Charles Davì

Archive for November, 2008|Monthly archive page

You’re Trespassing On My Credit Event

In Politicized Economy on November 20, 2008 at 9:10 pm

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.

Mark To No Market Accounting

In Politicized Economy, Systemic Counterparty Confusion on November 17, 2008 at 8:31 pm

The Meaning Of It All

In this article I explore an oft discussed topic: mark to market accounting. I will not come down on either side of the debate. Rather, I will try to make sense of the implications and assumptions of mark to market accounting. But before we can explore the world of mark to market accounting, we must understand the economic significance of the data reported under accounting regimes in general. And in order to do that, we must have a practical concept of economic loss/gain. From here on, we simply write the term loss to signify both loss and gain, except where context indicates otherwise (philosophers, please relax, the meaning is clear).

What Is Economic Loss?

In my mind, the answer depends on who you ask and when. That is, every economic endeavor involves multiple parties with different rights and obligations that vary over time, and so any meaningful concept of loss should consider both who incurs “loss” and when. As usual, we will proceed by way of example.

Assume that Tony (T) has had a life long passion for the manufacturing of shoes. He decides to raise money from investors to open up a factory that will manufacture a new line of shoes, “Tony’s Shoes.” The investors contribute a total of $100 to T’s endeavor through debt. Assume that T bought manufacturing equipment from M for $70 and that T’s debt to the investors is secured by the factory equipment. After 6 months, it becomes clear that the market is not ready for T’s postmodern shoe design, and so T’s factory generates no income whatsoever. As a result, T commits suicide. T leaves only $15 and title to the manufacturing equipment in his estate, having set his entire inventory on fire in a rage prior to his suicide. The investors successfully obtain title to the machinery and claim the remaining $15. Because the machinery has been used for 6 months, they are only able to recover $30 for it in an auction.

So who lost what and when? Well, as an initial matter, in order for there to be loss, there must be change. It follows that we should ask how the state of affairs has changed over some time frame. Let’s mark the beginning of our time frame at just before T’s purchase of the manufacturing equipment and the end at immediately after the investors liquidate the manufacturing equipment. So, our concept of loss will compare the state of affairs at those two points in time for each participant. In our example, T began alive with $100 cash and $100 in debt, and ended up dead with his estate owing $55 to the investors.  The investors started out with notes with a par value of $100 and ended up with $45 in cash. M started out with manufacturing equipment and ended up with $70 in cash.

The first problem we face is comparing dissimilar assets. That is, T started out with cash and debt, the investors started out with notes and ended up with cash, and the manufacturer started out with equipment and ended up with cash. While the choice of a common basis is arbitrary, we choose cash. So, assume that at the beginning of our time period T valued his debt at negative $100, the investors valued the notes at par ($100) and that M valued the equipment at $60. One reasonable interpretation of the facts is that over the relevant time period T lost nothing, the investors lost $55, and M gained $10. It is reasonable to say that T lost nothing because he began with a net cash value of zero and although his estate still owed the investors $55, there was nothing left to pay them with. We could be pedants and say that T ended with a negative $55 cash value, but what would that mean? Nothing. The investors’ claim is worthless since T is dead and his estate is empty. If T had survived or if his estate expected to receive assets or income at some future time, then T or T’s estate could be indebted in an economically meaningful way. But since this is not the case in our fact pattern, the investors have a worthless claim against T’s estate.

A Truly Human Story

In my mind, the goal of any accounting system is to tell a story about economically significant events that occurred over a given time period. And so, in designing a system of accounting, we must choose which aspects of each market participant’s state of affairs that we want to report, simply because there could be events we don’t find particularly relevant to our story. For example, T died. We may or may not want to report that. Whether or not we choose to report it, T’s death did have economic significance. Because T died and left an estate with inadequate resources to cover his liabilities, the debts owed by T’s estate were worthless. As is evident, it would be impractical to report the death of every market participant. But as T’s case demonstrates, there are some events we wouldn’t normally consider economically significant which turn out to have a meaningful impact on the rights and obligations of market participants.

