Credit Default Swaps.

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Credit default swaps are the most liquid instruments in the credit derivatives markets, accounting for nearly half of the total outstanding notional worldwide, and up to 85% of total outstanding notional of contracts with reference to emerging market issuers. In a CDS, the protection buyer pays a premium to the protection seller in exchange for a contingent payment in case a credit event involving a reference security occurs during the contract period.

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The premium (default swap spread) reflects the credit risk of the bond issuer, and is usually quoted as a spread over a reference rate such as LIBOR or the swap rate, to be paid either up front, quarterly, or semiannually. The contingent payment can be settled either by physical delivery of the reference security or an equivalent asset, or in cash. With physical settlement, the protection buyer delivers the reference security (or equivalent one) to the protection seller and receives the par amount. With cash settlement, the protection buyer receives a payment equal to the difference between par and the recovery value of the reference security, the latter determined from a dealer poll or from price quote services. Contracts are typically subject to physical settlement. This allows protection sellers to benefit from any rebound in prices caused by the rush to purchase deliverable bonds by protection buyers after the realization of the credit event.

In mature markets, trading is highly concentrated on 5 year contracts, and to certain extent, market participants consider these contracts a ‘‘commodity.’’ Usual contract maturities are 1, 2, 5, and 10 years. The coexistence of markets for default swaps and bonds raises the issue on whether prices in the former merely mirrors market expectations already reflected in bond prices. If credit risk were the only factor affecting the CDS spread, with credit risk characterized by the probability of default and the expected loss given default, the CDS spread and the bond spread should be approximately similar, as a portfolio of a default swap contract and a defaultable bond is essentially a risk-free asset.

However, market frictions and some embedded options in the CDS contract, such as the cheapest-to-deliver option, cause CDS spreads and bond spreads to diverge. The difference between these two spreads is referred to as the default swap basis. The default swap basis is positive when the CDS spread trades at a premium relative to the bond spread, and negative when the CDS spread trades at a discount.

Several factors contribute to the widening of the basis, either by widening the CDS spread or tightening the bond spread. Factors that tend to widen the CDS spread include: (1) the cheapest-to-deliver option, since protection sellers must charge a higher premium to account for the possibility of being delivered a less valuable asset in physically settled contracts; (2) the issuance of new bonds and/or loans, as increased hedging by market makers in the bond market pushes up the price of protection, and the number of potential cheapest-to-deliver assets increases; (3) the ability to short default swaps rather than bonds when the bond issuer’s credit quality deteriorates, leading to increased protection buying in the market; and (4) bond prices trading less than par, since the protection seller is guaranteeing the recovery of the par amount rather than the lower current bond price.

Factors that tend to tighten bond spreads include: (1) bond clauses allowing the coupon to step up if the issue is downgraded, as they provide additional benefits to the bondholder not enjoyed by the protection buyer and (2) the zero-lower bound for default swap premiums causes the basis to be positive when bond issuers can trade below the LIBOR curve, as is often the case for higher rated issues.

Similarly, factors that contribute to the tightening of the basis include: (1) existence of greater counterparty risk to the protection buyer than to the protection seller, so buyers are compensated by paying less than the bond spread; (2) the removal of funding risk for the protection seller, as selling protection is equivalent to funding the asset at LIBOR. Less risk demands less compensation and hence, a tightening in the basis; and (3) the increased supply of structured products such as CDS-backed collateralized debt obligations (CDOs), as they increase the supply of protection in the market.

Movements in the basis depend also on whether the market is mainly dominated by high cost investors or low cost investors. A long credit position, i.e., holding the credit risk, can be obtained either by selling protection or by financing the purchase of the risky asset. The CDS remains a viable alternative if its premium does not exceed the difference between the asset yield and the funding cost. The higher the funding cost, the lower the premium and hence, the tighter the basis. Thus, when the market share of low cost investors is relatively high and the average funding costs are below LIBOR, the basis tends to widen. Finally, relative liquidity also plays a role in determining whether the basis narrows or widens, as investors need to be compensated by wider spreads in the less liquid market. Hence, if the CDS market is more liquid than the corresponding underlying bond market (cash market), the basis will narrow and vice versa.

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Accelerating the Synthetic Credit. Thought of the Day 96.0

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The structural change in the structured credit universe continues to accelerate. While the market for synthetic structures is already pretty well established, many real money accounts remain outsiders owing to regulatory hurdles and technical limitations, e.g., to participate in the correlation market. Therefore, banks are continuously establishing new products to provide real money accounts with access to the structured market, with Constant proportion debt obligation (CPDOs) recently having been popular. Against this background, three vehicles which offer easy access to structured products for these investors have gained in importance: CDPCs (Credit Derivatives Product Company), PCVs (permanent capital vehicle), and SIVs (structured investment vehicles).

