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P2.T7.507. Model error cases (Malz)

Nicole Seaman

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Learning outcomes: Identify challenges related to mapping of risk factors to positions in making VaR calculations. Identify reasons for the failure of the long-equity tranche, short-mezzanine credit trade in 2005 and describe how such modeling errors could have been avoided. Identify two major defects in model assumptions which led to the underestimation of systematic risk for residential mortgage backed securities (RMBS) during the 2008-2009 financial downturn.

Questions:

507.1. According to Malz , each of the following statements is true about the mapping of risk factors to positions EXCEPT which is incorrect? (Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

a. Mapping is the process of assigning risk factors to positions; in order to compute risk measures, we have to assign risk factors to securities
b. When the underlying position and its hedge can be mapped to the same risk factor (or set of risk factors), the appropriate measure value at risk (VaR) is zero
c. Mapping decisions are often pragmatic; for example, fixed-income cash-flow mappings are more accurate than duration mappings, but are more complex and require more risk factors
d. As a practical matter, it may be difficult to find data that address certain risk factors, a problem that may merely mirror the real-world challenge of of hedging or expressing some trade ideas


507.2. About the long-equity tranche, short-mezzanine credit trade in 2005, Malz writes "A widespread trade among hedge funds, as well as proprietary trading desks of banks and brokerages, was to sell protection on the equity tranche and buy protection on the junior mezzanine tranche of the CDX.NA.IG. The trade was thus long credit and credit-spread risk through the equity tranche and short credit and credit-spread risk through the mezzanine. It was executed using several CDX.NA.IG series, particularly the IG3 introduced in September 2004 and the IG4 introduced in March 2005.

The trade was designed to be default-risk-neutral at initiation, by sizing the two legs of the trade so that their credit spread sensitivities were equal. The motivation of the trade was not to profit from a view on credit or credit spreads, though it was primarily oriented toward market risk. Rather, it was intended to achieve a positively convex payoff profile. The portfolio of two positions would then benefit from credit spread volatility. In addition, the portfolio had positive carry; that is, it earned a positive net spread. Such trades are highly prized by traders, for whom they are akin to delta-hedged long option portfolios in which the trader receives rather than paying away time value." (Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

But, of course, many of these traders suffered large losses. According to Malz, which of the following was the critical error in the trade?

a. The model ignored correlation altogether
b. The model failed to adequately capture and anticipate individual defaults
c. The model assumed a static implied correlation: deltas were partial derivatives that did not account for changing correlation which drastically altered the hedge ratio
d. The recovery amount was at risk; in the event of a default on one or more of the names in the index, the recovery amount was not fixed but a random variable


507.3. Among the costliest model risk episodes was the failure of subprime residential mortgage-based security (RMBS) valuation and risk models during the 2008-2009 financial downturn. These models were employed by credit-rating agencies to assign ratings to bonds, by traders and investors to value the bonds, and by issuers to structure them. Consider the following potential model risks:

I. Models neglected off-balance-sheet vehicles altogether
II. Models assumed positive future house price appreciation
III. Correlations among regional housing markets were assumed to be low
IV. Undue complexity of models including advanced mathematics that even models' authors did not understand
V. The heavy reliance on value at risk (VaR) which many practitioners did not realize was designed for market risk

According to Malz, while the models varied widely, two widespread MODEL defects were particularly important with respect to RMBS during the 2008-2009 downturn. (Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))

Among the above, which are the two major defects in model assumptions?

a. I. and II.
b. II. and III.
c. III. and IV.
d. IV. and V.

Answers here:
 
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