Truth In Numbers

We must also have a method of valuation. In our example above, we simply relied upon the subjective valuations of the market participants. Given that market participants will likely have an incentive to misrepresent the value of certain assets, we probably don’t want to rely too heavily on purely subjective valuations. For example, we calculated M’s gain based on M’s valuation of the equipment. What if M’s valuation was pure wishful thinking? What if his cost of inputs and labor suggested a price closer to $150? It would follow in that case that M actually lost money by selling the equipment for $70. What we need is a method of valuation that limits each participant’s ability to misrepresent, whether through wishful thinking or malice, the value of assets. There are several ways to go about doing so. We could establish guidelines, rules, or allocate valuation to trusted entities. Another approach is to simply quote the price of an asset from a market in which the asset is usually bought and sold.

Mark to Market Accounting

The basic premise of mark to market accounting is that the reported value of a given asset should be based upon the price at which that asset could be presently sold in a market that trades such assets. For example, assume that ABC stock is traded on the highly reputable XYZ exchange. The reported value of 1 share of ABC stock on September 10, 2008 under a mark to market regime should be based on the prices quoted for ABC stock over some period of time near September 10, 2008. You might want to construct an average, or exclude a particular day’s quotes, but the general idea is that the market provides the basis of the price. So if 1 share of ABC’s stock had an average closing bid price of $25 from September 1, 2008 to September 10, 2008, a company holding ABC stock could be required to use this average price as the basis for calculating the value of its holding of ABC stock for a report issued under some mark to market regime.

Market Prices And Expected Value

Returning to our example above, we determined that the investors had lost money once T’s estate was liquidated since they had no other methods of recovering the money that they had lent and was owed to them. But what if we wanted to consider their losses at some point before T was obligated to make a payment on his debts? Had the investors lost anything at that point? Any such loss would be anticipatory since the loss would occur before the repayment of debt was obligated. So, while the loss hasn’t been realized yet, we can still anticipate it. For example, if T had killed himself before any payment was due, losses would be anticipatory, but anticipated with certainty. As is evident, the amount of an anticipated loss, or expected loss, is a function of the probability that an expected cash flow will fail to materialize.

Market price quotes are used to estimate the expected value of an asset, which is the value of all the asset’s cash flows discounted to reflect the time value of money and the probability that any of the asset’s cash flows will fail to materialize. Many economists subscribe to the belief that the market price for an asset is the expected value of an asset. That is, they believe that the collective decision making of all market participants leads to the creation of a price which accurately reflects all relevant price inputs. But even if we accept this logical catapult, it is still possible for a market to produce inefficient prices. For example, market participants could have mistaken the correlation of default between certain investments, creating a short term shortage of cash, leading to massive and collective sell offs across asset classes. That should sound familiar. Such a scenario would arguably create opportunities for arbitrage for those fortunate enough to have cash on hand.

Even if you don’t buy the theoretical arguments for inefficient markets, or the glaring recent examples, you must still wonder when it was that markets became efficient. Were they always efficient? And even if they were, can they become inefficient?

The Takeaway

Whether or not you think that markets price assets efficiently, market price quotes are without question a good measure of how much cash you can exchange an asset for at any given point in time. So, whether or not markets price assets efficiently does not determine whether mark to market accounting is “good” or “bad.” Rather, we have to ask what it is that we are using mark to market accounting for. Then, we can determine whether a given application of mark to market accounting is “good” or “bad.”

Truly Derivative Dribble

In Uncategorized on November 13, 2008 at 2:17 am

Email: derivativedribble [at] yahoo [dot] com.

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Friday June 26, 2009

My breakfast of choice

Friday May 29, 2009

My latest for the Atlantic: Could Government Intervention Help Markets Function Better?

