This presentation explores the evaluation issues associated with Credit Default Swap Basis trades.

1. The Opacity of the CDS Basis
Gaetan Lion
March 30, 2012 1

2. Why is this an important topic?
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3. CDS is a huge Business
Nominal CDS contract outstanding exceeds World GNP.
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4. Two CDS Buyers have made a huge
amount of money
Michael Burry, the “one eyed
surgeon”, will create the first
CDS on Subprime CDOs with
Greg Lippman from Deutsche
Bank in 2005. Dr. Burry will
make $100 million for himself
and about $700 million for his
clients.
John Paulson enters this CDS on
Subprime CDOs market in 2006. He
will make $7 billion for himself and $23
billion for his hedge fund clients.
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5. Several CDS Sellers have lost a huge
amount
Also, European banks who invested in Synthetic CDOs
were by definition CDS sellers. They were the ones on the
other side of the trades who lost money to Michael Berry
and John Paulson. 5

6. CDS is a great source of Credit Risk
Information
Very Different Credit Risk for major US Banks.
6

7. People are focusing on the CDS Basis
CDS Basis = CDS premium – Bond Credit Spread. 7

8. Some Institutions have incurred large
losses on CDS Basis trades
In early 2009, Merril Lynch, Deutsche Bank and
several hedge funds did lose several $billions on CDS
basis trade commonly known as Negative Basis
trade*.
*When the CDS premium is lower than the Bond
spread, a trader buys the Bond (ie. Credit Spread
4%) and buys the CDS (pays premium 3%) and earns
a spread (1%) between the two… ideally anyway?!
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9. CDS & CDS Basis Introduction
9

10. CDS intro
The CDS buyer (the The CDS seller
insured) pays a credit sells credit
insurance premium on insurance against
a specific bond issuer, the default of a
covering the latter’s specific bond issuer
credit risk for the and receives a
duration of the CDS premium from the
contract. CDS buyer.
If the bond issuer
defaults, the CDS
seller (the insurer)
repays the CDS
buyer the par value
of the bond.
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11. A CDS is a Put Option on the Bond Par value
CDS Buyer pays a premium and "Puts" the Bond back to the Buyer in case of default.
CDS
value
positive
+
0% Repayment prob. or (1 - Default prob.) 100%
CDS Seller receives premium and repays Bond par value to the Buyer in case of default.
CDS
value
positive
+
Premium
0% Repayment prob. or (1 - Default prob.) 100%
CDS
value
negative
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12. Change in Default Probability impacts
CDS value
CDS Buyer pays a premium and "Puts" the Bond back to the Buyer in case of default.
Incr. in Default prob. Decrease in Default prob.
CDS
value
positive
When the Default probability
+ increases, the CDS value
rises and the CDS Buyer’s
CDS
0% Repayment prob. or (1 - Default prob.) 100%
Put is in the money. He can
value
negative resell it at a profit.
-
CDS Seller receives premium and repays Bond par value to the Buyer in case of default.
CDS Incr. in Default prob. Decrease in Default prob.
value
positive
+ Premium
0% Repayment prob. or (1 - Default prob.) 100%
CDS
value
negative
-
12

