Correlation

This entry is not directly related to credit derivatives per se, but discusses something more fundamental - correlation. Since we are taking a building block approach to understanding credit derivatives, correlation is something we should discuss.

Let’s just think of the term “correlation” in a general sense. The term suggests that we are talking of relationship between things, relationship in terms of their behavior. So correlation is trying to give some idea about how two or more things behave when observed together. This relationship becomes important to observe and use in any situation when we are dealing in a scenario where more than one variable affects us.

Let us take a common place example - Floods in Mumbai. The severity of floods in Mumbai is a function of several variables, and say, of them the two (for the sake of simplicity) most important ones are the amount of rainfall and high tides. Now if we want to find the probability of flood happening in Mumbai, statistics about average rainfall or the variance in rainfall, or the severity of high tide and its probability is incomplete to give us the inference unless we come to know that what is probability of high rainfall happening on a high tide day. In other words, the relationship or the correlation between the two variables is essential.

If we find that high rainfall is usually accompanied by high tides (high positive correlation) the probability of a flood is much higher than if the two are found not happening at the same time. A subtle distinction we need to understand is that, when we say that two occurrences have high positive correlation and suggest that they may happen together, we are not saying that one causes the other. In technical terms, correlation doesn’t imply causation. And it makes some common sense as well, like we cannot say that high rainfall would cause high tides or vice versa, but statistically they can be positively (or negatively for that matter) correlated.

Statistical discussions on correlation can be found at

http://www.socialresearchmethods.net/kb/statcorr.php http://www.surveysystem.com/correlation.htm

Let’s come to the importance of correlation in case of credit derivatives. In credit derivatives, correlation assumes almost the same (if not more) importance as volatility in case of options. So much so that as some treat volatility as an asset class itself, there is now increasing reference to correlation as an asset class.

For the time being we will stop here on correlation. Some time in future we will revisit correlation.

CreDs - An introduction

I think we jumped the gun when we went about discussing CDS without a proper introduction to credit derivatives (CreDs) per se. To make up for the mistake let us try to know a little about what are these CreDs.

If we are going to the basics, why not go a step further back and look at derivatives themselves. A standard definition of derivative, at least in some regulation and accounting directives defines derivative as a contract with three essential features. First, the value of this contract depends on an underlying, which can be an index, spot value, events et al. The second feature is that it is settled at some future date. And finally, derivatives involve little or no initial cash flows.

So we know what a derivative is. Let us look at credit derivatives (CreDs) then. Well a derivative in which the underlying is a credit exposure or a credit index or the risk involved is credit related, with the second and third characteristic of a derivative is a CreD. Let us try to look at the derivatives type tree then. It should be something like this:-

Financial derivatives are our equity/interest rate/forex forwards, futures, options and swaps. I guess most people are aware of these products and they are certainly not the focus of this blog. In ‘other derivatives’ we may have derivatives whose value depend on something other than a financial or credit related underlying. For example weather. Who knows in India we may have ‘cricket derivatives’. A dream product can be a CMS like structure, batting average of Sachin in 2006-07 minus average of Saurav in 2006-07 times 10 mio.. I wonder if that would become a legal way of betting in India.

Anyways, coming back to the main issue - CreDs. Under CreDs, we have Credit Default Swaps (CDS). Then we have options on credit underlying, mainly credit options and credit spread options. The two are slightly different. Then CLNs or credit linked notes which are not very different from CDS but put as a different category on populist grounds. Then you have Total Return Swaps, where both market and credit risk is hedged (NB TRS doesn’t hedge counterparty credit risk). Then there are Collateralized Debt Obligations (CDOs). CDOs are fast becoming an asset class in themselves and are becoming increasingly exotic and complex. And then finally you have exotic CreDs which are nothing but weird combination of basics CreDs, structured in a form to supposedly suit the requirements of the client but actually to dupe her.

Poof! That was pretty lengthy. But now that we have a broad classification in place, the blocks from the tree can be picked up and discussed without losing the BIG picture.

CreDs in India

Recently RBI has allowed single name CDS in India. Although detailed guidelines on the same are in draft stage.

In today's BS, Vinod Kothari has written something about this initiative. While he is not very amused by the idea and in some areas he is correct becoz RBI limits the contracts for hedging purpose and imposes limitation like "the reference asset/ obligation shall be identical to the underlying asset / obligation with reference to (a) nature of obligation; (b) seniority (equal or junior); and (c) maturity." Meaning that the CDS will have to be a reference specific CDS, meaning it will most probably be an OTC contract between two parties. Problems are illiquidity, lack of transprancy and difficulty of valuation.

