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¶ … Lehman and JP Morgan, we consider a period of four months as our observation window, for the years starting in 2006 to 2009. We use the KMV definition of debt as short-term liabilities plus half long-term liabilities. The interest rate is given by the 4-mos. LIBOR or swap rates. For illustration purposes, we use 5%. The benchmark index is given by the S&P500 index. The initial asset values are given by the sum of equity market cap plus liabilities and consequently derived via the Merton call option pricing framework described previously.
The table below depicts the range of minimum and maximum values for the component variables, whereby the EW Index score is given by the weighted average of the following indicators: idiosyncratic-specific volatility, default probability (given historical equity stock prices), default probability (given option prices), default probability (given CDS prices), market deviation (stock return vs. benchmark index return), country-specific risk, and rating grade. Meanwhile, market deviation from the S&P500 index, may range from 0 to 100%, and ought to be considered in complement with idiosyncratic risk to gauge entity-level fragility.
The table below depicts the range of values for the main indicators and their underlying component variables.
Asset
Asset Vol
Specific Vol
Yearly
Return
DD
PD
Equity
Dev
Asset
Asset
Vol
DD
PD
Options
PD
CDS
EW Index
LEH
min
0,014
0,191
-0,965
Idiosyncratic-specific volatility for Lehman and JP Morgan range from 20% and 10% respectively, up to 100%. In the case of Lehman, idiosyncratic risk sees a considerable spike higher within a span of three months, between 27/01/2008 to 27/04/2008, and reaches its maximum at default on 27/07/2008. Yearly returns depicted in the graph…
Distance-to-default, as expected, is inversely related to default probability, which is exemplified in the collapse of Lehman, whereby asset values fell below the default threshold of its liabilities between 27/07/2008 and 27/10/2008.
Corroborating the huge losses in asset values, distance-to-default followed a downward trend in the last Quarter of 2008. As validated by historical default behavior, distance-to-default is a leading indicator in predicting firm-wide distress 6 to 8 months prior to default.
As highlighted in the figure below, a comparison between Lehman and JP Morgan clearly highlights the fact that asset volatility is subject to considerable noise during the period immediately preceding default, to later flatten during the periods following maximum distress.
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