A CDPC is a rated company which buys credit risk via all types of credit derivative instruments, primarily super senior tranches, and sells this risk to investors via preferred shares (equity) or subordinated notes (debt). Hence, the vehicle uses super senior risk to create equity risk. The investment strategy is a buy-and-hold approach, while the aim is to offer high returns to investors and keep default risk limited. Investors are primarily exposed to rating migration risk, to mark-to-market risk, and, finally, to the capability of the external manager. The rating agencies assign, in general, an AAA-rating on the business model of the CDPC, which is a bankruptcy remote vehicle (special purpose vehicle [SPV]). The business models of specific CDPCs are different from each other in terms of investments and thresholds given to the manager. The preferred asset classes CDPC invested in are predominantly single-name CDS (credit default swaps), bespoke synthetic tranches, ABS (asset-backed security), and all kinds of CDOs (collateralized debt obligations). So far, CDPCs main investments are allocated to corporate credits, but CDPCs are extending their universe to ABS (Asset Backed Securities) and CDO products, which provide further opportunities in an overall tight spread environment. The implemented leverage is given through the vehicle and can be in the range of 15–60x. On average, the return target was typically around a 15% return on equity, paid in the form of dividends to the shareholders.

In contrast to CDPCs, PCVs do not invest in the top of the capital structure, but in equity pieces (mostly CDO equity pieces). The leverage is not implemented in the vehicle itself as it is directly related to the underlying instruments. PCVs are also set up as SPVs (special purpose vehicles) and listed on a stock exchange. They use the equity they receive from investors to purchase the assets, while the return on their investment is allocated to the shareholders via dividends. The target return amounts, in general, to around 10%. The portfolio is managed by an external manager and is marked-to-market. The share price of the company depends on the NAV (net asset value) of the portfolio and on the expected dividend payments.

In general, an SIV invests in the top of the capital structure of structured credits and ABS in line with CDPCs. In addition, SIVs also buy subordinated debt of financial institutions, and the portfolio is marked-to-market. SIVs are leveraged credit investment companies and bankruptcy remote. The vehicle issues typically investment-grade rated commercial paper, MTNs (medium term notes), and capital notes to its investors. The leverage depends on the character of the issued note and the underlying assets, ranging from 3 to 5 (bank loans) up to 14 (structured credits).

Credit Risk Portfolio. Note Quote.

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The recent development in credit markets is characterized by a flood of innovative credit risky structures. State-of-the-art portfolios contain derivative instruments ranging from simple, nearly commoditized contracts such as credit default swap (CDS), to first- generation portfolio derivatives such as first-to-default (FTD) baskets and collateralized debt obligation (CDO) tranches, up to complex structures involving spread options and different asset classes (hybrids). These new structures allow portfolio managers to implement multidimensional investment strategies, which seamlessly conform to their market view. Moreover, the exploding liquidity in credit markets makes tactical (short-term) overlay management very cost efficient. While the outperformance potential of an active portfolio management will put old-school investment strategies (such as buy-and-hold) under enormous pressure, managing a highly complex credit portfolio requires the introduction of new optimization technologies.

New derivatives allow the decoupling of business processes in the risk management industry (in banking, as well as in asset management), since credit treasury units are now able to manage specific parts of credit risk actively and independently. The traditional feedback loop between risk management and sales, which was needed to structure the desired portfolio characteristics only by selective business acquisition, is now outdated. Strategic cross asset management will gain in importance, as a cost-efficient overlay management can now be implemented by combining liquid instruments from the credit universe.

In any case, all these developments force portfolio managers to adopt an integrated approach. All involved risk factors (spread term structures including curve effects, spread correlations, implied default correlations, and implied spread volatilities) have to be captured and integrated into appropriate risk figures. We have a look on constant proportion debt obligations (CPDOs) as a leveraged exposure on credit indices, constant proportion portfolio insurance (CPPI) as a capital guaranteed instrument, CDO tranches to tap the correlation market, and equity futures to include exposure to stock markets in the portfolio.