Saturday May 16, 2009

My latest for the Atlantic: How NPR Mangled Geithner’s Plan For OTC Derivatives

Thursday May 7, 2009

My latest for the Atlantic: Boring Banking Will Not Save You

Friday May 1, 2009

My latest for the Atlantic: The Sorry State Of The Dismal Science

Thursday April 30, 2009

YOU MUST WATCH THIS: John Authers interviews Richard Thaler, behavorial economist and author of Nudge.

Friday April 17, 2009

My Latest for the Atlantic: Credit Default Swaps and Control Rights

Tuesday April 14, 2009

My latest for the Atlantic: The Art of the Banking Controversy

Friday April 10, 2009

My latest for the Atlantic: The Regulatory Pendulum and Electoral Guillotine

Wednesday April 8, 2009

My latest for the Atlantic

Friday April 3, 2009

Very nice chart from the FT on debt and demographics

Monday March 30, 2009

Recommended: FT interview with Obama

Friday March 27, 2009

Derivative Dribble on Twitter

My latest for the Atlantic Business

Wednesday March 25, 2009

High speed photos of exploding objects

Bank Executive’s home vandalized

MUST READ: Resignation letter of form AIGFP employee

HIGHLY RECOMMENDED: John Authers takes a look at the EMH and the future of wealth management

Friday March 20, 2009

HIGHLY RECOMMENDED: Washington Post takes us inside AIG-FP (“If they give back the money, then they will walk. And they will walk into the arms of AIG’s counterparties.”)

My latest for The Atlantic

HIGHLY RECOMMENDED: This Blog

Tuesday March 17, 2009

Fortune does a good job getting the facts straight about CDS

Friday March 13, 2009

Recommended: The Economist takes a look at credit markets

Berkshire downgraded by Fitch

Thursday March 12, 2009

Gates back on top as crisis wipes out other billionaires

Monday March 9, 2009

Hilarious

Friday March 6, 2009

Alpha Ville on the ocean of looming corporate defaults

Thursday March 5. 2009

Citi drops below $1

My latest for the Atlantic

Wednesday March 4, 2009

FDIC might go insolvent

Tuesday March 3, 2009

Derivatives market remains profitable business for J.P. Morgan

Very interesting data on the multiplier effect from the CBO

Tuesday February 24, 2009

My latest article for the Atlantic

Monday February 23, 2009

HIGHLY RECOMMENDED: Howard Davies, head of LSE and former FSA Chairman, on bank regulation