13. CDS Basis
CDS Basis = CDS premium – Bond Spread over Rfr.
In theory, under the no-arbitrage principle, the CDS
Basis would equal zero. In reality, the CDS Basis is
always away from zero, either positive or negative.
Positive Basis: CDS > Bond Spread
Negative Basis: CDS < Bond Spread
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14. Choices of Bond Spreads
That’s when
it gets foggy
(opaque)
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15. Clarity vs Opacity
Clarity: A CDS quote is crystal clear. The
premium is expressed in basis points per
annum.
Opacity: the Bond spread is calculated. And,
there are several underlying issues.
1) What is the appropriate discount rate (Rfr)?
2) What is the appropriate Spread calculations?
Different Spread calculations can result in the
CDS Basis changing sign!
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16. The Evolution of Bond Spread Calculations
1 Bond Spread: Bond Yield - Treasuries of same term.
2 Bond Spread: Bond Yield - Treasuries tax adjusted
Adjustment for Treasuries being State tax exempt.
3 Asset Swap Spread (ASW): Asset Swap Rate - LIBOR
Disaggregates Credit Risk from Interest Rate Risk.
Takes into account the term structure of interest rates.
4 Z-Spread or Zero Coupon Spread.
Uses Treasuries instead of LIBOR to construct term structure of interest rates.
5 I-Spread or Interpolated Spread.
Uses interpolated Treasury rates. A variation of the Z-Spread.
6 Option Adjusted Spread (OAS)
Takes into account the term structure of probabilities of default by
constructing a survival probability curve.
Legend
Not the main Spread established benchmark anymore.
Currently most common ones. Quoted on Bloomberg.
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17. Bond Spread vs ASW, Z-Spread, I-Spread
Difference in Spread Calculation
12%
Bond Spread ASW, Z-Spread, and I-Spread
10%
8%
Credit
Spread
6%
4% Rfr3
Rfr Rfr2
2%
Rfr1
0%
Constant rate
1 2 Period 1
3 Period 2
4 Period 3
5
Within the Bond Spread method, cash flows are discounted at the same rate.
Within the other Spreads, cash flows discounting reflects the term structure of
interest rates. Notice that the Credit Spread component is constant within either
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method. That’s even though the derived Credit Spread may be different.

18. Bond Spread vs OAS
Difference in Spread Calculation
14%
OAS
12%
Bond Spread
10% CS3
8% Credit
Spread CS2
6% (CS)
Rfr3
4% CS1
Rfr Rfr2
2% Rfr1
0%
Constant rate
1 2 Period 1
3 Period 2
4 Period 3
5
The Option Adjusted Spread (OAS) method of discounting captures
both the term structure of interest rates and credit risk or defaults. They
are low in Period 1 and continue rising in all future periods. The OAS is
the Credit Spread that corresponds to the discounted PV weighted of all
the various Credit Spreads (CS1, CS2, CS3, etc…). 18

