Redux And Reduction
In the previous article, we defined a highly abstract framework that considered the subjective expected payout of both sides of a fixed fee derivative. In this article, we will apply that model to the context of credit default swaps and will show that the presence of credit default swaps and synthetic bonds should be expected to reduce the demand for “real” bonds (as opposed to synthetic bonds) and thereby reduce the net exposure of an economy to credit risk.
The Demand For Credit Default Swaps
In the previous article, we plotted the expected payout of each party to a credit default swap as a function of the fee and each party’s subjective valuation of the probability that a default will occur. The simple observation gleaned from that chart was that if we fix the subjective probabilities of default, protection sellers expect to earn more as the price of protection increases and protection buyers expect to earn more as the price of protection decreases. Thus, as the the price of protection increases, we would expect protection seller side “demand” to increase and expect protection buyer side “demand” to decrease. But how can demand be expressed in the context of a credit derivative? The general idea is to assume that holding all other variables constant, the size of the desired notional amount of the CDS will vary with price. So in the case of protection sellers, the greater the price of protection, the greater the notional amount desired by any protection seller.
In order to further formalize this concept, we should consider each reference entity as defining a unique demand curve for each market participant. We should also distinguish between demand for buying protection and demand for selling protection. For convenience’s sake, we will refer to the demand for selling protection as the supply of credit protection and demand for buying credit protection as the demand for credit protection. For example, consider protection seller X’s supply curve and protection buyer Y’s demand curve for CDSs naming ABC as a reference entity. The following chart expresses the total notional amount of all CDSs desired by X and Y as a function of the price of protection.
As the price of protection approaches zero, Y’s desired notional amount should approach infinity, since at zero, Y is getting free protection and should desire an unbounded “quantity” of credit protection. The same is true for X as the price of protection approaches infinity.
Synthetic Bonds As Competing Goods With “Real” Bonds
Imagine a world without credit derivatives and therefore without synthetic bonds. In that world, there will be a demand curve for real ABC bonds as a function of the spread the bonds pay over the risk free rate, holding all over variables constant. Now imagine that credit default swaps were introduced to this world. We know that the cash flows of any bond can be synthesized using Treasuries and credit default swaps. For example, assume we have synthesized the cash flows of ABC’s bonds using the method described here. We would expect at least some investors to be indifferent between real ABC bonds and synthetic ABC bonds, since they both produce the same cash flows. Thus, the two are competing products in the sense that investors in real ABC bonds should be potential investors in synthetic ABC bonds. So because some investors will be indifferent between synthetic ABC bonds and real ABC bonds, synthetic ABC bonds will siphon some of the cash that would have otherwise gone to real ABC bonds. Thus, in a world with credit derivatives, we would expect there to be less demand for real bonds than would be present without credit derivatives. In the following chart we express the macroeconomic demand for real ABC bonds in terms of the spread over the risk free rate and the total par value desired by the market.
Thus, the demand for credit derivatives diminishes the demand for real bonds. Although we cannot know exactly what the effect on the demand curve for real bonds will be, we can safely assume that it will be diminished at all levels of return, since at each level, at least some investors will be indifferent to real bonds and synthetic bonds, since each offers the same return.
Real Cash Losses Versus Wealth Transfers Through Derivatives
Economics already has a term to describe payouts under credit default swaps: wealth transfers. Although ordinarily used to describe the cash flows of tax regimes, the term applies equally to the payments under a credit default swap. As described in the previous article, there are no net cash losses under a credit default swap. There is a payment of money from one party to another, the net effect of which is a wealth transfer. That is, credit default swaps, like all derivatives, simply rearrange the current allocation of cash in the financial system, and nothing is lost in process (ignoring transaction costs, which are not relevant to this discussion).
When a real bond defaults, a net cash loss occurs. The borrower has taken the money lent to it by investors, lost it, and the investors are not fully paid back. Therefore, both the borrower and the investors incur a cash loss, creating a net cash loss to the economy. So, in the case of a synthetic ABC bond, upon the default of one of ABC’s bonds, a wealth transfer occurs from the protection seller to the protection buyer and the net effect is null. In the case of a real ABC bond, upon the default of that bond, the investors will lose some of their principle and ABC has already lost some of the money it was lent, the net effect of which is a loss to the economy.