FT on the prospect of a depression in Spain

Rick Santelli rouses traders over Obama’s housing plan

Sunday February 22, 2009

Citi in talks with U.S. Government over common equity stake

Thursday February 19, 2009

Must read: Buiter rips apart Obama’s housing plan

Saturday February 14, 2009

Collective decision making in animals and humans

Thursday February 12, 2009

New York edges closer to expanding rent control

Wednesday February 11, 2009

Rep. Kanjorski tells us how close to the edge we were

Treasury’s 6 and a half page plan to save the world

Tuesday February 10, 2009

Great article by the FT’s John Authers on the prospects of an equity bounce-back

Friday February 5, 2009

U.S. cuts almost 600,000 jobs

Wednesday February 4, 2009

My latest article for the Atlantic Business Channel

Tuesday February 3, 2009

E.U. pushes CDS exchange

Monday February 2, 2009

For my fellow music lovers: Classic Arts Showcase on YouTube

Consumers turn to thrift

Unemployment hits China

S&P says 200 defaults expected

Thursday January 30, 2009

Crash like this expected only once over next 34,000 years

Contraction bad, but better than expected

Wednesday January 28, 2009

John Authors on the perception of a bargain

Capacity drops in France and Italy

World growth worst in 60 years

Tuesday January 27, 2009

Japanese CDS spreads widen

The original Carlo Ponzi

Madoff Jr. gets busted in $400 million Ponzi scheme

Great article from Atlantic’s new business section

Monday January 26, 2009

Iceland’s government tumbles under pressure

Unemployment rate looms over banking sector

Redemptions slam hedge funds

Wednesday January 23, 2009

Obama thinks stimulus package could be ready mid February

Muni derivatives under investigation

Cocoa prices on the move

Very interesting John Authers video on the prospect of a slow down in China

Pope goes digital

U.K. officially in a recession

Wednesday January 22, 2009

Google beats the heard

N.Y. Times provides some perspective on the severity of the crisis

U.S. accuses China of currency manipulation

Tuesday January 21, 2009

Bank market capitalization, then and now

John Authers article and video on the second wave of banking turmoil

Monday January 20, 2009

Obama sworn in

Reality might be a hologram

Banking crisis part II?

Thursday January 15, 2009

Volatility back on the rise

California to go insolvent in weeks

Big numbers for foreclosures in 2008

The wealthy slammed by the down turn

Testosterone and income

Roubini predicts more gloom

Bank stocks plummet

Mortgage rates hit record low

Wednesday January 14, 2009

Credit markets show signs of life despite rest of world

Martin Wolf takes on Obama’s stimulus package

CDS market predicts bleak future for sovereigns

Greece downgraded

Retail takes a nose dive

Banks need bigger TARP

Tuesday January 13, 2009

Citi gets closer to break up

Still no Russian gas flowing into E.U.

Pension funds hammered, seek Federal money

Release of TARP funds faces stiff opposition

U.S. imports plummet

Bernanke says fiscal measures not enough

Monday January 12, 2009

John Authers takes a look at sovereign default and the Euro

Proprietary trading winding down

Banks suspected in facilitating purchase of weapons for Iran

Barney Frank proposes drastic changes to TARP and Hope For Homeowners Act (a summary of the bill and the actual text can be found here)

A look at China

Sovereign downgrades looming

Friday January 9, 2009

Cash flowing back to emerging markets

No exit

Obama puts pressure on Congress over stimulus package

Congress points fingers at Treasury over TARP

Thursday January 8, 2009

Citi supports bankruptcy law reform

Very interesting article on government bonds

Dismal retail figures

Wednesday January 7, 2009

Gas supply to Europe cut

BofA finally sells stake in Chinese Bank

Rough month for employment

A closer look at Larry Summers

German bond auction fails: bad sign for sovereigns

Tuesday January 6, 2009

Pending home sales drop to record lows

Oil picks up steam

Monday January 5, 2009

Dim lights ahead

A bit of unexpected historical perspective on the credit crisis

Wednesday December 31, 2008

John Authers constructs a timeline of the disasters of 2008

Steepest drop ever for commodities

Muni market dries up as states face looming budget gaps

A brief history of numbers

Paulson says U.S. lacked tools to handle crisis

Tuesday December 30, 2008

Good series of video interviews of Roubini

All about numbers

U.S. home prices plummet 18%

Automakers consider change to supply model to prevent supply-side failures

The economics of climate change

Monday December 29, 2008

Retail bankruptcies and store closings on the rise

Corporate profits likely to continue losing streak

Conventional media outlets seek partnership with internet big wigs

John Authers sees gloomy future for equities

High hopes and big numbers

Tuesday December 23, 2008

U. Chicago points fingers at the bailout

Interactive applet rating financial big wigs

Monday December 22, 2008

Pound sinks to record low against basket of currencies

Toyota predicts first loss ever

Oil continues to slide despite OPEC cuts

Friday December 19, 2008

Mortgage interest rates drop

China blocks sale of assets

Sarkozy forces lending

Early Christmas for automakers

Thursday December 18, 2008

Gather ye rosebuds while ye may

Mining sector calls for unprecedented cut backs

Obama taps new SEC chief

Wednesday December 17, 2008

Tis dangerous on the high seas!

Deflation hits E.U.

Thrifty Texan to buy up banks

Public perception dims

More monoline madness

Tuesday December 16, 2008

Up to your ears

Free money!

