begin in January 1994, and the Hedge Fund Research Performance Index (HFRI) data begin in January 1990. The S&P 500 and Corporate Bond Fund data begin in January 1990. Table values in bold are t-statistics of at least 2 in absolute value.

March 2008 seemed to be a particularly unlucky month for convertible arbitrage funds, according to the table, as returns were extremely unlikely. Yet things worsened: September and October were greater than 10 standard deviations to the downside. The corporate bond fund and the S&P 500 returns were also much larger in absolute magnitude than history would suggest, so perhaps some of these shocking moves were simply volatility increasing above the unconditional levels. Still, convertible arbitrage appears to have experienced some very rare events.

Figure 1.1 illustrates a measure of convertibles mispricing from January 2005 to April 2009. The chart shows the ratio of the median price (average of bid and ask) to the median theoretical price for the entire U.S. convertible universe tracked by Deutsche Bank. Both the bid/ask midpoints and the theoretical prices are Deutsche Bank calculations. From 2005 until the end of 2007, this mispricing hovered around zero; one can see occasional divergences, such as the spring 2005 cheapening documented by Mitchell and colleagues (2007). Convertibles then cheapened dramatically in spring 2008 but bounced back toward fair value by July. Then the bottom fell out, with market prices collapsing to more than a 15 percent discount by November. The mispricing steadily diminished after that and fell to less than half by April 2009.

"Fair value" models of convertibles suggested a much higher value than observed market quotes of late 2008 would suggest. Outright buyers of convertibles should have moved in, according to the textbook no-arbitrage condition, and bought up the cheap instruments. Anecdotes suggest this is what happened eventually, but it was not instantaneous. September through November felt like really long months to market participants staring at the wrong side of arbitrage opportunities.

Figure 1.2 displays another way of exploring convertible mispricing in 2008, focusing on the option component of the bonds. The chart displays a market-capitalization weighted index of one-year, at-the-money implied volatilities for S&P 100 stocks (constructed from Bloomberg data) and an issue-weighted index of convertible bond implied volatilities. The convertible index is from Deutsche Bank; it is computed from near-the-money investment grade convertibles and is reweighted quarterly. Throughout 2007 and the first half of 2008, the two series track each other quite closely. The exception during this period is for March 2008, when listed option volatilities spiked even as convertible volatilities moved in the opposite direction. (This spike is distinctly noticeable in the convertible arbitrage standardized returns for March.)

The dramatic divergence in the two markets is in the second half of 2008, when listed volatilities doubled to more than 70 percent and convertible implieds sank to less than 20 percent. Over the course of autumn, listed volatilities began to decline as markets began to stabilize. By the end of the year, the listed option volatility index was hovering around 50 percent, yet convertible implieds were still less than 30 percent.

Convertibles apparently had a negative vega, that is, buying a convertible meant going short volatility. This is clearly counterintuitive and stands in contrast to the expected exposure. Arbitrage managers had hedged themselves using models that suggested they were close to delta neutral, but the models would never have suggested such perverse moves in pricing as had occurred, and the theoretical option models would surely have suggested a positive vega for convertibles.

Industry analysts suggested that by mid-November, one-third of convertible arbitrage funds had gated redemptions, suspended net assest value calculations, or were in some other way impaired. Some of the stabilization in pricing occurred as selling pressure abated due to reduced redemption pressure. The redemption pressure was artificially capped as some managers gated and simply refused to return investments to investors. The investor response was not a happy one. Anecdotally, some investors declared funds that gated as "uninvestible" going forward.

This discussion of convertible mispricing can be made less abstract, particularly with respect to hedging instruments. Figure 1.3 illustrates a particularly clear example using traded prices for two bonds issued by Smithfield Foods. The gray bars represent the straight bond due May 15, 2013, and the squares represent the convertible bond due June 30, 2013. The chart begins with the June 2008 issuance of the convertible and ends in late May 2009. Some interesting observations can be made. First, there are many gaps in the trade history of the bonds, particularly in November 2008. Only 12 of the 18 trading days in that month saw any action, and the median daily volume over the month was 60 bonds. The convertibles traded only six days during the month. Second, the price of the convertible is often below that of the straight bond, suggesting a negative value for the option to convert the bond into stock (these observations are the white squares).

Figure 1.4 focuses on the valuation of the option implicit in the convertible. The boxes represent the implied volatility (provided by Deutsche Bank) for the convertible, and the solid black line represents the implied volatility from the closest comparable listed option (provided by iVolatility.com). The convertible bond provides for a conversion price (i.e., the strike price of the option) of $22.685 per share. The listed implied volatility is for the January 2010 25-strike call option until December 12, 2008, and for the January 2011 22.5-strike call thereafter.

(Continues...)

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Dettagli dell?edizione

• Editore: McGraw Hill
• Data di pubblicazione: 2010
• ISBN 10: 0071663703
• ISBN 13: 9780071663700
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 528
• Contatto del produttore: non disponibile