Credit & Equity-Linked Strategy
Capital Structure ‘Arbitrage’
A Tradable Dollars and Cents Approach
Please refer to important disclosures on page 12 and Analyst Certification on page 11.
A Tradable Relative Value Approach
Credit and equity risk are unambiguously linked as the risk of debt holders not
receiving their claims is the risk of equity prices falling to zero.
Both credit and equity risk are directly tradable with derivatives in the
marketplace - credit default swaps and equity puts for instance. The close
similarity between credit and equity derivatives has recently led the marketplace to
search for any mis-pricing between these two asset classes.
At the forefront of understanding the linkages between credit and equity
valuations are structural models such as KMV and CreditGrades which are based
on Merton, Black and Scholes academic work in the early 70’s on evaluating
corporate liabilities. In short, these models use inputs from the equity market to
evaluate credit instruments, however they do not seek to identify trade
opportunities that capitalize on the potential mis-pricing of credit and equity
Our approach consists of searching the universe of liquid credit and equity
derivatives in order to identify tradable long / short pairs where either the credit
or equity risk may be mis-priced. Because credit and equity derivatives markets
operate largely independently, this can easily lead to the relative mis-pricing of the
Correlation between Credit and Equity Risk
TRACERS CDS vs S&P 500 Option Implied Volatility
Daily Data from Apr 23, 02 to Oct 22, 03
CDS Pricing vs Option Implied Volatility
As of Oct 22, 03
The cost of ‘Credit Protection’ (measured by the pricing of Credit Default Swaps) correlates
with the cost of ‘Equity Protection’ (measured by equity option implied volatilities), on the
aggregate over time (left chart) as well as cross-sectionally at one point in time (right chart).
Neither relation is perfect, however, and credit and equity risk may be mis-priced relative to
0 50 100 150 200 250 300 350 400 450 500
Apr 02 Jun 02 Aug 02 Oct 02 Dec 02 Feb 03 Apr 03 Jun 03 Aug 03 Oct 03
S&P 500 Implied Volatility
Short CDS vs Long Equity Put: Trade Mechanics
Searching for cases where the premia of a short CDS position exceed the cost of an equity put
Calculate the present value of CDS premia over the duration of the put option contract;
the present value approach is used to address any potential timing mismatches between the
CDSs, which most commonly trade with 5 year maturity, and the listed equity puts, where the
longest available expiration is currently Jan 06.
Determine the potential CDS liability, i.e. ( 1 - Recovery ) x CDS Notional.
Make an assumption what the stock price will be should debt default occur, e.g. $0.75
which was the average price for former S&P 500 companies at the time of default.
Determine the number of puts necessary to hedge the estimated credit risk, i.e. CDS
Liability / ( Put Strike - Assumed Stock Price if Default).
Determine the cost of the equity put credit hedge, i.e. Number of Puts x Put Ask Price.
Two decision variables:
Given a recovery assumption, does the present value of CDS premia over the life of the
Jan 06 option pay for the put hedge?
What recovery value equates the cost of the put hedge to the present value of CDS
premia over the duration of the put option?
Short CDS vs Long Equity Put: Screening for Opportunities
Open Interest as an Option Liquidity Measure:
91,082 contracts are outstanding, i.e. credit
protection worth $84,250,850 = 91,082 * 100 *
($10.00 - $0.75) = Open Interest x Multiplier x
(Strike Price - Default Stock Price Assumption).
Cost of Put Hedge:
$7.46 = (1 - Assumed Recovery) *100 /
(Strike Price - Assumed Stock Price if
Default) * Put Ask Price = ( 1 - 40% ) * 100 /
( $10 - $0.75 ) * $1.15.
Present Value of CDS Premia:
The value of CDS premia over the duration of
the put contract discounted by the libor rate
and adjusted for the probability that the CDS
premia will not be received should default
Decision Variable 1:
PV of the CDS premia exceeds the cost of the
put Hedge by $1.50 (assuming 40% recovery).