So every dollar siphoned away from real bonds by synthetic bonds is a dollar that will not be lost in the economy upon the occurrence of a credit event. If there were no credit derivatives, then that dollar would have been invested in real bonds and thereby lost upon the occurrence of a credit event. Therefore, the net losses to the economy upon the occurrence of a credit event is less with credit derivatives than without. In the following diagram, the two circles of each transaction represent the parties to that transaction. In the case of real bonds, one of the parties is ABC and the other is an investor. In the case of synthetic bonds, one is the protection seller and the other is the protection buyer of the credit default swap underlying the synthetic bond.
This diagram simply demonstrates what was described above. Namely, that with credit derivatives, some investors will choose synthetic bonds rather than real bonds, thereby reducing the amount of cash exposed to credit risk. Thus, rather than increase the impact of credit risk, credit default swaps actually decrease the impact of credit risk by placating the demand for exposure to credit risk with synthetic instruments that are incapable of producing net losses. However, there may be consequences arising from credit default swaps that cause actual cash losses to an economy, such as a firm failing because of its obligations under credit default swaps. But the failure is not caused by the instrument itself. The nature of the instrument is to reduce the impact of credit risk. The firm’s failure is caused by that firm’s own poor risk management.
Information Overload 
This is correct only if you consider the lender and borrower of the real bonds to be a closed system. When you consider the whole economy, the money the defaulting borrower lost went somewhere, and the picture looks the same as that of the synthetic bond arrangement, just with more involved parties.
Economic gains and losses aren’t about cash flows anyway, but about the creation and/or destruction of value.
Noah,
In the case of a bond, the cash was invested in assets that failed to produce a return sufficient to repay the investors. Therefore, value was destroyed since the cash, which had value, was turned into something with less value. Whenever you have a cash loss on both ends of a transaction, you are guaranteed to destroy value.
Although you raise a valid question, it is tangential to the main argument, so I didn’t discuss it as the argument already has quite a few moving parts.
Interesting and provocative. Even as I tend to agree with the conclusion, raises a few issues for me:
* The macroeconomics: If synthetic bonds are a substitute for real bonds, then I am not sure you’ve finished the supply/demand dynamic. If the introduction of synthetics creates additional supply, a traditional supply increase would lead to both lower price (compressed spreads) and higher quantity (more notional issued); i.e., issuer of bonds want to issue more bonds at lower spreads. I don’t really believe this, but just extending your argument, it seems you could argue that the introduction of a complements lower price and *increases* notional.
* Your final chart may have a fallacy because it suggest that CDS instruments replace principal rather than ADD NOTIONAL. Either your three credit derivative instruments (on the left) are synthetics or CDS. If synthetic bonds, then due to the funding, they have all of the credit risk (as you’ve defined) as the set on the right (i.e., from a credit risk standpoint, there is no difference). If they are only CDS (just derivatives such that by definition that have cost and risk = 0), then they do not replace (or divert from) three bonds on the right: the CDS sellers entered into these precisely to avoid the funding, they are not necessarily replaced by firms that want to fund loans! So, your fallacy does not ruin your argument. But, you should just have X physical bonds on the right, and X + Y derivatives on the left, such that the derivatives are additive (in terms of the number of instruments. Or if you like, CDS instruments are a notional layer that adds on top of the principle) but non-additive to the credit risk. You’ve defined credit risk, the part subject to value creation/destruction, as the *funded* loan. But unfunded contracts don’t (necessarily) divert funding. Or, to make this much simpler, why in the “world with credit derivatives” would companies seek less funding (bonds are for borrowing money)?
* I think you persuade that credit derivatives, being net zero in total, do not add to the total level of credit risk in the system (to prove they subtract, as above, it seems to me you have two issues to overcome). But, and i suspect you are well aware of this challenge, we still have the practical question: the additional instruments, while being net zero, do introduce additional *emergent* (emerging from the system) risks (the additional notional exposure is asymmetric counterparty risk which may introduce something to the system). So, we can agree they add zero total credit risks (defined as above) but credit risk is not encompassing and, by excluding the other risks, we are still a long way from showing the instruments have no systemic impact.
David H
David,
“issuer of bonds want to issue more bonds at lower spreads.”
