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Figure 12.8: Granularity Adjustment to the Loss Rate VaR as a function of Correlation

Figure 12.8: Granularity Adjustment to the Loss Rate VaR as a function of Correlation

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Other Aspects of Credit Risk



48



• Recovery Rates

• In the case of default part of the face value is typically

recovered by the creditors

• When assessing credit risk it is therefore important to have

an estimate of the expected recovery rate

• Moody’s defines recovery using the market prices of the

debt 30 days after the date of default

• The recovery rate is then computed as the ratio of the postdefault market price to the face value of the debt

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



Recovery Rate



49



Figure 12.9 shows the average (issuer-weighted) recovery

rates for investment grade, speculative grade, and all

defaults

• Figure is constructed for senior unsecured debt only

• The two-year recovery rate for speculative grade firms is

36.8%.

• This number shows the average recovery rate on

speculative grade issues that default at some time within a

two-year period

• The defaults used in Figure 12.9 are from the 1982 to 2010

period

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



Recovery Rate



Figure 12.9 shows that the average recovery rate is around

40% for senior unsecured debt

• Sometimes the loss given default (LGD) is reported instead

of the recovery rate (RR)

• They are related via the simple identity LGD = 1 – RR

• If we assume a constant proportional default rate across

loans then we can compute the credit portfolio $VaR taking

into account recovery rates using



• where RR denotes the recovery rate and DVPF denotes the

dollarElements

value

of

the

portfolio

of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



50



Figure 12.9 Average recovery rates for senior

unsecured bonds



Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



51



Recovery Rate

The VaR1-p is the VaR from the portfolio loss rate defined

earlier

• The granularity adjusted dollar VaR can similarly be

computed as



• Figure 12.2 showed that the default rate varied strongly

with time

• This has not been built into our static factor model for

portfolio credit risk but it could be by allowing for the

factor F to change over time

Elements of Financial Risk Management Second Edition â 2012 by Peter Christoffersen



52



Recovery Rate



53



We may also wonder if the recovery rate over time is

correlated with default rate.

• Figure 12.10 shows that it is negatively correlated in the data

• The higher the default rate the lower the recovery rate

• Stochastic recovery and its correlation with default present

additional sources of

• credit risk that have not been included in our simple model

but that could be built in

• In more complicated models, the VaR can be computed only

via Monte Carlo simulation techniques such as those

developed in Chapter 8

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Figure 12.10: Recovery Rates versus Default Rates.

Annual Data, 1982-2010



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



54



Credit Quality Dynamics



55



• The credit quality of a company typically declines well

before any eventual default

• It is important to capture this change in credit quality

because the lower the quality the higher the chance of

subsequent default

• One way to quantify the change in credit quality is by using

the credit ratings provided by agencies such as Standard &

Poor’s and Moody’s

• The following list shows the ratings scale used by Moody’s

for long-term debt ordered from highest to lowest credit

quality

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Credit Quality Dynamics



56



• Investment Grades

• Aaa: Judged to be of the highest quality, with minimal

credit risk

• Aa: Judged to be of high quality and are subject to very low

credit risk

• A: Considered upper-medium grade and are subject to low

credit risk

• Baa: Subject to moderate credit risk. They are considered

medium grade and as such may possess certain speculative

characteristics

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Credit Quality Dynamics



57



• Speculative Grades

• Ba: Judged to have speculative elements and are subject to

substantial credit risk

• B: Considered speculative and are subject to high credit risk

• Caa: Judged to be of poor standing and are subject to very

high credit risk

• Ca: Highly speculative and are likely in, or very near,

default, with some prospect of recovery of principal and

interest

• C: The lowest rated class of bonds and are typically in

default, with little prospect for recovery of principal or

interest

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Table 12.2: Average One-Year Rating Transition

Rates, 1970-2010

From/To:



Aaa



Aa



A



Baa



Ba



B



Caa



Ca_C



WR



Default



Aaa



87.395%



8.626%



0.602%



0.010%



0.027%



0.002%



0.002%



0.000%



3.336%



0.000%



Aa



0.971%



85.616%



7.966%



0.359%



0.045%



0.018%



0.008%



0.001%



4.996%



0.020%



A



0.062%



2.689%



86.763%



5.271%



0.488%



0.109%



0.032%



0.004%



4.528%



0.054%



Baa



0.043%



0.184%



4.525%



84.517%



4.112%



0.775%



0.173%



0.019%



5.475%



0.176%



Ba



0.008%



0.056%



0.370%



5.644%



75.759%



7.239%



0.533%



0.080%



9.208%



1.104%



B



0.010%



0.034%



0.126%



0.338%



4.762%



73.524%



5.767%



0.665%



10.544%



4.230%



Caa



0.000%



0.021%



0.021%



0.142%



0.463%



8.263%



60.088%



4.104%



12.176%



14.721%



Ca_C



0.000%



0.000%



0.000%



0.000%



0.324%



2.374%



8.880%



36.270%



16.701%



35.451%



Notes to Table: The table shows Moody's credit rating transition rates

estimated on annual data from 1970 through 2010. Each row represents

last year's rating and each column represents this year's rating. Ca_C

combines two rating categories. WR refers to withdrawn rating.

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



58



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Figure 12.8: Granularity Adjustment to the Loss Rate VaR as a function of Correlation

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