Monday December 15, 2008

The long arm of Madoff

Derivative Dribble spots economic news faster than the MSM

Friday December 12, 2008

Bifurcation of the debt markets

Goldman predicts slow recovery for oil

California gets downgraded

The story of 2008

The ever entertaining Jim Rogers

India gets roped into the slow down

Senate puts the brakes on the Big 3

Thursday December 11, 2008

When fiat fails

It was a very bad year

This time the floor is falling

Wednesday December 10, 2008

The beginning of a market for toxic instruments?

Deflationary pressure in China?

Costly advice

John Authers looks back

Tuesday December 9, 2008

The title speaks for itself

Russia walks the sovereign plank: debt downgraded

OTC commodities central clearing house ready for launch

Corporate default rates set to rise

Monday December 8, 2008

BREAKING NEWS: Federal legislation proposed to regulate OTC Market

The invisible hand and the sovereign strangle

Video game nerds prove recession proof

Friday December 5, 2008

Economics at ground level

More truly awful news, this time it’s California

Distraction from all the bad news

Thursday December 4, 2008

Black Friday yields red November for retail

China Investment Corp won’t invest in U.S. financial institutions

$25 Oil

Wednesday December 3, 2008

CDS Index hits record level

Some rather awful news

Great explanation of Money Markets

Real yield on Treasuries dip into negative territory

Tuesday December 2, 2008

Bigger than the bail out

The ever increasing interest in CDS

Paulson v. Paulson

Monday December 1, 2008

BRIC nations to offer consumption through downturn

U.S. officially in recession

The Swiss financial throne under siege

Wednesday November 26, 2008

Banker’s Compensation

The space near zero

Shift from OTC to exchanges gains more momentum

Ship while you can

Tuesday November 25, 2008

The science of petty crime

New lending facility for instruments backed by consumer debt

Monday Novemer 24, 2008

Treasury pony’s up huge money

Buffett discloses info on Berkshire’s portfolio of financial weapons of mass destruction

More historical data on declines

Daily Liquidation

Citi gets early Christmas present and Paulson works another weekend

Friday November 21, 2008

Goldman predicts bleak outlook for U.S. Economy

One way ticket to safety

Thursday November 20, 2008

Slightly cooler heads in Iceland after IMF/Nordic bailout

The CDS Market becomes the new economic indicator

I’ve seen more and more of this type of analysis. The CDS market is becoming more and more relevant as an economic indicator. Keep up the good work Alpha Ville!

Inventories Swell Kudos to Naked Capitalism!

Following the money supply

Wednesday November 19, 2008

More monoline downgrades

CDS markets predict bleak future

CDS clearing house seems likely

Tuesday November 18, 2008

Detroit gets coals for Christmas

Fun with economic data

Japan wins economic beauty contest

Historical perspective on volatility

CIA Factbook v2

Monday November 17, 2008

Highly recommended: Interviews with Jim Rogers

The dangers of subjective valuation

Good article, even though I disagree

New York City real estate falls from grace

Greetings from Earth!

Citibank throws garage sale

Japan in technical recession

Friday November 14, 2008

FDIC to insure home mortgages

Eurozone in technical recession

Pensioners driven to theft

Thursday November 13, 2008

More complex than a synthetic CDO

Derivative Dribble considers asking Fed for money

Germany in technical recession

Greenwich points to Wall Street

Would be CDS regulator vindicated (?)

Paulson pulls the TARP from under the market

Pounded

In The Shadows Of Geometry

Synthetic CDOs Demystified

In Politicized Economy, Systemic Counterparty Confusion on November 11, 2008 at 9:21 pm

Synthetic Debt

Before we can understand how a synthetic CDO works, we must understand how credit default swaps create synthetic exposure to credit risk. Let’s begin with an example. Assume that D sold protection on $100 worth of ABC bonds through a CDS. Assume that on the day that the CDS becomes effective, D takes $100 of his own capital and invests it in risk-free bonds, e.g., U.S. Treasuries (in reality Treasuries are not risk-free, but if they go, we all go). Assume that the annual interest rate paid on these Treasuries is R. Further, assume that the annualized swap fee is F. It follows that so long as a default does not occur, D’s annual income from the Treasuries and the CDS will be I = $100 x (R + F) until the CDS expires. If there is a default, D will have to payout $100 but will have received some multiple of I over the life of the agreement prior to default.

