KIRAN KUMAR K V

In the last two decades a number of financial crises have led to the growth of Credit Risk Analysis as a specialized proficiency. Events like the below have made the credit risk analysis models highly demanded by the financial world:

- The β
β: Due to a continued overinvestment that led for overvaluation of Japanese real estate and equity prices during the 80s, Japanese economic growth slowed down and the slowing down lasted for more than 2 decades by now.*Collapse of Japanese Bubble* - The β
β of Mexico: Due to devaluation of Mexican Peso in Dec-1994, the Mexican Government Bonds caused severe losses to the investors.*Tequila Crisis* - The β
β: The crash of Thai Baht in July 1997 spread its wings to the equity markets of other related Asian economies and also subsequently the global markets.*Asian Contagion* - The β
β: In August, 1998, Russia defaulted on its debt and thus its securities caused significant losses and later this spread to affect the global equities.*Russian Debt Crisis* - The β
β: The famous β*Global Financial Crisis**Housing Bubble Burstβ*in US, resulted in significant losses on securitized instruments based on home mortgages. This was one event that shook the whole worldβs security markets equally. A related crisis is the ββ, this led to crisis of confidence, indicated by a widening bond-yield spreads and rising cost of risk insurance on credit default swaps.*Greek Sovereign Debt Crisis*

Mostly caused by an unexpected shift of a macroeconomic factor, these events have caused the default risk increase during these times. Traditionally, CREDIT RATINGS were the only measures of credit risk analysis, which were only partly effective in capturing the changes in these correlated default risks. As a result, additional tools to quantify and manage risks have emerged. These tools include methods for estimating correlated default probabilities and recovery rates based on macroeconomic factors. Such new models incorporated the systemic risk similar to those occurred during the above crises.

Before we understand the new tools, it may be useful to have an idea of the basic credit risk measures that are generally estimated:

β The probability that the bond will default before maturity.*Probability of Default*β The amount of the remaining coupon and principal payments lost in the event of default (expressed as a percentage of the position of exposure).*Loss given Default*β The percentage of position received or recovered in default. Therefore, percentage of*Recovery Rate**loss given default*plus*recovery rate*would be 100%β The*Expected Loss**probability of default*multiplied by the*loss given default*.β Conceptually the largest price once would be willing to pay on a bond to a third party (for example, an insurer) to entirely remove the credit risk of purchasing and holding the bond.*Present Value of the Expected Loss*

Traditional models for credit risk analysis have been primarily β

**order credit riskiness of the borrowers in an ordinal ranking (applicable for small owner-operated businesses and individuals) and***(1) Credit Scorings***provide a simple statistics that summarized a complex credit analysis of a potential borrower (used for companies, sovereigns, sub-sovereigns and asset backed securities)***(2) Credit Ratings*As these traditional models fail to capture quantitatively the basic credit risk measures discussed above, but, only give an approximation ide0a of the risk involved, a number of analytical tools have been developed. Here we discuss one such quantitative model called

**STRUCTURED MODEL**.STRUCTURED MODEL EXPLAINED

This model attempts to understand the economics of companyβs liabilities and build on the insights of option pricing theory. This can be called

*structural model*because this is based on the*structure*of a companyβs balance sheet. Letβs say we assume the structure of an issuing companyβs balance sheet that has- Assets of
,*A*_{t} - Debt of
which is a zero-coupon bond with maturity*D(t,T),*and face value*T*and*K* - Equity of
*S*_{t}

Then the accounting equation of the companyβs balance sheet can be given as:

