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Greek Debt Default: Investors' and Risk Managers' Perspective
What do Bond Holders Receive after the First Eurozone Default in terms of Greek WriteDown, Portfolio Duration and CDS Credit Event Triggering?
April, 2012
According to the terms of the
Greek PSI agreement for debt restructuring,
holders of sovereign Greek bonds will be delivered a portfolio of EFSF "PSI notes" and
New Greek Bonds. In the context of the
European debt crisis, we calculate the price of the new portfolio to be 211€ for each 1000€ of initial face value, whatever the particular bond being held, 150€ (71%) of EFSF note, 61€ (29%) of New Greek Bonds, the GDPlinked securities counting for less than 0.2%. The combined Duration of the two EFSF notes is 1.5, while that of the New Greek Bonds is close to 10 years. The first phase of the swap, involving bonds issued under Greek law, was completed on March 12, cancelling more than 94.8 billion Euros in near and midterm debt. The deadline for Greek Debt securities issued under foreign law has been
extended to April 4, but the
Greek Ministry of Finance has warned that investors who refused
voluntary exchange would be forced to accept the same swap terms. Moreover the International Swaps and Derivatives Association (ISDA), which manages Credit Default Swap (CDS) rules, has declared
that a
Restructuring Credit Event
has occurred with respect to the Greek Private Sector Involvement (PSI). A
CDS auction on Mar 19, 2012
has valued sovereign Greek bonds at 21.5% of their face value for the purpose of
CDS settlement.
With the European Crisis in mind, a sufficient proportion of bond holders has accepted the swap provisions that will ultimately become mandatory for all investors. Moreover, whatever the term structure of previous bonds, they are being uniformly exchanged for a set of securities with clearly predefined characteristics. Specifically, 1000€ face value of old sovereign Greek bonds is replaced by a new basket with a combined face value of 465€: 150€ for EFSF notes (equally split between 1year and 2years) and 315€ for a set of New Greek Bonds, producing as a whole an amortizing structure from 11 years to 30 years (see Fig. 1). The GDPlinked securities represent a small coupon enhancement in case the Greek GDP meets certain conditions of level and growth. They have little impact on either price and or risk profile of the combined structure. Altogether, the portfolio of New Greek Bonds has an average duration of slightly under 10years (see Fig. 2). In terms of market value as of today, while the EFSF notes are approximately equal to their face value, the portfolio of New Greek Bonds is worth 61€ and the GDPlinked securities amount to a fraction of a Euro (exact price depending on Greek growth assumptions), making the whole structure slightly above 211€.
Fig. 1
Green bars represent the face value amount paid by the Hellenic Republic on Feb 24 of each year. Purple complements are the expected enhancement due to the GDPlinked securities, assuming an optimistic hypothesis that the coupon will gradually start being paid in 2020 up to being fully paid in 2030 and onwards. The orange bars represent the current value of these payments after discounting by the current zerocoupon yield curve (right scale), assuming yields based on current prices of the New Greek Bonds: 20% up to 11yrs, decreasing to 17.3% at 30yrs. Small brown complements on top of orange bars represent the discounted value of the GDPlinked coupon payments.
Fig. 2
Key Rate Durations are represented in this graph. The resulting modified Macaulay duration is indicated by the orange arrow: 9.79 years.
Greek Debt Terms of the Exchange
According to the terms of the exchange, holders of eligible bonds will receive, in exchange of each title with face value 1000€, regardless of the maturity of the title, a basket consisting of:
 Two interest bearing notes from the EFSF called "PSI Payment Notes"
 Each with face value 75€, for a total face value of 150€
 Maturing Mar 12, 2013 and Mar 12, 2014 respectively
 The interest rate, to be paid each year, will be EFSF's usual borrowing rate, around 0.30%0.50%.
 A sequence of 20 bonds issued by the Hellenic Republic called "New Bonds"
 Maturing on Feb 24 of each year from 2023 to 2042.
 Bonds with maturity from 2023 to 2027 have a face value of 15€, bonds with maturity from 2028 to 2042 have a face value of 16€, for a total face value of 315€
 For each bond, coupons are paid every year on Feb 24, with values depending on the payment date:
 2% from 2013 to 2015
 3% from 2016 to 2020
 3.65% in 2021
 4.3% from 2022 to 2042
 A "GDPlinked bond" issued by the Hellenic Republic, which is meant at enhancing the coupon of the outstanding New Bonds (i.e. not yet matured) in case the Greek GDP and growth reaches certain conditions.
 The GDPlinked Bond pays only interests, no principal.
