Value at Risk and Bank Capital Management

92 CHAPTER

♦

4 Credit Risk

recovery rates for utilities are substantially higher than those for real estate/construction

fi rms. In any case, industries show signifi cant differences in LGD through time, since

recoveries are much lower in years in which an industry is in distress (Acharya, Bharath,

and Srinivasan 2003; Gupton 2005).

This introduces the crucial issue of whether PD and LGD are linked. In recent years,

empirical evidence has shown that PD and LGD are positively correlated, since they both

tend to grow in recession years; see Hu and Perraudin (2002), Acharya, Bharath, and

Srinivasan (2003), Altman et al. (2005), and the survey by Altman, Resti, and Sironi

(2005). A simple picture of the problem is given in Table 4-8, comparing recovery rates

(i.e., 1 minus LGD) in recession and expansion years.

Despite the recent literature in favor of the existence of a PD–LGD link, empirical

studies are based essentially on market LGD for bonds, and this still leaves some theoreti-

cal questions open concerning the correlation between PD and bank loans’ workout LGD.

For instance, while Acharya, Bharath, and Srinivasan (2003) explain the correlation with

industry effects, Altman et al. (2005) fi nd a clear relationship among PD and LGD for

bonds but argue that a microeconomic model based on supply and demand of defaulted

bonds may explain the link more than a macroeconomic model linking both PD and LGD

to the phase of the economic cycle. In other words, lower recoveries (measured by bond

prices after default) may be explained because in bad years the higher default rate may

imply an excess of supply, and hence a lower market value, of defaulted bonds. If one

agrees on the demand-and-supply explanation for the PD–LGD link, it may still be ques-

tioned whether expected recovery from nontradable bank loans should be assumed to be

as correlated to PD as bonds’ recoveries are, or, instead, whether the variability of the

loans’ LGD should be driven almost exclusively by specifi c factors (such as the duration

of the workout process or the type of underlying assets). Through time, the efforts by

larger banks to increase the size and extent of internal databases for LGD quantifi cation

will make it possible to give an answer through detailed empirical tests.

The issue of the PD–LGD correlation is critical, since credit portfolio models (dis-

cussed later) usually assume LGD to be either fi xed or stochastic but independent of PD.

While even a stochastic LGD would not substantially change VaR estimates for a portfolio

as long as it is independent of the PD, a stochastic and positively correlated LGD would

make 99% or 99.97% potential losses become much higher (Altman et al. 2005).

4.7 Estimating Exposure at Default

Exposure at default is defi ned as “the expected gross exposure of the facility upon default

of the obligor” (Basel Committee 2006a). While for certain kinds of loans the amount

the bank is lending is fi xed and predetermined, the issue of EAD is particularly relevant

TA B L E 4 - 8 Recovery Rates in Expansion Versus Recession Years (Moody’s Data, 1970–2003;

Percentages)

Standard 25th 50th 75th Number of

Mean Deviation Percentile Percentile Percentile Observations

Recessions 32.07 26.86 10.00 25.00 48.50 322

Expansions 41.39 26.98 19.50 36.00 62.50 1703

All 39.91 27.17 18.00 34.50 61.37 2025

Source: Schuermann (2005), based on Moody’s 1970–2003 data.