The issuer would not want to issue more, rather the supply of credit risk would be larger because of the available of alternatives, which in this case are synthetics. But the level of demand should not change simply because there is a new method of obtaining exposure to credit risk, so the existence of credit derivatives should not add “notional value.”
“If synthetic bonds, then due to the funding, they have all of the credit risk”
They are supposed to be funded synthetics. The protection seller, the synthetic bond holder, has exposure to credit risk. But because the underlying instrument is a CDS there is no net loss to the economy.
“we are still a long way from showing the instruments have no systemic impact.”
That is not my position. I even address the issue by discussing firms failing. But that’s not the fault of the instrument itself.
Charles,
How do think about price dynamics within this framework? If demand for new issuance of a particular bond declines due to the availability of synthetic exposure, what do you think the impact on the cost of funding for the issuer would be for a given amount of notional issuance?
Cheers,
Daniel
Daniel,
I think you’ve hit the nail on the head. I’ve never seen this issue discussed, yet it must be the case that the availability of synthetics pushes the cost of funding up since bond issuers have to compete with synthetic products naming them as reference entities. This is a bizarre consequence and it’s tough to think of a way to actually test empirically, but as a theoretical matter it seems to be a necessary logical corollary.
* I’m not saying demand changes. Assume demand curve is unchanged and not perfectly inelastic. Then an increase in supply should lower price and increase quantity (notional).
* If they are funded synthetics, you have a glaring fallacy. The funded credit risk in the world “without credit derivatives” is, under your argument, replaced by synthetic bonds. The funding then becomes investment in default-free Treasuries or something. In this way, you replace credit risk with no risk. But you omit this replacement reduces the supply of funding. The three companies, on the right, which borrowed, are replaced with non-investment borrowing. This shows why the replacement is a problem. Rather, the derivatives add notional to the existing outstanding principle. If the derivatives replace, then the ex ante supply of investable credit is reduced.
David,
If you look to the conversation above between Daniel and I you’ll see we discussed this. While very interesting, it is a side issue. The point of the article is that credit derivatives actually operate to reduce the losses associated with credit events. The effect on funding is a different story. Interesting, but different.
Charles, under a no arbitrage assumption, isn’t this logically inconsistent then, given that cost of funding has increased despite no change in the premium implied by the riskiness of the firm’s cash flows?
I imagine you’re assuming that cost of synthetic protection reach equilibrium at a price reflecting the higher cost of funding for the institution as well, a sort of competitive market for the risk exposure resulting in higher consumer surplus to the detriment of providers of risk in the same way that a greater opportunity set with finite capital results in higher hurdle rates?
Charles,
The funding is key to your argument b/c you have borrowers (on the right, in the world w/o credit derivatives) being replaced by credit protection buyers (on the left, in the world with credit derivatives). But bond issuers do so TO RAISE CASH. They won’t suddenly be contented to become mere credit protection buyers because derivatives are introduced. The mistake is to assume bond issuers are fungible with credit protection buyers (just b/c they are both “short the bond”); economically, they are not fungible.
Your fallacy is: you reduce credit risk by only reducing total productive capital (as funds invested in companies are diverted to riskless assets). This is the reductio ad absurdum.
While the introduction of CDS into the system has a dynamic impact on the underlying physical bonds (supply/demand, pricing, liquidity), the notional exposure does not replace principal, it adds “on top of it.”
David
David,
Funding is key to my argument, but your point is tangential. You are saying that synthetic instruments are bad because they divert investment into risk free assets. Maybe that is a less than desirable feature. But my argument is that synthetic instruments do not add to exposure to credit risk, rather they reduce it for the very same reason: they divert investment into risk free assets and the CDSs produce no net losses.
Daniel,
“isn’t this logically inconsistent then, given that cost of funding has increased despite no change in the premium implied by the riskiness of the firm’s cash flows?”
No, because the cost of funding will go up across the board on all credits. This happens all the time without the probability of defaults changing. For example, changes in the risk free rate would change the rates that bonds offer, but not as a result of any change in the probability of default.
Charles,
Right, but the problem is, with the introduction of the synthetic, you assume away the original motive for the underying bond: the companies will still want to raise cash.