Decision Variable 2:
PV of the CDS premia equals the cost of a put
hedge if recovery equals 27%.
assumed bid premium pv
ask open strike stock stock price price assumed through cost of pv cds break-even
ticker name price interest price price if default (bp) recovery Jan 06 put hedge - put hedge recovery
EIX Edison International 1.10 9,000 15.0 19.82 0.75 474 40% 9.61 4.63 4.98 --
GM General Motors 0.50 7,934 10.0 41.88 0.75 191 40% 4.07 3.24 0.83 24%
RJR RJ Reynolds 1.15 91,082 10.0 42.42 0.75 439 40% 8.96 7.46 1.50 27%
MO Altria Group 0.90 1,732 15.0 45.30 0.75 212 40% 4.51 3.79 0.73 28%
GP Georgia-Pacific 0.80 1,022 10.0 25.84 0.75 281 40% 5.89 5.19 0.70 31%
BOW Bowater 1.75 24,480 20.0 41.75 0.75 288 40% 6.04 5.45 0.58 33%
Selected Cases as of Oct 22, 03.
by recovery assumption
Description Jan 06 Equity Put Hedge 3-Year CDS Put vs CDS
Short CDS vs Long Equity Put: The Opportunity Set
CDS Premia through Jan 06 vs Equity Put Hedge Cost
Assuming 40% Recovery; Selected Cases as of Oct 22, 03
Break-Even Recovery Values
Selected Cases as of Oct 22, 03
Assuming 40% recovery, Edison International (EIX), General Motors (GM), RJ Reynolds
(RJR), and Altria (MO), and are among the cases where the expected present value of CDS
premia through Jan 06 exceeds the cost of an equity put hedge.
For Edison International (EIX), the break-even recovery is ‘negative’ as the present value
of CDS premia over the duration of the option contract exceeds the cost of the equity put
hedge even under the zero recovery scenario.
2 4 6 8 10
Present Value of CDS Premiums over Duration of Jan 06 Put Hedge ($)
56% 56% 57%
Short CDS vs Long Put: Advantages & Risks
The Put Option is an ‘Over-Hedge’
The stock price can fall below the put strike without the occurrence of a credit
event that triggers a CDS liability. Thus the holder of the short CDS / long put
position could potentially obtain a put pay-off without being liable to pay out on
The most frequently traded CDSs have a 5 year maturity while the currently available
longest dated listed put options expire Jan 05 or Jan 06. Any timing difference between 5-
year CDSs and shorter dated puts leave investors at maturity of the puts with non-
expired CDS positions. This creates the risk that the value of credit protection may rise by
maturity of the put while the put option is out-of-the-money.
Shorter dated CDSs can also be available, although CDS contracts with 5-year
maturity are most commonly traded.
Longer dated equity puts may be available in the over-the counter options market.
At expiry (or over the duration) of the put contract, the short CDS position may be
re-hedged with puts of later expiry.
The trade may be unwound profitably before the put expiry.
Short CDS vs Long Put: Advantages & Risks
Trade Risks (Continued)
The stock price might not fall to (or below) $0.75 as assumed in the event that the short
CDS position triggers a liability.
A higher, more conservative stock price may be set when calculating the number of
puts used to hedge the credit risk.
Equity put hedges based on options with higher strike prices are less sensitive to
the assumed ‘default’ stock price.
The Present Value of CDS premia through option expiration is an expected value, but
not necessarily a realized outcome.
The present value calculations can be improved by studying the arrival of
corporate liabilities (on Bloomberg via the DDIS function, for instance). Although this
should improve the accuracy of the present value estimate, it is nonetheless subject to
In the even of credit default, it may take a long time to ‘recovery’ any claims on the
company’s assets and the recovery value may be lower than expected.
Alternative Capital Structure Models
Short CDS vs Long Equity Variance Swap
An alternative to the short CDS / long put model to take advantage of ‘cheap’ equity risk.
