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## Credit Risk Plus and Credit Metrics

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**Credit Risk Plus and Credit Metrics**By: A V Vedpuriswar October 4, 2009**Introduction**• CreditRisk+ is a statistical credit risk model launched by Credit Suisse First Boston (CSFB) in 1997. • CreditRisk+ can be applied to any type of credit product, including loans, bonds, financial letters of credit and derivatives.**Credit Risk Plus**• Credit Risk + allows only two outcomes – default and no default. • In case of default, the loss is of a fixed size. • The probability of default depends on credit rating, risk factors and the sensitivity of the obligor to the risk factors. 3**Analytical techniques**• CreditRisk+ uses analytical techniques, as opposed to simulations, to estimate credit risk. • The techniques used are similar to those applied in the insurance industry. • CreditRisk+ makes no assumptions about the cause of default. • It models credit risk based on sudden events by treating default rates as continuous random variables.**Data requirements**• Exposure • Default rates • Default rate volatilities • Recovery rates**Methodology**• Model the frequency of default events • Model the severity of default losses • Model the distribution of default losses • Sector analysis • Stress testing**Factors for Estimating Credit Risk**• When estimating credit risk, CreditRisk+ considers : • credit quality and systematic risk of the debtor • size and maturity of each exposure • concentrations of exposures within a portfolio • CreditRisk+ accounts for the correlation between different default events by analyzing default volatilities across different sectors, such as different industries or countries. • This method works because defaults are often related to the same background factors, such as an economic downturn. • To estimate credit risk due to extreme events such as earthquakes, CreditRisk+ uses stress testing. • For low probability events that can't be covered under the statistical model, it uses a scenario-based approach.**Frequency of default events**• The timing of default events cannot be predicted. • The probability of default by any debtor is relatively small. • CreditRisk+ concerns itself with sudden default – as opposed to continuous change – when estimating credit risk.**Poisson Distribution**• CreditRisk+ uses the Poisson distribution to model the frequency of default events. • The Poisson distribution is used to calculate the probability that a given number of events will take place during a specific period of time. • The Poisson distribution is useful when the probability of an event occurring is low and there are a large number of debtors. • For this reason, it is more appropriate than the normal distribution for estimating the frequency of default events.**Using the Poisson distribution**• Suppose there are N counterparties of a type and the probability of default by each counterparty is p. • The expected number of defaults, , for the whole portfolio is Np. • If p is small, the probability of n defaults is given by the Poisson distribution, i.e, the following equation: • p (n) = 10**Modeling the Severity of Default Losses**• After calculating the frequency of default events, we need to look at the exposures in the portfolio and model the recovery rate for each exposure. • From this, we can conclude the severity of default losses.**Modeling the Distribution of Default Losses**• After estimating the number of default events and the severity of losses, CreditRisk+ calculates the distribution of losses for the items in a portfolio. • In order to calculate the distributed losses, CreditRisk+ first groups the loss given default into bands of exposures. • The exposure level for each band is approximated by a common average. .**Sector analysis**• Each sector is driven by a single underlying factor, which explains the volatility of the mean default rate over time. • Through sector analysis, CreditRisk+ can measure the impact of concentration risk and the benefits of portfolio diversification. • As the number of sectors is increased, the level of concentration risk is reduced.**Stress Testing**• Stress tests can be carried out in CreditRisk+ and outside CreditRisk+. • CreditRisk+ can be stress tested by increasing default rates and the default rate volatilities and by stressing different sectors to different degrees. • Some stress tests, such as those that model the effect of political risk, can be difficult to carry out in CreditRisk+. • In this case, the effect should be measured without reference to the outputs of the model.**Applications of CreditRisk+**• Calculating credit risk provisions • Enforcing credit limits • Managing credit portfolios**Calculating Credit Risk Provisions**• When credit losses are modelled, the most frequent loss tends to be much lower than the estimated average loss. • This is because the estimated average takes into account the risk of occasional extreme losses. • Credit provisions, also known as economic capital, need to be set aside to protect against such losses. • CreditRisk+ can be used to set provisions for credit losses in a portfolio.**Enforcing Credit Limits**• High concentrations of a small number of exposures can significantly increase portfolio risk. • Credit limits are an effective way of avoiding concentrations. • They provide a means of limiting exposure to different debtors, maturities, credit ratings and sectors. • An individual credit limit should be set at a level that is inversely proportional to the default rating associated with a particular debtor's credit rating.