Credit Risk & R Language

Credit risk is the risk of counter-party/client defaulting on the payment as per the payment schedule.Investor investing in corporate bonds or providing loans need to be aware of credit quality of client to ensure repayment of loans and interest to realize upon the gains. Risk taken by investor in such investments is compensated by the higher returns that he/she will be making on such investments.The excess return which investor makes on such investments is known as credit spread.

Credit Spread = Interest return (corporate bond) - Risk free rate
Risk free rate : rate of return given by Govt. securities, it is called risk free because probability of default by Govt. is almost negligible.

For a retail investor it becomes very difficult to measure/value the credit quality of corporate bonds to reach right credit spread which he/she should ask, for taking that additional risk. Such bonds/loans are rated by national rating agencies who will rate corporate issues using various models (KMV,Credit Metrics or Merton model).Rating agencies give grade to each issue,bonds depending upon the probability of default by issuing authority/institution. Rating of BBB and above are called investment grade bonds while bonds below BBB are called Junk bonds(not good for investment).

Financial institutions investing in bonds/loans needs to set aside capital to bear any shocks arising out of credit default by issuing institutions. Basel II has set guidelines for capital requirements for credit risk , credit risk can be measured using following three techniques (Basel recommend moving to next level of approach to measure credit risk depending upon maturity of central bank of country).

1. Standardized approach
2. Foundation internal rating based approach ( Pd measured by financial institutions while LGD provided by central bank)
3. Advanced IRB : PD and LGD both measured by financial institutions..
   

Standardized approach is quite easy where we directly use credit ratings by national agencies to find out capital requirements for credit portfolio but this can lead to wrong estimation as this does not take into account correlation and diversification of the portfolio.

On the other hand both internal rating based approach gives independence of measuring PD for the portfolio, while finding out PD for the portfolio we can account for the dependency and correlation of the portfolio.We will discuss following models to measure PD for single bond or group of bonds (portfolios) and will also model this in R language:

• Altman Z score
• Merton Model
• Credit KMV
  
• Credit Metrics

Before getting into other models, let me explain Z score model (info from Wikipedia)

T₁ = Working Capital / Total Assets

T₂ = Retained Earnings / Total Assets

T₃ = Earnings before Interest and Taxes / Total Assets

T₄ = Market Value of Equity / Total Liabilities

T₅ = Sales/ Total Assets

Z score Bankruptcy Model:

Z = 1.2T₁ + 1.4T₂ + 3.3T₃ + 0.6T₄ + .999T₅

Zones of Discrimination:

Z > 2.99 -“Safe” Zones

1.81 < Z < 2.99 -“Grey” Zones

Z < 1.81 -“Distress” Zones