The synthetics cannot divert cash because, even if the pricing of the underlying bonds is altered due to the liquidity created by the synthetic market, you will still have the original appetite for the *principal* (the debt capital). There are two ways to look at it. 1. You can accept your argument; in which case, the price of less systemic credit risk is (almost tautalogically) less principal deployed. A not very helpful conclusion. or 2. You can improve your argument by accepting that the introduction of synthetics is notionally additive to the principal (i.e., the debt capital demanded, more or less).
Sure, corporations will still want to raise money through debt. But there will be less available for them, because some has been diverted to synthetics.
Right, agreed, but that impacts pricing/quantity (principal) at the margin; i.e., higher price, maybe slightly less principal
but your argument is more severe: you have corporate borrowers eliminated from the picture, to be replaced by *unfunded* credit protection buyers, merely because a synthetic market is introduced. I don’t know why borrowers would go away and lenders, otherwise apparently willing to engage in *funded* synthetics, would disappear for them. i.e., you haven’t shown me why the borrowers on the right side of your picture disappear on the left.
But, okay, I appreciate the consistency of your argument and I thank you for a provocative post/thread. You can have the last work and i will look forward to your next post 🙂
Think of it like Coke and Pepsi. If only Coke were around, they would soak up all the demand for cola. But because Pepsi exists, the demand for Coke is diminished because at least some purchasers are indifferent to the two.
Too easy. A bond is credit risk (coke) plus funding (call it a hamburger, for the metaphor’s sake). To introduce synthetics is to introduce a substitute for the credit risk only; i.e., to introduce pepsi. Coke and pepsi succeed as a metaphor for the fungibility of the credit risk only; the hamburger is not substituted in any obvious way. The company still wants funding (hamburger); that the company can buy credit protection does not satsify its appetite for a hamburger.
…sorry, just to be complete: I should say, to introduce synthetics is to introduce substitutes for credit risk and interest rate risk; i.e, the synthetic bond (which isn’t realistic here anyway) = interest rate swap + CDS + riskless bond.
Now I understand why you are not getting it. The company is not buying credit protection. The company is issuing bonds. The people buying credit protection in my example are 3rd parties.
i got that (obviously). You replace, as economic agents, bond issuers (in the word before synthetics) with credit protection buyers (in the synthetic world); i.e., you argument is they (companies) are me with credit protection sellers who compete with bond investors (both wanting to be long credit risk).
But you’ve used the fungibility of credit protection (bets for/against credit risk) to divert principal (FUNDING) from productive to non-productive assets. I don’t think you understand funding. First, it’s theoretically wrong; but more importantly, it’s not even nearly realistic. To really have an argument, you’d want to show the synthetic world with largely unfunded instruments. But you’d need to see the first problem first, and I think you are too concerned with being correct such that you are actually willing to be wrong in order to hold onto a bad position. I am willing to be corrected, but you don’t even care to see the issue, so you cannot reply to it.
David,
Final round. Synthetic investors are not competing with bond investors. They are the same people. The point is that investors are given a choice between real and synthetic bonds. They shouldn’t care so long as they pay the same. Therefore, some investors will choose synthetics over real bonds. The competition is between the real and synthetic bonds.
Yes, that will take money away from companies seeking capital, and thereby divert from productive capital, but that is not the point of the article. I have already said that Daniel and I are discussing that very point above.
As for the funding issue, you think I don’t understand funding? Are you joking me? All the synthetic bonds under discussion in this article are fully funded so that they completely mimic the underlying reference obligation. The issue of funding has no other part in this article.
Credit protection sellers ARE synthetic bond investors. To buy a synthetic bond IS TO SELL PROTECTION.
Charles,
Yes, thank you, it is very satsifying to get back to basics. I really do love the basics! Let’s end the final round on that…David
Charles, you said (13 January 2009 at 1pm to David Harper): “Synthetic investors are not competing with bond investors. They are the same people. The point is that investors are given a choice between real and synthetic bonds. They shouldn’t care so long as they pay the same. Therefore, some investors will choose synthetics over real bonds. The competition is between the real and synthetic bonds.”
There is is significant difference if the actual bond is downgraded by the rating agency referenced in the CDS contract. The buyer of the actual bond experiences a liquidity shortfall: if he must sell the bond prior to maturity, he will get a lower price. The buyer of the synthetic bond experiences something like a margin call: he must post additional collateral — quickly — or lose his shirt.