Nonetheless it's a calibrated beginning.

The BS article can be found at http://www.business-standard.com/common/storypage_c.php?leftnm=10&autono=286365

Settlements in credit derivatives

Let us try to understand the cash or rather the value flow in case of simple credit derivative contracts like CDS. Credit derivative contracts, are much like insurance contracts. So, one leg of the contract if the payment of premium which is upfront and paid periodically, like one pays one’s insurance premiums. This premium is unconditional and is to be paid till the contract expires by expiry of term or the credit event(s) happening.


We know that in most credit derivatives, on the occurrence of a credit event covered by the contract, a sum of money becomes due to the protection buyer from the protection seller. This conditional leg of the contract is contingent on the happening of the pre-specified credit events, else the contracts expires like an insurance contract. This leg, called the settlement, can normally be of three broad types – physical, cash or binary.


Cash – In a cash-settled credit default swap, no bonds or loans are delivered. Instead, the protection seller simply pays the protection buyer an amount of money calculated as the notional value of the contract minus the recovery rate.

Physical - After the credit event, with the delivery of a ‘notice of physical settlement’, the protection buyer delivers to the protection seller bonds or loans (‘deliverable obligations’) with a notional amount identical to the notional amount of the credit default swap. The protection seller then pays the protection buyer the notional amount of the credit default swap.

For example, for a standard Rs.10 crore contract on RIL, when RIL defaults, the protection buyer delivers defaulted bonds with a 10 crore face value and receives 10 crore from the protection seller. If the defaulted bonds are worth 4 crore (40% of their face value, where 40% is called the recovery rate), the protection buyer has effectively made 6 crore as a result of buying protection. The seller of protection could choose to sell the defaulted bonds, so achieving their recovery value.

Binary – Also known as ‘digital’ credit default swaps, here the settlement amount is pre-determined and the post facto recovery rate is ignored as it is fixed at the inception. For example, if two counterparties trade Rs.10 cr CDS on RIL with a 40% fixed recovery rate, the protection seller will simply pay the protection buyer $6 million in the event of a default by RIL. The post event recovery from RIL will not impact the settlement of the contract.

This form of a settlement is simple because estimating recovery rate is difficult and can take time. But the disadvantage is that the protection buyer doesn’t know if she is adequately hedged.

Example of a CDS

Continuing on CDS, let us try to explore more about them for they are basic building blocks of most credit derivative transaction. Like in case of financial derivatives where most exotic structures can be broken into simple contracts of forwards and options, similarly in credit derivatives most structures are combinations of simple contracts like CDS.

The simplest – and most common – type of credit default swap is one where there is just one reference entity. This is called a single-name credit default swap. The reference entity can be any borrower, but is most often one of a few hundred widely traded companies (corporates or financials) or a handful of governments (sovereigns).

Let us try to think of a hypothetical CDS. An investor who wants to take a view on Reliance Industries might sell credit default swap protection. In May 2007, dealers quoted five-year credit default swap spreads on RIL at 47/53 basis points. This means the dealer quotes 47bp for a trade where the investor sells five-year protection and the dealer buys protection, and 53bp for a trade where the investor buys protection. (The difference between the two quotes is known as the ‘bid-offer spread’.)

On a typical trade size of Rs.10 crore, the protection seller would receive 470,000 a year, usually in four quarterly payments. Alternatively, the investor could buy protection for 53bp, paying Rs. 530,000 a year. If RIL defaults during the life of the trade and, following the default, say the value of the company’s debt falls to 30% of face value (the ‘recovery rate’), the protection seller will compensate the protection buyer for the Rs.7 crore loss.

Credit default swap (CDS)

Credit default swap (CDS)

Technical Definition : An over-the-counter contract to transfer the credit risk of a reference entity, in which the protection buyer pays a premium and the protection seller makes a payment in the event of a default (credit event) by the reference entity.

Non_technical explanation: The most common and simple of credit derivatives. It is not a swap in the conventional sense, but is more like an 'conditional' option. Much like an insurance contract, where on happening of a loss, the holder of the contract can ask to be reimbursed for the loss upto the contract amount. Similarly in CDS, the loss is a credit loss trigerred by a defined list of "credit events" (something like we have in accident policies in non-life insurance).

So in CDS, one party agrees to compensate the credit loss of the other in consderation of a premium upfront. The rationale for the existence and popularity of such contrcts - the party bearing the risk gets a premium (think of him as LIC), and the person buying the protection can manage the credit risk and get out of ("sell") credit positions which are not liquid. There can be other reasons as well, but more of that sometime later.