So, D sets aside $100 and receives the risk free rate plus a spread in exchange. If ABC defaults, D loses $100. If ABC doesn’t default, D keeps $100 plus the income from the Treasuries and the swap fee. Thus, the cash flows from the CDS/Treasuries package look remarkably similar to the cash flows from $100 worth of ABC bonds. As a result, we say that D is synthetically exposed to ABC credit risk.

But what if D doesn’t want this exposure? Well, we know that he could go out to the CDS market and buy protection, thereby hedging his position. But let’s say he’s tired of that old trick and wants to try something new. Well, he could issue synthetic ABC bonds. How? D receives $100 from investors in exchange for promising to: pay them interest annually in the amount of 100 \cdot (R + F - \Delta); 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 (\Delta). 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.

Synthetic CDOs

In reality, if D is a swap dealer, D probably sold protection on more than just ABC bonds. Let’s say that D sold protection on k different entities, E_1, ... , E_k, where the notional amount of protection sold on each is n_1, ..., n_k and the total notional amount is N = \sum_{i=1}^k n_i. 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.

So, after selling protection to the swap market as described above, D asks investors for a total of N dollars. D sets up an SPV, funds it with the money from the investors, and buys n_i dollars worth of protection on E_i for each i \leq k 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 N - L 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 (R + F - \Delta) \cdot (N - L), where F is the sum of all swap fees received by D.

So, if every entity on which the SPV sold protection defaults, the investors get no principle back, but may have earned some interest depending on when the defaults occurred. If none of the entities default, then the investors get all of their principle back plus interest. So each investor has synthetic exposure to a basket of synthetic bonds. That is, if any single synthetic bond defaults, they still receive money. Thus, the process allows investors to achieve exposure to a broad base of credit risk, something that would be very difficult and expensive to do in the bond market.

synthetic-cdo

A Conceptual Framework For Analyzing Systemic Risk

In Politicized Economy, Systemic Counterparty Confusion on November 8, 2008 at 7:24 pm

The Cart Before The Horse

There has been a lot of chatter about the systemic risks posed by derivatives, particularly credit default swaps. Rather than offer any formal method of evaluating an enormously complicated question, pundits wield exclamation points and false inferences to distract from the glaring holes in their logic. Below I will not offer any definite answers to any questions about the systemic risks posed by derivatives. Rather, I will describe what I think is a reasonable and useful framework for analyzing systemic risks posed by derivatives. Unfortunately for some, this will involve the use of mathematics. And while the math used is fairly elementary, the concepts are not. This is especially true of the last section. That said, even if you do not fully understand the entirety of this article, one thing should be clear: questions about systemic risk are complex and anyone who gives declarative answers to such questions is almost certain to have no idea what they are talking about.

Risk Magnification And Syndication

As discussed here, derivatives operate by creating and allocating risks that did not exist before the two parties entered into the transaction. That is an unavoidable fact. Moreover, there is no physical limit to the notional amount of any given contract or the number of derivative contracts that parties can enter into. It is entirely up to them. That said, derivatives can be used to negate risks that parties were already exposed to in exchange for assuming other risks, thereby acting as a risk-switching/risk-transferring device. So, a corollary of these observations is that derivatives could be used to create unlimited amounts of risk but through that risk creation they could be used to negate an unlimited amount of risk that parties are already exposed to and thereby effectively “transfer” an unlimited amount of risk to those willing to be exposed to it.