A long Variance Swap position generates cash in-flow (out-flow) should volatility increase
above (decrease below) the set volatility strike.
Should debt default occur, the stock’s realized equity volatility should increase and thus the
long Variance Swap position can offset the CDS liability.
Should no default occur, one bears the risk that the realized volatility falls below the Variance
Swap strike. Such liability can however be offset by the cash-flow generated from the CDS
Buy-Write (Long Stock & Short Equity Call) vs Long CDS
Taking advantage of ‘expensive’ equity risk.
A buy-write consists of the simultaneous purchase of a stock and the sale of an out-of-the-
money call option.
The call premium may be used to finance multiple CDSs to protect the downside of the buy-
The combined position allows for stock appreciation to the strike price of the call, while the
downside can be protected with the long CDS position.
Other Capital Structure Models
Synthetic Convertible Bonds
Obtaining ‘cheap’ equity exposure with ‘expensive’ credit risk.
A convertible bond is essentially (a) short a CDS, (b) long a risk-free asset, and (c) long a call
option and thus may be created synthetically.
Though the correlation of credit risk and equity risk is significant (see page 3), for a given
level of credit risk, the cost of equity risk can vary substantially, i.e. one can identify
candidates where for similar downside risk (e.g debt default) one obtains the most upside via
Equity Put Ratio Spreads
Taking advantage of steep equity put skew.
The demand for credit protection via low strike puts has steepened the strike skew for many
equities, i.e. lower strike options have significantly higher implied volatilities than that higher
Equity put ratio spreads can take advantage of a steep strike skew by selling multiple far
out-of-the-money put options for every near the money put option one is long (for instance, a
6 x 1 ratio spread could consist of selling six $5 strike puts while buying one $30-strike put).
Though a ratio spread requires a premium, the cost of the position is substantially reduced
when the strike skew is steep. The option pay-off cannot be negative and reaches its
maximum at the low strike put. Thus, holders of ratio spreads take the view that the stock
price will fall, but not collapse below the low strike put.
Credit & Equity-Linked Strategy
Michael Maras +44 20-7996-2510
Benjamin Bowler +1 212-449-3199
Yaw Debrah +1 212-449-0174
Heiko Ebens +1 212-449-1049
Equity Derivatives Sales
Mickey Strasser +1 212-449-3313
Credit Derivatives Sales
Doug Mallach +1 212-449-6190
I, Heiko Ebens, hereby certify that the views expressed in this research report accurately reflect my personal views
about the subject securities and issuers. I also certify that no part of my compensation was, is, or will be, directly or
indirectly, related to the specific recommendations or view expressed in this research report.
MLPF&S or one or more of its affiliates acts as a market maker for the recommended securities to the extent that MLPF&S or such affiliate is willing to buy and sell such securities for its
own account on a regular and continuous basis: Genl Motors; Edison Intl; R.J. Reynolds; Altria Group. MLPF&S or an affiliate was a manager of a public offering of securities of this
company within the last 12 months: Genl Motors. An officer, director or employee of MLPF&S or one of its affiliates is an officer or director of this company: Genl Motors. MLPF&S
or an affiliate has received compensation for investment banking services from this company within the past 12 months: Genl Motors; Altria Group. MLPF&S or an affiliate expects to
receive or intends to seek compensation for investment banking services from this company within the next three months: Genl Motors; Edison Intl; R.J. Reynolds. MLPF&S together
with its affiliates beneficially owns one percent or more of the common stock of this company calculated in accordance with Section 13(d) of the Securities Exchange Act of 1934: Genl
Motors; Edison Intl; R.J. Reynolds; Altria Group. Additional information pursuant to Section 34b of the German Securities Trading Act: Merrill Lynch and/or its affiliates was an
underwriter in an offering of securities of the issuer in the last five years: Genl Motors; Edison Intl; R.J. Reynolds. The analyst(s) responsible for covering the securities in this report
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