casemark/analyzing-correlation-trading

Analyzing Correlation Trading

When To Use

• Pricing or relative-value assessment of synthetic CDO tranches (equity, mezzanine, senior)
• Evaluating index vs. single-name basis (e.g., CDX.NA.IG/HY vs. constituent CDS)
• Analyzing correlation skew across the capital structure of a credit index
• Structuring or assessing dispersion trades (long index protection / short single-name protection, or vice versa)
• Reviewing implied correlation surfaces for mark-to-market or risk reporting
• Stress-testing a correlation book against regime shifts (crisis spikes, mean-reversion)

Inputs To Gather

• Index data: Current and historical spreads for the relevant index (CDX, iTraxx) and series/roll
• Tranche quotes: Mid-market prices or upfronts for standard tranches (e.g., 0-3%, 3-7%, 7-15%, 15-30%, 30-100% for CDX.IG)
• Single-name CDS spreads: Constituent spreads, recovery rate assumptions, and any jump-to-default premia
• Implied correlation levels: Base correlations or compound correlations per tranche from dealer runs or internal models
• Historical realized correlation: Pairwise or average asset-correlation estimates from equity proxies or CDS co-movements over chosen lookback windows
• Model parameters: Copula type (Gaussian, Student-t, Marshall-Olkin), number of simulation paths, granularity of loss distribution [VERIFY: confirm model convention used by the desk]
• Market context: Recent credit events, index rolls, on-the-run vs. off-the-run dynamics, funding/repo costs

Workflow

1. Reconstruct the base correlation curve

   • Compute compound correlation for each tranche using the standard Gaussian copula and quoted tranche spreads/upfronts
   • Convert to base correlation by bootstrapping from equity tranche up through super-senior
   • Flag any non-monotonicity in the base correlation curve — this indicates arbitrage or stale quotes

2. Assess correlation skew

   • Compare current base correlation levels to 3-month, 6-month, and 1-year historical ranges
   • Identify whether equity tranche implied correlation is rich or cheap relative to mezzanine/senior
   • Note skew steepness: a flat skew suggests low differentiation between subordination levels; a steep skew signals tail-risk repricing

3. Index vs. intrinsics analysis

   • Calculate the theoretical index spread from the sum of single-name constituents weighted by notional
   • Compute the index basis (market index spread minus intrinsic spread)
   • A persistently negative basis (index trading tight to intrinsics) may indicate correlation supply; a positive basis suggests demand for index protection or single-name tightening

4. Dispersion trade evaluation

   • Define the trade structure: long index vs. short basket of single names (or reverse), specifying delta-neutral notionals
   • Estimate P&L sensitivity to parallel spread moves (DV01), idiosyncratic spread moves, and correlation changes (CR01)
   • Model carry and roll-down under stable-spread scenarios
   • Stress-test against historical episodes: 2008 credit crisis, 2011 European sovereign stress, 2020 COVID dislocation [VERIFY: update with most recent relevant stress period]

5. Risk decomposition

   • Break total tranche risk into spread risk (CS01), default risk (jump-to-default), and correlation risk (CR01)
   • Quantify gamma/convexity for equity and thin mezzanine tranches — these exhibit significant non-linearity
   • Assess vega exposure if using stochastic-correlation or stochastic-recovery extensions

6. Compile findings and relative-value view

   • Summarize whether the current skew environment favors long or short correlation positioning
   • Provide specific trade recommendations with entry levels, target P&L, stop-loss thresholds, and horizon
   • Note key risks: credit event clustering, sudden correlation spikes, liquidity withdrawal in off-the-run series

Output

• Correlation Surface Summary: Table of base correlations by tranche detachment with historical percentile ranks
• Skew Analysis: Chart-ready data showing current vs. historical skew with commentary on regime
• Index Basis Report: Intrinsic vs. market spread, basis time series, and drivers
• Dispersion Trade P&L Profile: Scenario table with carry, spread, default, and correlation P&L columns
• Risk Dashboard: CS01, CR01, JTD, and gamma by tranche or position
• Trade Recommendation: Directional view with rationale, sizing, and risk limits

Quality Checks

• Base correlation curve must be monotonically increasing from equity to super-senior — if not, investigate quote staleness or interpolation error
• Sum of tranche expected losses must equal the index expected loss (no-arbitrage constraint)
• CR01 signs must be internally consistent: long equity tranche = long correlation; long senior tranche = short correlation
• Verify recovery rate assumptions match market convention (typically 40% for IG, 25-30% for HY) [VERIFY: confirm current market standard]
• Confirm index series and roll date — mixing on-the-run and off-the-run quotes invalidates basis calculations
• Stress scenarios should include at least one idiosyncratic (single-name blowup) and one systemic (market-wide spread widening) event
• All implied correlations should fall within [0, 1]; values near boundaries indicate model breakdown or extreme market conditions requiring manual review