Insurable Interests
When you purchase fire insurance on your own home, you are said to have an insurable interest. That is, you have an interest in something and you’d like to insure it against a certain risk. In the case of fire insurance, the insurable interest is your house and the risk is fire burning your house down. Through an insurance policy, and in exchange for a fee, you can effectively transfer, to some 3rd party, financial exposure to the risk that your insurable interest (house) will burn down.
When you purchase protection on a bond through a credit default swap, you may or may not own the underlying bond. As such, you may or may not have something analogous to an insurable interest. David Merkel over at The Aleph Blog brought this issue to my attention in a comment on one of my many rants about credit default swaps. Although you should read his article in its entirety, his argument goes like this: just like you wouldn’t want someone you don’t know taking out a life insurance policy on you (because that would give them an incentive to contribute to your death), corporation ABC doesn’t want swap dealers selling protection on their bonds to those who don’t own them (since these buyers would profit from ABC’s failure). Technically, ABC wouldn’t want protection being sold to those that have a negative economic interest in ABC’s debt.
Courting Disaster
We might find it objectionable that one person takes out an insurance policy on the life of another. This is understandable. After all, we don’t want to incentivize murder. But we already incentivize creating illness. Doctors, hospitals, and pharmaceutical companies all have incentives to create illnesses that only they can cure, thus diverting money from other economic endeavors their way. More importantly, even if you don’t accept the “it’s no big deal” argument, insurance contracts have a feature that prevents the creation of incentives to destroy life and property: they are voluntary, just like derivatives.
In order for you to purchase a policy on my life, someone has to sell it to you. And like most businesses, insurance businesses are not engaged in an altruistic endeavour. So, when you come knocking on their door asking them to issue a $100 million policy on my life, they will be suspicious, and rightfully so. They will probably realize that given the fact that you are not me, $100 million is probably enough money to provide you with an incentive to have me end up under a bus. And of course, they will not issue the policy. But not because they care whether or not I end up under a bus. Rather, they will not issue the policy because it’s a terrible business decision. They know that it doesn’t cost much to kill someone, and therefore, as a general idea, issuing life insurance policies to those who have no interest in the preservation of the insured life is a bad business decision. The same applies to policies on cars, houses, etc that the policy holder doesn’t own. As is evident, the concept of an insurable interest is simply a reflection of common sense business decisions.
You Sunk My Battleship
So why do swap dealers sell protection on ABC’s bonds to people that don’t own them? Isn’t that the same as selling a policy on my life to you? Aren’t they worried that the protection buyer will go out and destroy ABC? Clearly, they are not. If you read this blog often, you know that swap dealers net their exposure. So, is that why they’re not worried? No, it is not. Even though the swap dealer’s exposure is neutral, if the dealer sold protection to one party, the dealer bought protection from another. While the network of transactions can go on for a while, it must be the case that if one party is a net buyer of protection, another is a net seller. So, somewhere along the network, someone is exposed as a net buyer and another is exposed as a net seller.
So aren’t the net sellers worried that the net buyers will go out and destroy ABC? Clearly, they are not. The only practical way to gain the ability to run a company into the ground is to gain control of it. And the only practical way to gain control of it is to purchase a large stake in it. This is an enormous barrier. A would be financial assassin would have to purchase a large enough stake to gain control and at the same time purchase more than that amount in protection through credit default swaps, and do so without raising any eyebrows. If this sounds ridiculous it’s because it is. But even if you think it’s a viable strategy, ABC should be well aware that there are those in the world who would benefit from the destruction of their company. This is not unique to protection buyers, but applies also to competitors who would love to take ABC over and liquidate their assets and take over their distribution network; or plain vanilla short sellers; or environmentalist billionaires who despise ABC’s tire burning business. In short, ABC should realize that there are those who are out to get them, whatever their motive or method, and plan accordingly.
Hands Off My Ether
The fact that others are willing to sell protection on ABC to those who don’t own ABC bonds suggests that any insurable interest that ABC has is economically meaningless. For if it weren’t the case, as in the life policy examples, no one would sell protection. But they do. So, it follows that protection sellers don’t buy the arguments about the opportunities for murderous arbitrage. So what is ABC left with? An ethereal and economically meaningless right to stop other people from referencing them in private contracts. This is akin to saying “you can’t talk about me.” That is, they are left with the right to stop others from trespassing on their credit event. And that’s just strange.