**The companyβs shareholders have limited liability, that is to the maximum of***A*_{t}= D(t,T) + S_{t. }**. In other words, if the equity holders default on the debt payment at time***A*_{t}**, the debt holderβs only recourse is to take over the company and assume the ownership of***T***Thus, we say equity shareholdersβ liability in this case is limited, which becomes the basis of analogy between companyβs equity and a call option. A call optionβs payoff at time***A*_{t}.**is***T***In our example, if we consider companyβs asset as the underlying of the call option and the asset price at time***max[S*_{T}β K, 0].**as the spot price of the underlying at maturity, the payoff of the said option would be***T, (A*_{T})**(Note that***max[A*_{T}β K, 0].**is the principal repayment of the zero coupon bond). Debt holders in this case, become the writer of the call option, and their payoffs would be***K***What is means is that, debt holders would get***min[K, A*_{T}].**, if the***K***, as the equity holders find it beneficial to exercise the option (i.e., repay***A*_{t}>K**to debt holders)***K***and**debt holders would get**, if the***AT***, as the equity shareholders find it unviable to exercise the option and they would default, and thus debt holders get to own the assets at price***At<K***.***AT*Thus, it implies that:

*Probability of default*is probability that the*T*, and*AT<K*is*Loss given default**K-AT*

The assumptions we make implicitly, in the above construct are:

- The companyβs assets trade in frictionless markets that are arbitrage free
- The riskless rate of interest,
*r**,*is constant over time and - The time
value of the companyβs assets has a lognormal distribution with*T*and variance*Β΅*_{T}*Ο*^{2}_{T}

The above three assumptions are identical to those for stock price behaviour in the original Black-Scholes option pricing model. Hence, we can apply the BS model to find out the equityβs time

*t**value because it is a European call option on the companyβs assets. Thus, the valuation model becomes:*The first term in this expression

**refers to the present value of the payoff on a companyβs debt if default occurs. The second term***At N(-d1 )***refers to present value of the payoff on the companyβs debt if default does not occur. Thus, the sum of these two terms, therefore, gives the present value of the companyβs debt.***Ke^(-r(T-t) ) N(d2)***A Case Study**

Let us take the case of the below bond currently traded at NSE WDM:

NSE & BSE – Corporate Bonds Trade Repository for 08-Sep-2017 | |||||||||

xchange | ISIN | Security Description | Coupon Rate | Maturity Date | Last Traded Price (in Rs.) | Price (Average weighted price) | Yield (Weighted Avg. Yield ) % | Turnover (in Lacs) | Credit Rating |

NSE | INE155A08183 | TATA MOTORS LIMITED 10.3 NCD 30NV18 FVRS10LAC LOA UPTO 11MR14 | 10.30 | 30-Nov-2018 | 103.7962 | 103.7962 | 6.9000 | 10500.00 | – |

Source: https://nseindia.com/products/content/debt/corp_bonds/cbm_tr.htm (dt: 11-09-2017) |

The information required to conduct a credit analysis have been obtained from the financial statements of the company as below:

- Time
asset value= = 2737.54 crores (Non-current assets of Tata Motors as on 31-03-2017)*t* - Expected return on assets =
= 4.97% per year (Average return on assets of Tata Motors between FY 2006 to FY 2017)*Β΅*_{T} - Risk free rate =
= 6.01% per year (Yield on 10-year GOI from www.rbi.org)*r* - Face Value of debt = = Rs. 2050.608 (Non-current interest bearing liabilities of Tata Motors as on 31-03-2017)
- Time to maturity = = 445 days or 1.22 years (number of days between 11-Sep-2017 to 30-Nov-2018)
- Asset return volatility =
= 1.52% (standard deviation of return on assets of Tata Motors between FY 2006 to FY 2017)*Ο*_{T}

Using the above model various credit analysis outputs are obtained as below:

Input | Value (in crores) |

At | 145019.6 |

u | 0.83500 |

r | 0.0501 |

K | 60629 |

T-t | 1.22 |

sd | 0.4764 |

d1 | 2.03660 |

d2 | 1.510399705 |

N(-d1) | 0.0208 |

N(-d2) | 0.0655 |

e1 | 3.85640 |

e2 | 3.3301948 |

N(-e1) | 0.0000575 |

N(-e2) | 0.0004339 |

Probability of Default | 0.0004339 |

Expected Loss | 3.200 |

Present Value of Expected Loss | 711.133 |

The above present value of expected loss can be reduced from the value of the debt, based on a certain market discount rate to arrive at the value of total debt of this compan