Hi Pierre,
Thank you for your comment. Synthetic bonds are fully funded, so there’s no need for collateral. The investor, by paying par value for the synthetic, posts the entire notional amount. You should check out my article on synthetics.
https://derivativedribble.wordpress.com/2008/11/11/synthetic-cdos-demystified/
Pierre is correct. Charles, you are mis-using terms.
No instrument in finance posts the full notional; rather, principal is funded, notional is referenced.
Similarly, to be synethic is to be unfunded (and, often but not necessarily, therefore, to be subject to margin. Which has a subtly different meaning than collateral, but let’s forget that now)
What you previously called a synthetic bond is a misnomer. You should call it a credit linked note, CLN, (i.e., investor D pays on notes but the notes are contingent on some credit reference. See Culp or see Tavakoli.
Pierre is correct because he refers to the margin call initiated by the CDS counterparty, which is by definition, not the note holde. It is oxymoronic to refer to a synthetic funded instrument.
The CLN, being funded by definition (this is the key difference between a CDS and a CLN: funding), does not require collateral. But your first transaction, which sets up the should-be-called-a-CLN, has investor D selling credit protection and investing in Treasuries. Pierre is correct; the CDS counterparty may have a margin call; he is not holding the collateral! (if he were, it would just be a bond!).
About the margin call: it depends. First, whether the CDS is marked-to-market; Second, typically, the CDS seller is required to post margin (e.g., the counterparties in AIG CDS typically did, but only because there were uncapitalized hedge funds). But in practice, the margin did not happen. Going forward, you bet it will.
This gets back to why the original theory here, while interesting, is not relevant from any practical standpoint: it is a useful academic exercise to deconstruct bonds into synthetics but, you have to understand. The appeal of the CDS market is their unfunded status: investors do not (will not) divert productive (at risk) capital to Treasuries in order to synthesize. This a a long way of saying: notional CDS exposure adds to outstanding debt principal, it does not replace it (except perhaps due to marginal feedback impact on price/quantity due to the introductio of the synthetic market).
…sorry to append and clarify one point. What Charles mislabels a synthetic bond has two transaction. So, I am referring to the (possible, not necessary) margin call on the CDS. Charles is correct that the CLN itself, being funded, will not require margin. But, the important point (again) if we refer to whether credit risk in the system, is that the introduction of synthetics won’t cause bond investors to park capital. It’s actually the opposite: the introduction of CDS, being unfunded, has liberated capital to go out and find more risk.
David and Pierre,
I don’t like the term CLN because IT is a misnomer. Synthetic CDOs can be funded or unfunded, yet they don’t call the funded variety Credit Linked CDOs, they just call them funded Synthetic CDOs.
The term “synthetic” is used to describe the fact that an instrument is being synthesized using swaps. For example, a synthetic fixed rate bond. The term has nothing to do with funding. Calling bonds constructed with swaps and Treasuries “synthetic bonds” makes the etymology consistent.
As for the appeal of unfunded credit instruments, see my latest article.
And finally, we cannot assume that investors in ordinary bonds will be indifferent to real bonds and unfunded CDSs naming that bond as a reference obligation. Some investors might prefer the unfunded nature, but others will not because there is added risk if you invest in non-risk free assets. So, THE INSTRUMENTS HAVE DIFFERENT RISK PROFILES. That is why I have assumed only that investors will be indifferent to real bonds and fully funded CDSs, because they have the same risk profiles and returns.
Yes, but that’s a semantic confusion. Synthetic funded CDO is two labels for two transactions. Synthetic CDOs can be unfunded (which typically means “partially funded”), but that’s only because that particular label combines two different aspects of the operation: ‘synthetic’ refers to writing (unfunded) CDS protection. ‘Unfunded’ (partially funded, really) refers the liability side of the transaction: notes are issues against notional rather than principal. So, a partially funded synthetic CDO is writing synthetic (unfunded) protection on the asset side to pay, on the liabilities side,
The reason that treating synthetic synonymous with unfunded is: a synthetic instrument is a replicating portfolio (which, to your point, may include a swap, but may not). To replicate is mimic by not investing directly (to not fund). The funding criteria is more encompassing of replication than the swaps criteria. (but you are close with swaps!).
