How profitable is capital structure arbitrage?

38 Pages·2005·0.31 MB·English

How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 1
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How pro(cid:222)table is capital structure arbitrage?
Fan Yu
University of California, Irvine
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 2
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Fresh off the press...
(cid:147)The most signi(cid:222)cant development since the invention of the credit
default swap itself nearly 10 years ago.(cid:148)
(cid:147)Trading default protection versus equity is going to become the
hottest strategy in the arbitrage community next year.(cid:148)
(cid:147)For bank prop desks, it(cid:146)s the next big thing, a handy strategy to
replace the riches several garnered from playing the interest rate
and forex markets.(cid:148)
(cid:150)Euromoney, December 2002
(cid:147)During May and June, capital structure arbitrage was one of the
few hedge fund techniques in positive territory.(cid:148)
(cid:150)Financial Times, July 21, 2004
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 3
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What is a credit default swap?
A credit default swap (CDS) is an insurance contract against
(cid:149)
credit events such as the default on a bond by a speci(cid:222)c issuer
(the obligor).
The buyer pays a premium to the seller once a quarter until
(cid:149)
the maturity of the contract or the credit event, whichever
occurs (cid:222)rst.
The seller is obligated to take delivery of the underlying bond
(cid:149)
from the buyer for face value should a credit event take place.
The de(cid:222)nition of the credit event can include bankruptcy,
(cid:149)
failure to pay, or restructuring.
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 4
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What is capital structure arbitrage?
The capital structure arbitrageur uses a structural model to
(cid:149)
gauge the richness/cheapness of the CDS spread.
The model, typically a variant of Merton (1974), predicts
(cid:149)
spreads based on a company(cid:146)s liability structure and its market
value of equities.
When the arbitrageur (cid:222)nds that the market spread is
(cid:149)
substantially larger than the predicted spread, he sells CDS
and sells equity.
When the arbitrageur (cid:222)nds that the market spread is
(cid:149)
substantially smaller than the predicted spread, he buys CDS
and buys equity.
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 5
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If market disagrees with model...
The equity market may be more objective, and the CDS
(cid:149)
market may be gripped by fear.
Or, it may be the other way around. The CDS market is
(cid:149)
correct, and the equity market is slow to react.
The equity position is determined by delta-hedging, lest the
(cid:149)
arbitrageur guessed wrong.
Caveats:
(cid:149)
(cid:151) The model itself can be misspeci(cid:222)ed.
(cid:151) Inputs to the model can be mis-measured.
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 6
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Possible scenarios when shorting
1. c , S . The arbitrageur pro(cid:222)ts from both positions.
t t
↓ ↓
2. c , S . The arbitrageur loses from equity but pro(cid:222)ts from
t t
↓ ↑
CDS.
3. c , S . The arbitrageur loses from CDS but the equity
t t
↑ ↓
position acts as a hedge against this loss.
4. c , S . The arbitrageur suffers losses from both positions
t t
↑ ↑
regardless of the size of the equity hedge.
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 7
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Research questions
Apparently, this is no textbook arbitrage.
(cid:149)
If this is merely taking risk, what is the risk involved?
(cid:149)
What is the risk and return of this strategy? Any abnormal
(cid:149)
return after adjusting for risk?
Does this constitute (cid:147)statistical arbitrage(cid:148)?
(cid:149)
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 8
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Related literature
The performance of structural models for pricing CDS.
(cid:149)
(cid:151) Jones, Mason, and Rosenfeld (1984), Eom, Helwege, and
Huang (2004), and Ericsson, Reneby, and Wang (2004).
The methodology is similar to Duarte, Longstaff, and Yu
(cid:149)
(2005) on (cid:222)xed income arbitrage, and Mitchell and Pulvino
(2001) on merger arbitrage.
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 9
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Capital structure arbitrage started with trading bonds against
(cid:149)
CDS, or bonds against equities.
(cid:151) Bond spread vs. CDS spread. Duffie (1999), Hull, Predescu,
and White (2003), Houweling and Vorst (2003), Blanco,
Brennan, and Marsh (2003).
(cid:151) Bonds versus equities. Schaefer and Strebulaev (2004),
Chatiras and Mukherjee (2004).
(cid:151) Lead-lag relations. Longstaff, Mithal, and Neis (2003),
Berndt and de Melo (2003), Zhu (2004).
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How pro(cid:222)table is capital structure arbitrage? Universit·e d(cid:146)Evry June 2005 10
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CDS pricing
First, the present value of the premium payments is equal to
(cid:149)
T s
E c exp r du 1 ds .
u τ>s
−
ˆ 0 0 { } !
Z (cid:181) Z ¶
Second, the present value of the credit protection is equal to
(cid:149)
τ
E (1 R) exp r du 1 .
u τ<T
− −
{ }
0
(cid:181) (cid:181) Z ¶ ¶
The CDS spread is then determined by setting the initial value
(cid:149)
of the contract to zero:
T
(1 R) P (0, s) q (s) ds
0 00
c = − .
T
−
P (0, s) q (s) ds
R 0
0
R
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