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 days (.02,.05,30,.005) most parameter combinations produced losses

Theoretical vs. Market CDS rates Some converge Eastman Kodak Halliburton Market Theoretic CDS spread Days

Theoretical vs. Market CDS rates Some diverge Dow Chemical Sprint Nextel Market Theoretic CDS spread Days

Theoretical vs. Market CDS rates Some discrepancies converge and reopen Tyco General Motors Market Theoretic CDS spread Days

Theoretical vs. Market CDS rates Some appear to be persistent American Electric Power International Paper Market Theoretic CDS spread 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.Rebalancing period length = T. 2.At each T, trade the top 10% discrepancies. 3.Take profits daily 4.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 10^4 $ H = 60 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) Days For combs tried cum P/L was positive Results seem more Volatile in the interval Length than in H

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 10^4 $ formation = 30 hold = 60 Days (15, 60,90)

Areas for Further Analysis 1.Margin effects. 2.Maximum draw-downs effect 3.Sharpe ratios analysis 4.Transaction costs 5.Out-of-sample testing 6.Leverage cycle strategies 7.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 q- alpha dynamics. The option surface implies the S distribution: dP/dK = exp(-rT)Q{S T <K} Default probabilities computed by numerically differentiating deep OTM puts.