Practically speaking, there is a limit to the amount of risk that can be created using derivatives. This limit exists for a very simple reason: the contracts are voluntary, and so if no one is willing to be exposed to a particular risk, it will not be created and assigned through a derivative. Like most market participants, derivatives traders are not in engaged in an altruistic endeavor. As a result, we should not expect them to engage in activities that they don’t expect to be profitable. Therefore, we can be reasonably certain that the derivatives market will create only as much risk as its participants expect to be profitable. Whether their expectations are correct is an entirely different matter, and any criticism on that front is not unique to derivatives traders. Rather, the problem of flawed expectations permeates all of human decision making.

Even if we ignore the practical limits to the creation of risk, derivatives allow for unlimited syndication of risk. That is, there is no smallest unit of risk that can be transferred. Consequently, any fixed amount of risk can be syndicated out to an arbitrarily large number of parties, thereby minimizing the probability that any individual market participant will fail as a result of that risk.

Finally, we should ask ourselves, what does the term systemic risk even mean? The only thing it can mean in the context of derivatives is that the obligations created by two parties will have an effect on at least one other third party. So, even assuming that derivatives create such a “problem,” how is this “problem” any different than that created by a landlord who plans to pay a contractor with the rent he receives from his tenants? It is not.

A Closer Look At Risk

As stated here, my own view is that risk is a concept that has two components: (i) the occurrence of an event and (ii) a magnitude associated with that event. This allows us to ask two questions: What is the probability of the event occurring? And if it occurs, what is the expected value of its associated magnitude? We say that P is exposed to a given risk if P expects to incur a gain/loss if the risk-event occurs. As is evident, under this rubric, that whole conversation above was grossly imprecise. But that’s ok. Its import is clear enough. From here on, however, we will tolerate no such imprecision.

Identifying And Defining Risks

Using the definition above, let’s try to define one of the risks that all parties who sold protection on ABC’s series I bonds through a CDS that calls for physical delivery are exposed to. This will allow us to begin to understand the systemic risk that such credit default swaps create. There is no hard rule about how to go about doing this. If we do a poor job of identifying and defining the relevant risks, we will have a poor understanding of those relevant risks. However, common sense tells us that any protection seller’s risk exposure is going to have something to do with triggering a payout under a CDS. So, let’s define the risk-event as any default on ABC series I bonds. For simplicities sake, let’s limit our definition of default to ABC’s failure to pay interest or principle. So, our risk-event is: ABC fails to pay interest or principle on any of its bonds. But what is our risk-magnitude? Since we are trying to define a risk that protection sellers are exposed to, our associated magnitude should be the basis upon which all payments by protection sellers are made. So, we will define the risk-magnitude as M=1 - \frac{P_d}{P} where P_d is the price of an ABC series I bond after the risk-event (default) occurs and P 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, M = .7 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.

One Man’s Garbage Is Another Man’s Glory

When one party to a derivative makes a payment, the other receives it. That seems simple enough. But it follows that if we consider only those payments made under the derivative contract itself, the net position of the two parties is unchanged over the life of the agreement. That is, derivatives create zero-sum games and simply shift and reallocate money that already existed between the two parties. So in continuing with our example above, it follows that we’ve also defined a risk that buyers of protection on ABC series I bonds are exposed to. However, protection buyers have positive exposure to that risk. That is, if ABC defaults, protection buyers receive money.

Exposure To Risk And Settlement Flow Analysis

If our concept of exposure is to have any real economic significance, it must take into account the concept of netting. So, we define the exposure of P_i 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 P_i is a counterparty, which we will call N_i, and (ii) M. 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 P_i. So, if P_i is a net seller of protection, N_i will be negative and therefore its exposure, N_i \cdot M, will be either negative or zero.

Because the payments between the two counterparties of each derivative net to zero, it follows that the sum of all net notional amounts is always zero. That is, if there are k market participants, \sum_{i=1}^kN_i = 0. The total notional amount of the entire market is given by N_T = \frac{1}{2} \sum_{i=1}^k|N_i|. 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).