; pay them $100 in principle at the time at which the underlying CDS expires; with both promises conditioned upon the premise that ABC does not trigger an event of default, as that term is defined in the underlying CDS. In short, D has passed the cash flows from the Treasury/CDS package onto investors, in exchange for pocketing a fee (
). As noted above, the cash flows from this package are very similar to the cash flows received from ABC bonds. As a result, we call the notes issued by D synthetic bonds.
, where the notional amount of protection sold on each is 
and the total notional amount is 
. Rather than maintain exposure to all of these swaps, D could pass the exposure onto investors by issuing notes keyed to the performance of the swaps. The transaction that facilitates this is called a synthetic collateralized debt obligation or synthetic CDO for short. There are many transactions that could be categorized fairly as a synthetic CDO, and these transactions can be quite complex. However, we will explore only a very basic example for illustrative purposes.
dollars. D sets up an SPV, funds it with the money from the investors, and buys 
dollars worth of protection on 
for each 
from the SPV. That is, D hedges all of his positions with the SPV. The SPV takes the money from the investors and invests it. For simplicity’s sake, assume that the SPV invests in the same Treasuries mentioned above. The SPV then issues notes that promise to: pay investors their share of 
dollars after all underlying swaps have expired, where L is the total notional amount of protection sold by the SPV on entities that triggered an event of default; and pay investors their share of annual interest, in amount equal to 
, where 
is the sum of all swap fees received by D.
where 
is the price of an ABC series I bond after the risk-event (default) occurs and 
is the par value of an ABC series I bond. For example, if ABC’s series I bonds are trading at 30 cents on the dollar after default, 
and a protection seller would have to payout 70 cents for every dollar of notional amount. The amount that bonds trade at after a default is called the recovery value.
to the risk-event defined above as the product of (i) the net notional amount of all credit default swaps naming ABC series I bonds as a reference obligation to which 
, and (ii) 
. The net notional amount is simply the difference between the total notional amount of protection bought and the total notional amount of protection sold by 
, will be either negative or zero.
market participants, 
. The total notional amount of the entire market is given by 
. This is the figure that is most often reported by the media. As is evident, it is impossible to determine the economic significance of this number without first knowing the structure of the market. That is, we must know how much is owed and to whom. However, after we have this information, we can choose different recovery values and then calculate each party’s exposure. This would enable us to determine how much cash each participant would have to set aside for a default at various recovery values (simply calculate each party’s exposure at the various recovery values).
. As is evident, we can vary the recovery value to determine what each market participant’s exposure would be in that case. We could then consider other risk-events that occur in conjunction with any given risk-event. For example, we could consider the conjunctive risk-event “ABC defaults and B fails to pay under any CDS” (in which case D’s exposure would not be zero) or any other variation that addresses meaningful concerns. For now, we will focus on our single event risk for explanatory purposes. But even if we restrict ourselves to single event risks, there’s more to a CDS than just default. Collateral will move through the above system dynamically throughout the lives of the contracts. In order to understand how we can analyze the systemic risks posed by the dynamic shifting of collateral, we must first examine what it is that causes collateral to be posted under a CDS.
?” Because collateral will be posted as the price of protection changes over the life of the agreement and the price of protection provides an implied probability of default, it follows that the answer to this question should have something to do with the flow of collateral.
where 
is our assumed implied probability of default and 
different prices. For example, he entered into four contracts at 20 bp and eight contracts at 50bp, and no others. In this case, 
. For each 
, to the sets of contracts that were entered into at different prices by 
be the set of eight contracts entered into at 50bp and let 
be the set of four contracts entered into at 20 bp. Each of these sets will have a net notional amount and an implied probability of default (since each is categorized by price). Define 
as the net notional amount of the contracts in 
and 
as the implied probability of default of the contracts in 
. We define the expected exposure of 
.
,
.
Information Overload 