For an integrated credit portfolio management approach, it is of central importance to aggregate risks over various instruments with different payoff characteristics. In this chapter, we will see that a state-of-the-art credit portfolio contains not only linear risks (CDS and CDS index contracts) but also nonlinear risks (such as FTD baskets, CDO tranches, or credit default swaptions). From a practitioner’s point of view there is a simple solution for this risk aggregation problem, namely delta-gamma management. In such a framework, one approximates the risks of all instruments in a portfolio by its first- and second-order sensitivities and aggregates these sensitivities to the portfolio level. Apparently, for a proper aggregation of risk factors, one has to take the correlation of these risk factors into account. However, for credit risky portfolios, a simplistic sensitivity approach will be inappropriate, as can be seen by the characteristics of credit portfolio risks shows:

  • Credit risky portfolios usually involve a larger number of reference entities. Hence, one has to take a large number of sensitivities into account. However, this is a phenomenon that is already well known from the management of stock portfolios. The solution is to split the risk for each constituent into a systematic risk (e.g., a beta with a portfolio hedging tool) and an alpha component which reflects the idiosyncratic part of the risk.

  • However, in contrast to equities, credit risk is not one dimensional (i.e., one risky security per issuer) but at least two dimensional (i.e., a set of instruments with different maturities). This is reflected in the fact that there is a whole term structure of credit spreads. Moreover, taking also different subordination levels (with different average recovery rates) into account, credit risk becomes a multidimensional object for each reference entity.
  • While most market risks can be satisfactorily approximated by diffusion processes, for credit risk the consideration of events (i.e., jumps) is imperative. The most apparent reason for this is that the dominating element of credit risk is event risk. However, in a market perspective, there are more events than the ultimate default event that have to be captured. Since one of the main drivers of credit spreads is the structure of the underlying balance sheet, a change (or the risk of a change) in this structure usually triggers a large movement in credit spreads. The best-known example for such an event is a leveraged buyout (LBO).
  • For credit market players, correlation is a very special topic, as a central pricing parameter is named implied correlation. However, there are two kinds of correlation parameters that impact a credit portfolio: price correlation and event correlation. While the former simply deals with the dependency between two price (i.e., spread) time series under normal market conditions, the latter aims at describing the dependency between two price time series in case of an event. In its simplest form, event correlation can be seen as default correlation: what is the risk that company B defaults given that company A has defaulted? While it is already very difficult to model this default correlation, for practitioners event correlation is even more complex, since there are other events than just the default event, as already mentioned above. Hence, we can modify the question above: what is the risk that spreads of company B blow out given that spreads of company A have blown out? In addition, the notion of event correlation can also be used to capture the risk in capital structure arbitrage trades (i.e., trading stock versus bonds of one company). In this example, the question might be: what is the risk that the stock price of company A jumps given that its bond spreads have blown out? The complicated task in this respect is that we do not only have to model the joint event probability but also the direction of the jumps. A brief example highlights why this is important. In case of a default event, spreads will blow out accompanied by a significant drop in the stock price. This means that there is a negative correlation between spreads and stock prices. However, in case of an LBO event, spreads will blow out (reflecting the deteriorated credit quality because of the higher leverage), while stock prices rally (because of the fact that the acquirer usually pays a premium to buy a majority of outstanding shares).

These show that a simple sensitivity approach – e.g., calculate and tabulate all deltas and gammas and let a portfolio manager play with – is not appropriate. Further risk aggregation (e.g., beta management) and risk factors that capture the event risk are needed. For the latter, a quick solution is the so-called instantaneous default loss (IDL). The IDL expresses the loss incurred in a credit risk instrument in case of a credit event. For single-name CDS, this is simply the loss given default (LGD). However, for a portfolio derivative such as a mezzanine tranche, this figure does not directly refer to the LGD of the defaulted item, but to the changed subordination of the tranche because of the default. Hence, this figure allows one to aggregate various instruments with respect to credit events.

Energy Trading: Asian Options.

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Consider a risky asset (stock, commodity, a unit of energy) with the price S(t), where t ∈ [0, T], for a given T > 0. Consider an option with the payoff

Fu = Φ(u(·), S(·)) —– (1)

This payoff depends on a control process u(·) that is selected by an option holder from a certain class of admissible controls U. The mapping Φ : U × S → R is given; S is the set of paths of S(t). All processes from U has to be adapted to the current information flow, i.e., adapted to some filtration Ft that describes this information flow. We call the corresponding options controlled options.

For simplicity, we assume that all options give the right on the corresponding payoff of the amount Fu in cash rather than the right to buy or sell stock or commodities.