 Payment dates are Oct 15 of each year between 2015 and 2042
 Interests are computed each year y on a face value amount N(y) which starts at 315€, then decreases by 15€ each year from 2024 to 2028, then 16€ from 2029 to 2042
 Each year y, the growth rate g(y) with respect to the previous year is computed with respect to the current GDP G(y), that of the previous year G(y — 1) and the inflation rate:
 g(y) = G(y)/G(y — 1) x I(y — 1)/I(y) — 1
where I(y) is the inflation index for year y
 g(y) is compared to a reference rate r(y) and the difference c(y) = g(y) — r(y) is capped and floored within the interval [0%, 1%]
 The GDP G(y) itself is compared to a reference GDP value R(y)
 If G(y) < R(y) then the GDPlinked bond delivers no coupon, in other words, the only coupon being paid is that of the New Bonds, as stated above
 If G(y) > R(y) then the GDPlinked bond delivers, on top of the New Bonds, a coupon equal to N(y) x c(y), which can still equal 0 if g(y) < r(y), and will never exceed 1% x N(y)
 Assuming that c(y) will reach its cap value 1% every year, the GDPlinked bond represents a small fraction of the New Bonds, themselves having altogether a lesser value than the EFSF notes. Due to the low probability of such an event and, on the contrary, to the high probability of the event c(y) = 0, the GDPlinked security represents a marginal improvement of the set of New Bonds in value.
Consequences for the Risk Computation
The portfolio risk implications of the exchange for Greek bond holders are fairly easy to explain: owners of Greek bonds for a total face value of N€ will all get the same portfolio of bonds with a face value proportional to their initial face value amount N. As explained above, the portfolio consists of 3 pockets:

EFSF notes delivering N x (1 + 2r) x 0.075 on 03/12/13 and N x (1 + r) x 0.075 on 03/12/14 where r is the applicable borrowing interest rate by EFSF, not set yet, but will probably be between 0.30% and 0.50%.
 This can be modeled by a combination of two bonds maturing on 03/12/13 and 03/12/14, with face value N x 0.075, coupon r and yearly frequency
 The level and risk of the EFSF yield curve can be taken as that of Germany, its most solid guarantor
 The combined value of the two EFSF notes is close to their face value, i.e. 15% of the initial face value prior to restructuring.
 The sequence of New Greek Bonds can be summarized in a cash flow schedule as follows (see fig. 1), where percentages on each date are to be taken with respect to the initial face value N:
Table 1
Date  Payment  Date  Payment  Date  Payment 
2/24/2013  0.6300%  2/24/2023  2.8545%  2/24/2033  2.2880% 
2/24/2014  0.6300%  2/24/2024  2.7900%  2/24/2034  2.2192% 
2/24/2015  0.6300%  2/24/2025  2.7255%  2/24/2035  2.1504% 
2/24/2016  0.9450%  2/24/2026  2.6610%  2/24/2036  2.0816% 
2/24/2017  0.9450%  2/24/2027  2.5965%  2/24/2037  2.0128% 
2/24/2018  0.9450%  2/24/2028  2.6320%  2/24/2038  1.9440% 
2/24/2019  0.9450%  2/24/2029  2.5632%  2/24/2039  1.8752% 
2/24/2020  0.9450%  2/24/2030  2.4944%  2/24/2040  1.8064% 
2/24/2021  1.1498%  2/24/2031  2.4256%  2/24/2041  1.7376% 
2/24/2022  1.3545%  2/24/2032  2.3568%  2/24/2042  1.6688% 
 Such a cash flow schedule can be modeled by a sequence of zerocoupon bonds with face values given by the specified percentage of the initial face value N.
 Applying a discounting rate corresponding to the current Greek yield curve, that is, 20% up to 15 yrs, sloping down to 14% at 30 yrs, the combined value of the New Bonds is approx. 6.1% of the face value, which represents 29% of the whole structure, incl. EFSF notes.
 The GDPlinked bond is rather hard to model because of its complexity, depending on both the GDP value and growth rate.
 For the short to medium term market risk, it can simply be modeled as a sequence of cash flows with expected values at each date, like the New Greek Bonds;
 Longterm risk modeling (several years) may require a model for the growth rate and the inflation rate.
 The table below shows the enhancement of the New Bonds coupons one can optimistically expect from the GDPlinked bond: at best 3% of the total value of the New Greek Bonds and 1% of the whole structure.
