Capital Structure Arbitrage with
a Non-Gaussian Pricing Model
Market CDS Rates vs Our Model
When markets differ from model predictions, will they
converge? How do we profit from convergence?
Our Theoretical CDS Model:
• Theoretical CDS Rates via Options market:
– Stock Default = -95%
– q-Alpha model to obtain default probabilities
→ numerically differentiate deep OTM puts
from the option price surface
– Bootstrap CDS curve from implied default
probabilities
Strategy 1: Basic Threshold Strategy
• If (theoretic – market) > α then go long $10M notional CDS and short a
delta neutral call option hedge.
• If (theoretic – market) < α do the opposite
• Every day, check for daily convergence, and take profits
if abs(theoretic – market) < ε
• Stop loss if the trade diverges by β
• In case of stop-loss, then flag the name and don’t trade again for T time.
• Our data set: 100 companies over 2 years
Strategy 1 (cumulative P/L)
• (.01,.02,90,.0025)
trade trigger level = .01
stop loss level = .02
Kick-out period = 90
Convergence level
= .0025
• (.02,.05,30,.005)
most parameter
combinations produced
losses
$
days
Theoretical vs. Market CDS rates
Some converge
Eastman Kodak
Halliburton
CDS spread
Market Theoretic
Days
Theoretical vs. Market CDS rates
Some diverge
Dow Chemical
Sprint Nextel
CDS spread
Market Theoretic
Days
Theoretical vs. Market CDS rates
Some discrepancies converge and reopen
Tyco
General Motors
CDS spread
Market Theoretic
Days
Theoretical vs. Market CDS rates
Some appear to be persistent
American Electric Power
International Paper
CDS spread
Market Theoretic
Days
Caveats
• This is a convergence trading strategy
• Spread may widen further, producing losses
• Discrepancies may be from:
- Model or parameter misspecification
- Unperceived systematic risk factors
- Inherent liquidity differences
- “Genuine” mispricings
• NO guarantee that the difference will dissipate
over a reasonable horizon
Strategy 1
• Many parameter combinations produce losses
• Many discrepancies do not converge
• We take on all openings & too many bad trades.
• Stop-loss is the dominating trade
• Maybe the biggest discrepancies are more likely
to have genuine mispricings which converge?
Strategy 2: Rank and Hold
1.
2.
3.
4.
Rebalancing period length = T.
At each T, trade the top 10% discrepancies.
Take profits daily
At the end of T close everything, go back to 1.
→ We only trade egregious differences
→ We capture partial convergence during each holding
period
Strategy 2 (cumulative P/L)
• H = 30
Flat regions mean
no trades
• H = 60
10^4 $
Days
15 different combinations
gave positive P/L
Strategy 3: Active Holding Period
1. Interval length = I, Holding period = H
2. In strategy 2, we are idle during the holding periods but
here we form new portfolios at every I.
3. At each I, close out the positions from t-H and form a
new portfolio. Take profits daily.
Strategy 3 (cumulative P/L)
• (interval, hold)
= (15,45)
10^4 $
Days
• (10,120)
Strategy 3 (cumulative P/L)
• (50,150)
10^4
• (40,160)
For combs tried cum
P/L was positive
Results seem more
Volatile in the interval
Length than in H
$
Days
Strategy 4: Capture the Momentum
In previous strategies we saw that wide differences may
become wider.
Use a different ranking criteria: convergence momentum.
Similar to strategy 3, but compute and rank the rates of
spread convergence during a lookback/formation
period for each company
Strategy 4 (cumulative P/L)
• (15,30,60)
interval = 15
formation = 30
hold = 60
10^4$
Days
• (15, 60,90)
Areas for Further Analysis
1.
2.
3.
4.
5.
6.
7.
Margin effects.
Maximum draw-downs effect
Sharpe ratios analysis
Transaction costs
Out-of-sample testing
Leverage cycle strategies
Check constrained mean, long term time-averaged
variance decay. Statistical arbitrage?
More of an instinct than science?
Appendix: Default Probabilities
• Monte Carlo is best, but too slow. Instead:
• We have formulas for option prices under qalpha dynamics.
• The option surface implies the S distribution:
dP/dK = exp(-rT)Q{ST<K}
• Default probabilities computed by numerically
differentiating deep OTM puts.