Consider a risky asset with the price S(t). Let T > 0 be given, and let g : R → R and f : R × [0, T] → R be some functions. Consider an option with the payoff at time T

Fu = g(∫0u(t) f (S(t), t)dt) —– (2)

Here u(t) is the control process that is selected by the option holder. The process u(t) has to be adapted to the filtration Ft describing the information flow. In addition, it has to be selected such that

0T u(t)dt = 1

A possible modification is the option with the payoff

Fu = ∫0T u(t) f(S(t), t)dt + (1 – ∫0T u(t)dt) f(S(T), T)

In this case, the unused u(t) are accumulated and used at the terminal time. Let us consider some examples of possible selection of f and g. We denote x+ = max(0, x)

Important special cases are the options with g(x) = x, g(x) = (x − k)+, g(x) = (K − x)+,

g(x) = min(M, x), where M > 0 is the cap for benefits, and with

f(x, t) = x, f(x, t) = (x − K)+, f(x, t) = (K − x)+ —– (3)

or

f(x, t) = er(T−t)(x − K)+, f(x, t) = er(T−t)(K − x)+ —– (4)

where K > 0 is given and where r > 0 is the risk-free rate. Options (3) correspond to the case when the payments are made at current time t ∈ [0, T], and options (4) correspond to the case when the payment is made at terminal time T. This takes into account accumulation of interest up to time T on any payoff.

The option with payoff (2) with f(x, t) ≡ x represents a generalization of Asian option where the weight u(t) is selected by the holder. It needs to be noted that an Asian option , which is also called an average option, is an option whose payoff depends on the average price of the underlying asset over a certain period of time as opposed to at maturity. The option with payoff (2) with g(x) ≡ x represents a limit version of the multi-exercise options, when the distribution of exercise time approaches a continuous distribution. An additional restriction on |u(t)| ≤ const would represent the continuous analog of the requirement for multi-exercise options that exercise times must be on some distance from each other. For an analog of the model without this condition, strategies may approach delta-functions.

These options can be used, for instance, for energy trading with u(t) representing the quantity of energy purchased at time t for the fixed price K when the market price is above K. In this case, the option represents a modification of the multi-exercise call option with continuously distributed payoff time. For this model, the total amount of energy that can be purchased is limited per option. Therefore, the option holder may prefer to postpone the purchase if she expects better opportunities in future.

Open Market Operations. Thought of the Day 93.0

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It can be argued that it would be much more democratic if the Treasuries were allowed to borrow directly from their central bank. By electing a government on a program, we would know what deficit it intends to run and thus how much it will be willing to print, which in the long run is a debate about the possible level of inflation. Instead, it has been argued that decisions made on democratic grounds might be unstable as they are affected by elections. However, the independence of central banks is also serving the interest of commercial bankers as we argue now.

In practice, the central bank buys and sells bonds in open market operations. At least it is always doing so with short term T-bonds as part of the conventional monetary policy, and it might decide sometimes to do it as well with longer maturity T-bonds as part of the unconventional monetary policy. This blurs the lines between a model where the central bank directly finances the Treasury, and a model where this is done by commercial banks since they result in the same final situation. Indeed, before an open market operation the Treasury owes central bank money to a commercial bank, and in the final situation it owes it to the central bank itself, and the central bank money held by the commercial bank has been increased accordingly.

The commercial bank has accepted to get rid of an IOU which bears interest, in exchange of a central bank IOU which bears no interest. However the Treasury will never default on its debt, because the state also runs the central bank which can buy an infinite amount of T-bonds. Said differently, if the interest rates for short term T-bonds start to increase as the commercial banks become more and more reluctant to buy these, the central bank needs to buy as many short-term bonds as necessary to ensure the short term interest rates on T-bonds remain at the targeted level. By using these open market operations a sovereign state running a sovereign currency has the means to ensure that the banks are always willing to buy T-bonds, whatever the deficit is.

However, this system has a drawback. First when the commercial bank bought the T-bond, it had to pretend that it was worried the state might never reimburse, so as to ask for interests rates which are at least slightly higher than the interest rate at which they can borrow from the central bank, and make a profit on the difference. Of course the banks knew they would always be reimbursed, because the central bank always stands ready to buy bonds. As the interest rates departed from the target chosen by the central bank, the latter bought short term bonds to prevent the short term rate from increasing. In order to convince a commercial bank to get rid of a financial instrument which is not risky and which bears interest, the only solution is to pay more than the current value of the bond, which amounts to a decrease of the interest rate on those bonds. The bank thus makes an immediate profit instead of a larger profit later. This difference goes directly into the net worth of the banker and amounts to money creation.