Let’s consider a concrete example. In the diagram below, an edge coming from a participant represents protection sold by that participant and consequently an incoming edge represents protection bought by that participant. The amounts written beside these edges represent the notional amount of protection bought/sold. The amounts written beside the nodes represent the net notional amounts.

cds-market-diagram

In the example above, D is a dealer and his net notional amount is zero, and therefore his exposure to the risk-event is 0 \cdot M = 0 . 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.

We’re In The Money

CDS contracts come in and out of the money to a party based on the price of protection. If a party is out of money, the typical market practice is to require that party to post collateral. For example, if I bought protection at a price of 50bp, and suddenly the price jumps to 100bp, I’m in the money and my counterparty is out of the money. Thus, my counterparty will be required to post collateral. We can view the price of protection as providing an implied probability of default. Exactly how this is done is not important. But it should be clear that there is a connection between the cost of protecting debt and the probability of default on that debt (the higher the probability the higher the cost). Thus, as the implied probability of default changes over the life of the agreement, collateral will change hands.

Collateral Flow Analysis

In the previous sections, we assumed that the risk-event was certain to occur and then calculated the exposures based on an assumed recovery value. So, in effect, we were asking “what happens when parties settle their contracts at a given recovery value?” But what if we want to consider what happens before any default actually occurs? That is, what if we want to consider “what happens if the probability of default is p?” 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.

Continuing with the ABC bond example above, we can examine how collateral will move through the system by asking two questions: (i) what is the implied probability of the risk-event (ABC’s default) occurring and (ii) what is the expected value of the risk-magnitude (the basis upon which collateral payments are made). As discussed above, the implied probability of default will change over the life of the agreement, which will in turn affect the flow of collateral in the system. Since our goal in this section is to test the system’s behavior at different implied probabilities of default, the expected value of our risk-magnitude should be a function of an assumed implied probability of default. So, we define the expected value of our risk-magnitude as M_e = p^* \cdot M where p^* is our assumed implied probability of default and M is defined as it is above. It follows that this analysis will break CDS contracts into categories according to the price at which they were entered into. That is, you can’t ask how much something changed without first knowing what it was to begin with.

Assume that P_i entered into CDS contracts at m_i different prices. For example, he entered into four contracts at 20 bp and eight contracts at 50bp, and no others. In this case, m_i = 2. For each P_i, assign an arbitrary ordering, (c_{i,1}, ... , c_{i,m_i}), to the sets of contracts that were entered into at different prices by P_i. In the example where m_i = 2, we could let c_{i,1} be the set of eight contracts entered into at 50bp and let c_{i,2} 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 n_{i,j} as the net notional amount of the contracts in c_{i,j} and p_{i,j} as the implied probability of default of the contracts in c_{i,j} for each 1 \leq j \leq m_i. We define the expected exposure of P_i as:

EX_i = M_e \cdot \sum_{j = 1}^{m_i}\left(\frac{p^* - p_{i,j}}{1 - p_{i,j}} \cdot n_{i,j}\right) .

Note that when p^* = 1,

EX_i = M \cdot \sum_{j = 1}^{m_i}\left(\frac{1 - p_{i,j}}{1 - p_{i,j}} \cdot n_{i,j}\right) = M \cdot N_i .

That is, this is a generalized version of the settlement analysis above, and when we assume that default is certain, collateral flow analysis reduces to settlement flow analysis.

So What Does That Awful Formula Tell Us?

A participant’s expected exposure is a reasonable estimate for the amount of collateral that will be posted or received by that participant at an assumed implied probability of default. The exact amount of collateral that will be posted or received under any contract will be determined by the terms of that contract. As a result, our model is approximate and not exact. However, the direction that collateral moves in our model is exact. That is, if a party’s expected exposure is negative, it will not receive collateral, and if it is positive, it will not post collateral. It also shows that even if a party is completely hedged in the event of a default, it is possible that it is not completely hedged to posting collateral. That is, even if it bought and sold the same notional amount of protection, it could have done so at different prices.

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