Dear reader, congrats on reaching to Part-3 of this series. If you’re here, I’m assuming that you must’ve already gone through the Basics of CDS in Part-1 & Part-2 of this series. If not, kindly click here (Part 1) or here (Part 2) and go through the previous parts before proceeding further for a better understanding.

**The Vodafone Debt Crisis:**

For understanding the Structural valuation of CDS, we’re going to explore a Case Study – ‘**The Vodafone Debt Crisis**‘. In late 2019, Vodafone (having a BBB rating) faced huge regulatory issues due to outstanding AGR payments (> Rs. 50,000 cr.) which posed serious threat to the ‘going concern’ nature of the company. Several banks had outstanding loans to Voda and multiple Mutual Funds had also invested in its bonds. The fund managers were so worried that some were desperately looking for a CDS on Vodafone which could hedge them from the surmounting credit risk. The best ask price for such a CDS was 13.50, which had the following T&Cs:

Underlying | Rating | Bankruptcy loss | CDS premium | Seller | Maturity | Reset | Price |

Vodafone | BBB | 100% (No recovery) | 500 bps | ICICI Bank | 3 yrs | Q/Q | 13.50 |

Now. we need to analyze this case study in light of the following questions:

- Was the Voda-CDS overvalued or undervalued?
- How’d a Black Swan event like COVID-19 affect the value of the Voda-CDS?

**Step 1: Default Lattice**

The Default Lattice charts various paths for the Company’s credit rating throughout the period of a CDS contract (3 years in this case). We assume that re-rating happens at the beginning of every FY and then probabilities are assigned to whether the company would survive or default at the end of the FY. The lattice moves to the next period/FY only if a company has survived at the end of the previous period/FY. One can interpret the lattice as follows:

- At the beginning of 1st year, Voda has a rating of BBB. At the end of the 1st year, it might either
**default**with the last rating of BBB**(BBB-D)**or it might**not default**and move to the next period of the lattice**(BBB-ND)**, - Similar Default & Non-Default probabilities are paired with chances of rating retainment, upgrade or downgrade in the following years of the lattice (discussed in details in Step 2).

**Step 2: Calculating Probabilities of Default & Survival**

For calculating the probabilities, we need to refer to the Rating Transition Matrix we discussed about in Part 2 of this series. The RTM (in Dec, 2019) was as follows:

From/To | AAA | BBB | CCC | D |

AAA | 93% | 4% | 2% | 1% |

BBB | 9% | 66% | 20% | 5% |

CCC | 2% | 30% | 48% | 20% |

**1st Year:**Voda can have a BBB rating at the beginning of the year & still default at the end of the 1st year. Probability of this event is**5%**(from BBB to D in Table 2), thus probability of survival at the end of 1st year is (100 – 5)% =**95%.****2nd Year:**There can be 3 possibilities in the 2nd year –**Rating upgrade:**Voda might be upgraded to AAA from BBB (probability = 9%) and still default at the end of the 2nd year (probability = 1%, from AAA to D in Table 2),**Rating retained:**Voda might retain its BBB rating (prob = 66%) and still default at the end of the 2nd year (probability = 5%, from BBB to D in Table 2),**Rating downgrade:**Voda might be downgraded to CCC from BBB (prob = 20%) at the beginning of 2nd year & then default at the end of the year (prob = 20%, from CCC to D in Table 2).- Thus,
**cumulative probability of default**= (Probability of survival after 1st year x Probability of defaulting in 2nd year) = 95% x [(9% x 1%) + (66% x 5%) + (20% x 20%)] =**7.02%**. - Probability of survival at the end of 2nd year = 95% – 7.02% =
**87.98%**.

**3rd Year:**Unlike at the end of 1st year when Voda’s BBB rating was certain, the rating of Voda at the end of 2nd year is probabilistic. So, Voda can have any rating at the end of 2nd year – AAA, BBB or CCC. There can be 9 possibilities in the 3rd year:**AAA rating at the end of 2nd year:**From a AAA rating at the end of 2nd year, it can be either retained (AAA) or downgraded (BBB or CCC). Each one has got a chance of defaulting at the end of the 3rd year (AAA-D, BBB-D and CCC-D). The total probability comes out to be**1.53%**.**BBB rating at the end of 2nd year:**From a BBB rating at the end of 2nd year, it can be either upgraded (AAA), retained (BBB) or downgraded (CCC). Each one has got a chance of defaulting at the end of the 3rd year (AAA-D, BBB-D and CCC-D). The total probability comes out to be**7.39%**.**CCC rating at the end of 2nd year:**From a CCC rating at the end of 2nd year, it can be either retained (CCC) or upgraded (BBB or AAA). Each one has got a chance of defaulting at the end of the 3rd year (AAA-D, BBB-D and CCC-D). The total probability comes out to be**11.12%**.**Cumulative probability of default**= (Probability of survival after 2nd year x Probability of defaulting in 3rd year) = 87.98% x (1.53% + 7.39% + 11.12%) =**17.63%.**- Probability of survival at the end of 3rd year = 87.98% – 17.63% =
**70.35%**.

**Step 3: Tabulation of Associated Cashflows with the CDS:**

There are 2 primary Cashflow streams associated with a CDS contract – **Premium Outgoing** (the premiums the CDS buyer pays each year as the protection fee to the CDS seller) and **Default Incoming** (expected pay-outs from the CDS seller in case of a Credit event trigger). While PO is paid on the Survival value of the contract (Notional x Prob. of survival), DI is always on the Notional value of the contract. The Cashflows for the Voda-CDS are as follows:

Year | Premium Outgoing (-ve) | PV (outflows) | Default Incoming (+ve) | PV (inflows) |

1 | -5.000 | -4.839 | 5.000 | 4.839 |

2 | -4.750 | -4.444 | 7.021 | 6.568 |

3 | -4.399 | -3.975 | 17.631 | 15.930 |

Net | -13.257 | 27.337 | ||

FV of CDS | 14.079 |

- Premiums are always calculated for a notional of 100. At the origination of the contract, 1st period premium = 500 bps x 100 =
**-5.000**(-ve since the CDS buyer is paying it), premiums in the subsequent periods are**(-5.750 x 95%)**&**(-5.750 x 87.98%)**based on the survival probabilities of Vodafone, - Default incoming starts from the 1st year end (
**5%**x 100 =**5.000**), for subsequent periods, it is a function of the default probability in that particular period (**7.02%**& 1**7.63%**in 2nd & 3rd year respectively), - All expected cashflows are discounted to present value using risk-free rate (annualized 91-DTB yield from Part 2) & we get a
**Net CF of + 14.079**associated with the CDS, - Since the price of the available CDS was 13.50, it was undervalued & the Fund manager can definitely go for the contract. Fair value gains = [(14.08 – 13.50)/13.50]*100% =
**4.3%.**

**Step 4: CDS – A Shield against Black Swans?**

If you’re a Finance enthusiast or have watched ‘** The Big Short**‘, you might be aware of the crucial role CDS played during the Sub-prime crisis of 2008. CDS values went up so much that US Fed had to pump in billions of dollars to bail out AIG. But how does a crisis affect the value of a CDS? How’d a Black swan like COVID-19 affect the value of the Voda-CDS? Let’s go to the next part of the CDS series (Part-4) and find out.

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