Table 2
Date  New Bond  Max GDP Coupon  Expected Coefficient  Exp. GDP Coupon  Total 
Total  6.11%  1.10%  —  0.20%  6.30% 
2/24/2013  0.6300%  —  —  0.6300%  — 
2/24/2014  0.6300%  —  —  0.6300%  — 
2/24/2015  0.6300%  0.3150%  0  0.0000%  0.6300% 
2/24/2016  0.9450%  0.3150%  0  0.0000%  0.9450% 
2/24/2017  0.9450%  0.3150%  0  0.0000%  0.9450% 
2/24/2018  0.9450%  0.3150%  0  0.0000%  0.9450% 
2/24/2019  0.9450%  0.3150%  0  0.0000%  0.9450% 
2/24/2020  0.9450%  0.3150%  0.1  0.0315%  0.9765% 
2/24/2021  1.1498%  0.3150%  0.2  0.0630%  1.2128% 
2/24/2022  1.3545%  0.3150%  0.3  0.0945%  1.4490% 
2/24/2023  2.8545%  0.3150%  0.4  0.1260%  2.9805% 
2/24/2024  2.7900%  0.3000%  0.5  0.1500%  2.9400% 
2/24/2025  2.7255%  0.2850%  0.6  0.1710%  2.8965% 
2/24/2026  2.6610%  0.2700%  0.7  0.1890%  2.8500% 
2/24/2027  2.5965%  0.2550%  0.8  0.2040%  2.8005% 
2/24/2028  2.6320%  0.2400%  0.9  0.2160%  2.8480% 
2/24/2029  2.5632%  0.2240%  1  0.2240%  2.7872% 
2/24/2030  2.4944%  0.2080%  1  0.2080%  2.7024% 
2/24/2031  2.4256%  0.1920%  1  0.1920%  2.6176% 
2/24/2032  2.3568%  0.1760%  1  0.1760%  2.5328% 
2/24/2033  2.2880%  0.1600%  1  0.1600%  2.4480% 
2/24/2034  2.2192%  0.1440%  1  0.1440%  2.3632% 
2/24/2035  2.1504%  0.1280%  1  0.1280%  2.2784% 
2/24/2036  2.0816%  0.1120%  1  0.1120%  2.1936% 
2/24/2037  2.0128%  0.0960%  1  0.0960%  2.1088% 
2/24/2038  1.9440%  0.0800%  1  0.0800%  2.0240% 
2/24/2039  1.8752%  0.0640%  1  0.0640%  1.9392% 
2/24/2040  1.8064%  0.0480%  1  0.0480%  1.8544% 
2/24/2041  1.7376%  0.0320%  1  0.0320%  1.7696% 
2/24/2042  1.6688%  0.0160%  1  0.0160%  1.6848% 
For a total face value of 465€, while the EFSF notes can be considered as being priced at face value, that is, 150€, the current price of the New Greek Bonds is 61€ (19.4% of the face value) and the GDPlink securities amount to between a fraction of a Euro and at best 2€ in an optimistic scenario, as assumed in the table.
Impact of the PSI agreement on Greek yields
As one could expect, sovereign Greek yields sharply dropped after the exchange proposal was accepted. Bonds that traded with yields above 30% (and even over 1000% for the short term) mechanically saw their yields drop, once the new face value has been taken into account. The fact that 10yrs yields still are higher than 30yrs ones is an indication that markets anticipate another restructuration of the Greek debt.
NYU Prof. Nouriel Roubini
supports this idea, although Former Argentinian Economy Minister Cavallo,
talking with experience in Bloomberg Businessweek, has doubts that this will be necessary.
Fig. 3
This Bloomberg® chart of the 10Y sovereign Greek yield shows the mechanical drop on March 12 from 36.55% to 18.45% upon restructuring, corresponding to the change in face value.
Duration and Risk Analysis
The risk profile of such a portfolio can already be accurately described, regardless of its original term structure: Firstly, the swap provisions have already been accepted by a sufficient proportion of bond holders to ultimately become mandatory for all investors; Secondly, whatever the term structure of previous bonds, they are being exchanged against a set of instruments with clearly predefined characteristics. The coupon being very low, each EFSF note has duration close to its maturity and the combination of the two has duration about 1.5yrs. Altogether, the portfolio of New Greek Bonds has an average duration of 9.8 years. As said above, the GDPlinked securities have little impact on either price and on the risk profile of the combined structure.
Table 3
10y Yield  Duration  NGB Price 
15%  12.34  98.05 
16%  11.78  88.20 
17%  11.24  79.81 
18%  10.73  72.62 
19%  10.24  66.42 
20%  9.79  61.04 
21%  9.36  56.36 
22%  8.96  52.25 
23%  8.58  48.63 
24%  8.23  45.42 
25%  7.89  42.57 
Assuming that the yield curve is parallel shifted with respect to its current position, and ignoring the GDPlinked payments, the duration of the New Greek Bonds stream of payments is given by the above table, where the first column is the assumed 10Y yield (currently 20.3%).
Some sources on the PSI debt restructuring operation
The exact terms of the exchange are provided by the Greek Ministry of Finance
Summaries by brokers
Results of the PSI votes (Eurobank research)
On the fact that restructuring does trigger CDS and March 19 auction
On the level of yields after restructuring:
Wikipedia articles on European and Greek sovereign debt crisis

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