**Managing Portfolios**• CreditRisk+ incorporates all the factors that determine credit risk into a single measure. • This is known as a portfolio-based approach. • The four factors that determine default risk are: • size • maturity • probability of default • concentration risk • CreditRisk+ provides a means of measuring diversification and concentration by sector. • More diverse portfolios with fewer concentrations require less economic capital.**Introduction**• CreditMetrics™ was launched by JP Morgan in 1997 • It evaluates credit risk by predicting movements in the credit ratings of the individual investments in a portfolio. • CreditMetrics consists of three main components: • Historical data sets • A methodology for measuring portfolio Value at Risk (VAR) • A software package known as CreditManager®**Transition Matrices and Probability of Default**• CreditMetrics uses transition matrices to generate a distribution of final values for a portfolio. • A transition matrix reflects the probability that a bond with a given rating will be upgraded or downgraded within a given time horizon. • Transition matrices are published by ratings agencies such as Standard and Poor's and Moody's.**Data requirements**• Credit ratings for the debtor • Default data for the debtor • Loss given default • Exposure • Information about credit correlations**Methodology**• CreditMetrics™ measures changes inportfolio value by predicting movements in a debtor's credit ratings and accordingly the values of individual portfolio investments. • After the values of the individual portfolio investments have been determined, CreditMetrics™ can then calculate the credit risk.**CreditMetrics™ Software – CreditManager®**• The software used by Credit Metrics is called CreditManager. • CreditManager® enables a financial institution to consolidate credit risk across its entire organization. • CreditManager® automatically maps each credit that the user loads into the system to its appropriate debtor and market data • It computes correlations and changes in asset value over the risk horizon due to upgrades, downgrades and defaults. • In this way, it arrives at a final figure for portfolio credit risk. • The software uses two types of data : • Position • Market**Steps for calculating credit risk for a single-credit**portfolio • Determine the probability of credit rating migration. • Calculate the current value of the bond's remaining cashflows for each possible credit rating. • Calculate the range of possible bond values for each rating. • Calculate the credit risk.**Steps for calculating credit risk for a two-credit portfolio**• Examine credit migration. • Calculate the range of possible bond values for each rating using independent or correlated credit migration probabilities. • Calculate the credit risk.**Steps for calculating credit risk for a multiple-credit**portfolio • Calculate the distribution of values using a Monte Carlo simulation. • Use the standard deviation and percentile levels for this distribution to calculate credit risk for the portfolio.**Single credit portfolios**• The steps to calculate distributed values for single-credit portfolios are: • Determine the probability of change in credit ratings. • Calculate the value of remaining cash flows for each possible credit rating. • Calculate the range of possible credit values for each rating. • The first step is to examine the probability of the bond moving from an one credit rating to another say within of one year. • The movement from one credit rating to another is known as credit migration. • Credit rating agencies publish credit migration probabilities based on historic data.**Bond values for different ratings**• Having examined the different probabilities for credit rating migration, the next step is to calculate the range of possible bond values for each rating. • That means calculating the value of Bond X for a credit rating of Aaa, Aa, A, Baa, Ba, B, Caa, Ca, C. • To do this, we first need to calculate the value of the bond's remaining cash flows for each possible rating.**Discounting the cashflows**• We use discount rates to calculate the current value of the bond's remaining cashflows for each credit rating. • These discount rates are taken from the forward zero coupon curve for each rating. • The forward zero coupon curve ranges from the end of the risk horizon – one year from now – to maturity.**Given a distribution of final values for Bond X, we can then**calculate two risk measurements for the portfolio: • Standard deviation • Percentile**Multiple-Credit Portfolios**• Because of the exponential growth in complexity as the number of bonds increases, a simulation-based approach is used to calculate the distribution of values for large portfolios. • Using Monte Carlo simulation, CreditMetrics simulates the quality of each debtor, which produces an overall value for the portfolio. • This procedure is then repeated many times in order to get the distributed portfolio values. • After we have the distributed portfolio values, we can then use the standard deviation and percentile levels for this distribution to calculate credit risk for the portfolio.**Portfolio Value Estimates at Risk Horizon**• CreditMetrics requires three types of data to estimate portfolio value at risk horizon: • coupon rates and maturities for loans and bonds • drawn and undrawn amounts of a loan, including spreads or fees • market rates for market driven instruments, such as swaps and forwards**Correlations**• One key issue in using Credit Metrics is handling correlations between bonds. • While determining credit losses, credit rating changes for different counterparties cannot be assumed to be independent. • How do we determine correlations? 34**Gausian Copula**• A Gaussian Copula Model comes in useful here. • Gaussian Copula allows us to construct a joint probability distribution of rating changes. • The Copula correlation between the ratings transitions for two companies is typically set equal to the correlation between their equity returns using a factor model.