To conclude, we reach the same stage as if the Treasury had sold directly its bond to the central bank, except that now we have increased by a small amount the net worth of the bankers. By first selling the bonds to the commercial banks, instead of selling directly to the central bank, the bankers were able to realize a small profit. But this profit is an immediate and easy one. So they have on one side to pretend they do not like when the Treasury goes into debt, so as to be able to ask for the highest possible interest rate, and secretly enjoy it since either they make a profit when it falls due, or even better immediately if the central bank buys the bonds to control the interest rates.

The commercial banks will always end up with a part of their assets denominated directly in central bank money, which bears no interest, and T-bonds, which bear interest. If we adopt a consolidated state point of view, where we merge the Treasury and the central bank, then the commercial banks have two types of accounts. Deposits which bear no interests, and saving accounts which generate interests, just like everybody. In order to control the interest rate, the consolidated state shifts the amounts from the interest-less to the interest-bearing account and vice-versa.

Credit Bubbles. Thought of the Day 90.0

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At the macro-economic level of the gross statistics of money and loan supply to the economy, the reserve banking system creates a complex interplay between money, debt, supply and demand for goods, and the general price level. Rather than being constant, as implied by theoretical descriptions, money and loan supplies are constantly changing at a rate dependent on the average loan period, and a complex of details buried in the implementation and regulation of any given banking system.

Since the majority of loans are made for years at a time, the results of these interactions play out over a long enough time scale that gross monetary features of regulatory failure, such as continuous asset price inflation, have come to be regarded as normal, e.g. ”House prices always go up”. The price level however is not only dependent on purely monetary factors, but also on the supply and demand for goods and services, including financial assets such as shares, which requires that estimates of the real price level versus production be used. As a simplification, if constant demand for goods and services is assumed as shown in the table below, then there are two possible causes of price inflation, either the money supply available to purchase the good in question has increased, or the supply of the good has been reduced. Critically, the former is simply a mathematical effect, whilst the latter is a useful signal, providing economic information on relative supply and demand levels that can be used locally by consumers and producers to adapt their behaviour. Purely arbitrary changes in both the money and the loan supply that are induced by the mechanical operation of the banking system fail to provide any economic benefit, and by distorting the actual supply and demand signal can be actively harmful.

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Credit bubbles are often explained as a phenomena of irrational demand, and crowd behaviour. However, this explanation ignores the question of why they aren’t throttled by limits on the loan supply? An alternate explanation which can be offered is that their root cause is periodic failures in the regulation of the loan and money supply within the commercial banking system. The introduction of widespread securitized lending allows a rapid increase in the total amount of lending available from the banking system and an accompanying if somewhat smaller growth in the money supply. Channeled predominantly into property lending, the increased availability of money from lending sources, acted to increase house prices creating rational speculation on their increase, and over time a sizeable disruption in the market pricing mechanisms for all goods and services purchased through loans. Monetary statistics of this effect such as the Consumer Price Index (CPI) for example, are however at least partially masked by production deflation from the sizeable productivity increases over decades. Absent any limit on the total amount of credit being supplied, the only practical limit on borrowing is the availability of borrowers and their ability to sustain the capital and interest repayments demanded for their loans.

Owing to the asymmetric nature of long term debt flows there is a tendency for money to become concentrated in the lending centres, which then causes liquidity problems for the rest of the economy. Eventually repayment problems surface, especially if the practice of further borrowing to repay existing loans is allowed, since the underlying mathematical process is exponential. As general insolvency as well as a consequent debt deflation occurs, the money and loan supply contracts as the banking system removes loan capacity from the economy either from loan repayment, or as a result of bank failure. This leads to a domino effect as businesses that have become dependent on continuously rolling over debt fail and trigger further defaults. Monetary expansion and further lending is also constrained by the absence of qualified borrowers, and by the general unwillingness to either lend or borrow that results from the ensuing economic collapse. Further complications, as described by Ben Bernanke and Harold James, can occur when interactions between currencies are considered, in particular in conjunction with gold-based capital regulation, because of the difficulties in establishing the correct ratio of gold for each individual currency and maintaining it, in a system where lending and the associated money supply are continually fluctuating and gold is also being used at a national level for international debt repayments.

The debt to money imbalance created by the widespread, and global, sale of Asset Backed securities may be unique to this particular crisis. Although asset backed security issuance dropped considerably in 2008, as the resale markets were temporarily frozen, current stated policy in several countries, including the USA and the United Kingdom, is to encourage further securitization to assist the recovery of the banking sector. Unfortunately this appears to be succeeding.