The problem is that you mislabel an aribtrage as a synthetic bond. Your Investor D is an arbitrageur (i.e., short CDS + issue CLN + invest CLN proceeds in riskless asset). They you say the arbitrageur competes with bond investors (?!). This is how you reduce credit risk: you drop out the CLN buyers. If you restore CLN buyers (under your definition of synthetic bond issuer, what i call an arbitrageur), you will restore the credit risk to the left hand side!
You say: “And finally, we cannot assume that investors in ordinary bonds will be indifferent to real bonds and unfunded CDSs naming that bond as a reference obligation. Some investors might prefer the unfunded nature, but others will not because there is added risk if you invest in non-risk free assets. So, THE INSTRUMENTS HAVE DIFFERENT RISK PROFILES. That is why I have assumed only that investors will be indifferent to real bonds and fully funded CDSs, because they have the same risk profiles and returns.”
Charles, I understand this paragraph, and on this point, I do not doubt the theory of your argument. So, I am on a different practical point. You are smart to replicate entirely (although, again, where did the CLN buyers go?). But, from a practical standpoint, and this is not an attack on your argument per se, this won’t happen: the bond investors will redeploy. In fact, they will redeploy to risky assets. So, from a practical standpoint, it’s easier to show more risk is created because more capital can go to risky bonds.
…sorry, i can’t edit the comment. About the synthetic funded CDO, these are tricky, but i was trying to explain that the synthetic refers to the unfunded asset side (i.e., write/go short CDS) and funded/partially funded refers to the liability side of the SPE/SPV.
David,
I just don’t understand the confusion. This is a very simple argument. The only cogent point I can tease from your comments is that as a practical matter investors will go for the unfunded CDSs instead of the synthetic bonds aka CLNs, which would free money up to be invested in other bonds. Fine, but then my argument applies again. Those investors shouldn’t care whether or not they invest their newly freed up cash in real or synthetic bonds, so long as they pay the same.
Charles,
No worries, I shouldn’t have weighed back in today. (Sincerely, as i teach this stuff, i sometimes love to dwell on definitions. The definitions are so critical to the argument).
I tried my best, but i see that i did not budge you. It’s been fun sharpenins saws on this one…David
Small quibble with your opening setup – the protection seller will sell an infinite amount of protection when the price is at the notional amount, rather than at a price of ‘infinity’. When the price of protection for debt is equal to the amount of debt, then selling protection for it is equivalent to acquiring the underlying for free – if the underlying fails, the seller simply returns the fee, and if it doesn’t fail then the seller pockets the notional amount.
Anonymous,
You are spot on, given that my language in that section is ambiguous at best. Shoot me an email.
Charles, this discussion is interesting, but seems to dwell in the frictionless world of textbook finance. In the real world, there are bid-ask spreads, which represent a deadweight loss to creating a plethora of synthetic bonds, since those bonds are not needed to finance projects in the real economy. I guess this is a hedging vs. speculating argument that we could have about grain futures instead of CDS. I do think there is a place for speculation, but with physical commodity spec you may have to deliver the actual good (or settle daily in cash with the exchange). No such CDS exchange exists (yet).
Second, prices in the short run are determined by the eagerness of buyers vs. sellers, not “value” or the present value of future cash flows. So those bid-ask spreads can get very costly, particularly for a CDS counterparty with excess leverage. I guess this is an argument against leverage rather than CDS specifically.
Third, I think we have all seen the consequences of loss of confidence on an ostensibly “textbook finance” system that assumes infinite supply of risk-free assets is always available, information is instantaneously diseminated to all parties. The last one is a poor assumption, and pushes the Newtonian version of CDS mechanics you describe aside, and replaces it with a game theory model of Old Maid or poker.
So I’m in favor of a CDS market, but want it on an exchange like ICE to eliminate my market microstructure and agency problem concerns.
Bond newbie,
“may have to deliver the actual good”
Although most CDS are cash settled, some still call for physical delivery of the underlying bond.
“Second, prices in the short run are determined by the eagerness of buyers vs. sellers, not “value””
I think that’s the point of this article.
“I’m in favor of a CDS market, but want it on an exchange like ICE”
ISDA holds auctions for many of the biggest name and index CDSs, this effectively operates like an exchange for those CSDs.
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