19. The Asset Swap Spread
7%
Fixed rate 7% Bd. Investor I.R. Swap
bond Counterparty
LIBOR + 3% (ASW)
An Investor invests in a fixed rate bond paying 7%. To hedge his
interest rate risk, he enters into an Interest Rate Swap with a
counterparty and passes on the 7% fixed rate payment in exchange for
floating rate LIBOR + 3%. The 3% is the Asset Swap Spread (ASW).
PV of 7% fixed rate payments = PV LIBOR + 3% payments
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20. Asset Swap with a CDS
7%
Fixed rate 7% Bd. Investor I.R. Swap
bond CDS Buyer Counterparty
LIBOR + 3% (ASW)
CDS premium
3%
CDS
Seller
The Bond Investor has already hedged his interest rate risk. He now
wants to hedge his credit risk. He buys a CDS on the bond issuer and
pays a CDS Seller a premium.
Now, we can define the CDS Basis: CDS premium – ASW.
In this case it is zero. Net result, Investor earns Libor.
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21. Asset Swap with CDS at Default
7%
Bd. Investor I.R. Swap
CDS Buyer Counterparty
LIBOR + 3% (ASW)
Puts
pays Bd
Bonds
Par value
Bond issuer. Puts
Ch 11 or 7: Bonds CDS
Reorg./ Seller
Recovery
Liquidation
Note that for the initial Bond Investor the Interest Rate Swap is still going on!
He can unwind that swap, but he is now exposed to a mark-to-market risk on
this IR swap. While the Bond issuer was solvent, the Bond Investor’s interest
rate risk was hedged. But, upon default it is not.
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22. Factors affecting the CDS Basis
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23. Basic Economic Principles
Any factor increasing the risk of a CDS Seller relative to the
ASW will increase the CDS basis (and vice versa).
Any factor increasing the return of a CDS Seller relative to
the ASW will decrease the CDS basis (and vice versa).
Any factor boosting the Demand for CDS (Seller side)
relative to the ASW will increase the CDS basis (and vice
versa).
Any factor boosting the Supply for CDS (Seller side) relative
to the ASW will decrease the CDS basis (and vice versa).
Those concepts of Risk, Return, Demand, Supply are
universal and affect all insurance products (car insurance,
etc…).
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24. Some Factors affecting the CDS Basis
• Change in interest rates (+ or -);
• Funding considerations (+ or -);
• Relative liquidity (bid & ask spread) in both markets (+ or -);
• Synthetic CDO Issuance, Loan syndication, etc…: It boosts
Seller Supply (-);
• Relative counterparty risk considerations (CDS Seller credit
quality vs Interest Rate Swap counterparty risk);
• Difficulty in shorting bonds: when CDS basis > 0, arbitrage
of selling the CDS and selling the bond is rarely feasible (+).
• CDS credit event trigger definition is often broader than for
the Bond. It increases the CDS Seller risk (+).
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25. Change in Interest Rates
1. At time of default, the loss of the CDS Seller is equal to
Par value of the bond minus recovery. The loss of
bondholder is Market value of the bond minus recovery.
If interest rates have risen:
Market value < Par value; and
CDS loss > Bondholder loss.
And, vice versa. This affects the CDS basis accordingly.
5. Change in interest rates also affect the mark-to-market
value of the embedded interest rate swap within the asset
swap structure (ASW). Remember, the interest rate swap
survives after default!
6. Change in Repo rates affects ability to short a bond. But,
it is really difficult to short a bond anyway.
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26. Funding Considerations
When you invest in the Credit risk of a
company by purchasing a bond you pay
money. If you invest in Credit risk by selling a
CDS you actually receive money (premium).
Thus, changing capital market conditions affect
CDS and Bonds differently.
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27. An Arbitrage Opportunity Decision Tree
Major Fog
Warning
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28. The Basic Decision Tree
CDS > OAS No arbitrage
CDS < ASW
CDS < OAS Negative basis trade: buy Bond & buy CDS
CDS > OAS No arbitrage
CDS > ASW
CDS < OAS Negative basis trade: buy Bond & buy CDS
You can’t rely on just the Asset Swap Spread (ASW) or its
equivalents (Z-Spread, I-Spread). You have to look at the
Option Adjusted Spread (OAS).
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29. The OAS Decision Tree
> Bid & Ask Spreads Negative basis trade
[CDS < OAS]
< Bid & Ask Spreads No arbitrage
The absolute value of the CDS negative basis has to be
greater than related Bid & Ask spreads. Otherwise, the
transaction costs eliminate the arbitrage opportunity.
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30. Opacity?!
OAS Model underestimated factors Negative basis trade loses money
[CDS < OAS]>Bid-Ask
OAS Model got it right Negative basis trade is profitable
The mentioned factors are the ones affecting the CDS Basis
described earlier. Several are qualitative in nature and
challenging to predict and quantify precisely. It is uncertain
whether such OAS models can provide reliable information.
This questions the viability of arbitrage opportunities.
[CDS < OAS]>Bid-Ask Arbitrage opportunity
or disaster?
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31. Appendix Section
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32. Working Papers Findings
Working papers analyzing the CDS Basis (using mainly
the I-Spread as proxy for Bond Spread) through various
time periods from January 1999 through December
2005 have found the following:
2) CDS Basis: the Average CDS basis is very small and
typically positive (ranging from – 2 bp to 16 bp). The
Median is even smaller (0 to 7 bp). The CDS Basis can
depend on time, place (US vs Europe), and company.
3) Price discovery: using sophisticated methods* they
found that at times CDS tend to lead bonds spreads. It
is more so in the US, and less so in Europe.
*Cointegration, Granger Causality, VECM methods.
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33. Morgan Stanley CDS vs Bond Spread
Between 8/31 and 11/24/2011 the Bond Spread (Bond Yield – Treasury) has been
much higher than the CDS. For other time periods, the reverse may have been 33
observable.

34. CDS always lead in both the decline and increase in credit risk until
convergence in early 2010.
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35. As the title suggests, Italian bond spreads take the lead in May 2011.
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36. Here Spain CDS clearly lead bond spread for an entire year, until the
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two converge by second half of 2010.

37. Except for a couple of quarters in 2009, Belgian CDS are chronically
higher than Belgian bond spreads. 37

38. For Further Study read this book
Moorad Choudhry, the author, is Head of
Treasury at Corporate Banking Division,
Royal Bank of Scotland, a Visiting
Economics Professor at London
Metropolitan University, a renowned
expert on CDS, and an avid cricket
player.
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