Constant Maturity Default Swaps: Disentangling Spread&Default Risk

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Constant Maturity Default Swaps: Disentangling Spread&Default Risk

Constant maturity default swaps are a new credit derivative instrument that bifurcates credit risk into spread and default components.

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Constant maturity default swaps are a new credit derivative instrument that bifurcates credit risk into spread and default components. Similar to a plain default swap, a CMDS contract transfers the default and recovery risk of a Reference Entity from the Protection Buyer to the Protection Seller. But, in contrast to a default swap, which has a fixed premium payment for the duration of the transaction, the premium of a CMDS resets periodically. For example, the CMDS protection premium may reset quarterly to 80% of the five-year CDS premium. Since the CMDS protection seller receives an increasing premium as spreads widen, the mark-to-market sensitivity of a CMDS contract is, in most instances, much lower than the spread sensitivity of a simple CDS.

 

The Mechanics

Most of the terms of a CMDS contract are identical to a standard CDS contract. In particular, the Credit Events and the trigger/settlement mechanism are usually standard. Instead of setting a fixed premium the CMDS contract specifies a reference constant maturity, typically five years, a percentage factor, and a reset frequency. The initial CMDS protection premium is set to the percentage factor multiplied by the spot CDS premium with the reference constant maturity.

On each reset date, which can occur every quarter or six months, the reference constant maturity CDS premium is established and the CMDS premium is set equal to this premium multiplied by the percentage factor. An example market quote for a CMDS contract is 80%/90% with the reference constant maturity equal to five years and a quarterly reset. Specifically, the maturity date of the on-the-run five-year CDS contract (i.e. March 20, 2009 today) is selected. This means that the dealer is willing to buy protection at 80% of the five-year CDS premium and will sell protection at 90% of the five-year CDS.

If an investor buys protection at 90%, the first quarterly premium is set to 90% of the five-year CDS premium. The next quarter, the new five-year CDS premium is determined and the CMDS protection premium is reset to 90% of the new value.

Since CDS contracts begin to trade with points upfront as the underlying Reference Entity becomes distressed, CMDS contracts typically set a cap on the reference constant maturity CDS premium. If the underlying spread widens above the cap, say 900 basis points, the CMDS premium stays at the cap multiplied by the percentage factor.

There are several possible mechanisms for determining the reference constant maturity CDS premium on CMDS reset dates. A dealer poll average may be used as the reference constant maturity premium. Alternatively, depending on the wishes of the counterparties, a pricing service or a single calculation agent could be used.

 

CMDS Strategies

The constant maturity contract allows investors to buy protection without taking on spread exposure. Figure 1 shows the spread DV01 of a five-year CMDS contract as a function of the initial CDS curve along with the spread DV01 of a standard CDS contract. The CMDS contract resets quarterly, has a constant reference maturity of five years, and includes a 900bps cap. The spread DV01 of the CMDS is virtually zero, while the spread DV01 of the CDS is in the neighborhood of 4.5 depending on the initial CDS spread level.

Unlike a simple CDS contract, however, the CMDS is sensitive to the entire curve out to 10 years. Figure 1 also breaks out the sensitivity to small shifts of the CDS curve front-end while holding constant the back-end, as well as the sensitivity to small curve shifts in the back-end of the curve while holding constant the front-end. The front- and back-end sensitivities are relatively large in absolute value (around 6) but have opposite signs. The net spread DV01 of the CMDS contract is simply the sum of the two sensitivities.

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Small increases in the front-end of the CDS curve increase the likelihood of default and lower the forward reference constant maturity CDS rates. This results in a spread DV01 that is higher than the spread DV01 of a simple CDS, which reflects only the higher default probability. Increases in the CDS curve beyond the five-year point affect only the reference constant maturity forward rates, not the likelihood of receiving them. In Figure 1, the short- and long-end curve sensitivities offset to produce a spread DV01 of close to zero. The high front- and back-end curve spread DV01s of the CMDS contract imply a slope sensitivity, which is discussed below.

Figure 2 shows the instantaneous mark-to-market on a five-year CMDS and CDS contract as the underlying CDS curve changes. Initially, both instruments are priced on a 60bps flat CDS curve. As expected, the CMDS exhibits low mark-to-market sensitivity relative to the CDS contract even for large parallel spread moves.

This result demonstrates how investors can use CMDS in conjunction with CDS to decouple spread and default risk. To achieve exposure solely to default risk--either long or short--investors can transact in CMDS. To create a spread exposure without default risk, investors can enter a CMDS contract with an offsetting CDS position.

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CMDS Valuation & Sensitivities

The value of a CMDS contract depends on the entire forward CDS curve with the last maturity equal to the term of the CMDS contract plus the reference constant maturity. For example, a typical five-year CMDS contract with a five-year reference constant maturity is sensitive to the entire CDS curve up to 10 years. The four-year forward CMDS rate is dependent on the four-year forward five-year CDS premium, which in turn is influenced by the nine-year point. For this reason, we expect CMDS markets to first appear for Reference Entities with liquid curves out to the 10-year point, such as the autos, telecoms, and some sovereigns.

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The CMDS contract value also depends on the CDS spread volatility term structure. To see why, consider the extreme case of zero spread volatility. The future CMDS premiums are known to be the forward five-year CDS rates. In this case, the CMDS percentage factor is 100%--the premiums are simply the forward five-year CDS rates.

Spread volatility introduces a downward adjustment of the forward CDS premiums when setting CMDS rates. The theoretic reason for this adjustment is that the future CMDS premium settings last for a short period, say, a quarter, relative to the reference constant maturity. Dynamic hedging of these settings using the forward CDS markets (if these are liquid) would exhibit convexity, which results in a downward adjustment of the forward CDS rates.

The volatility term structure also impacts the value of the cap. The higher the forward CDS spreads relative to the cap level and the higher the assumed spread volatility, the greater is the value of the cap. In extreme cases--a low cap level relative to today's CDS spread and high spread volatility--the value of the cap could overwhelm the convexity adjustment resulting in CMDS percentage factors greater than 100%.

The theoretical sensitivity of the CMDS percentage factor to the implied volatility is presented in Figure 3. For the range of flat volatility term structures in the figure, the percentage factor decreases dramatically with higher volatility values. We assume a flat CDS premium curve of 60bps and a 900bps cap.

As we alluded above, the CMDS sensitivity to curve slope changes is much greater than the sensitivity of a simple CDS. Figure 4 shows the instantaneous mark-to-market of both instruments for a range of 5s-10s CDS spreads. The initial flat CDS curve is set at 60bps. Selling CMDS protection provides curve exposure similar to a 5s-10s curve steepener.

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This week's Learning Curve was written by Alex Reyfman, head of credit derivatives research at Bear Stearnsin New York.

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