Liquidity Risk in Credit Default Swap Markets

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1 Liquidity Risk in Credit Default Swap Markets Anders B. Trolle (joint work with Benjamin Junge) Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute Paris, March 25, / 14

2 Contribution Two dimensions of liquidity: expected liquidity (e.g. Amihud and Mendelson (1986, JFE)) and liquidity risk (e.g. Pastor and Stambaugh (2003, JPE)) In CDS markets, Bongaerts, de Jong, and Driessen (2011, JF) argue that expected liquidity is important, while liquidity risk is not. We revisit this question. In particular, we 1. Construct a market-wide CDS illiquidity measure 2. Investigate if exposure to market-wide CDS illiquidity is priced in the cross-section of single-name CDS returns Main finding: liquidity risk matters! 2 / 14

3 Market-wide CDS illiquidity measure A credit index is a standardized credit derivative that provides insurance against any defaults among its constituents Its cash-flow can be replicated by trading a portfolio of single-name CDSs on the index constituents theoretical index level Difference between actual and theoretical levels referred to as index-to-theoretical basis, B(t, τ) In perfect capital markets, index arbitrage keeps the basis close to zero Frictions such as illiquidity and lack of arbitrage capital give rise to non-zero basis 10 credit indices, 5Y maturity CDX.NA.IG CDX.NA.HY itraxx Eur itraxx Eur Xover CDX.NA.IG.HVOL CDX.NA.HY.BB itraxx Eur HiVol CDX.NA.HY.B itraxx Eur Sr Finls itraxx Eur Sub Finls Market-wide illiquidity measure CDSILLIQ t = 10 i=1 w i,t B i (t, 5Y ) C i (t, 5Y ) 3 / 14

4 Example, index-to-theoretical basis for CDX.NA.IG CDX.NA.IG Jun07 Jul08 Aug09 Sep10 Oct11 CDX.NA.HY /

5 Market-wide CDS illiquidity measure 25 CDS illiquidity Nov06 Jun07 Dec07 Jul08 Jan09 Aug09 Mar10 Sep10 Apr11 Oct11 Liquidity risk factor / 14

6 25 Traded liquidity risk factor CDS illiquidity 20Based on index arbitrage If index < theoretical level (negative basis), buy protection on 15 index and sell protection on index constituents 10 If index > theoretical level (positive basis), vice versa Positive average return with Sharpe ratio of High negative correlation with market-wide CDS illiqidity measure (positive return when illiquidity decreases and bases 0 Nov06 Jun07 Dec07 Jul08 Jan09 Aug09 Mar10 Sep10 Apr11 Oct11 contract) Liquidity risk factor Nov06 Jun07 Dec07 Jul08 Jan09 Aug09 Mar10 Sep10 Apr11 Oct11 6 / 14

7 Factor pricing model Time-series. Realized excess return on CDS contract i: r CDS i,t = α i + β MKT i rmkt e,t + β CDSILLIQ i rcdsilliq,t e + βi DEF rdef e,t + ɛ i,t, where rmkt e,t, r CDSILLIQ,t e, and r DEF e,t denote the excess return on a market factor, liquidity risk factor, and default risk factor Cross-section. Expected excess CDS returns: E[r CDS i,t ] = E[c CDS i,t ]ζ + β MKT i λ MKT + β CDSILLIQ i λ CDSILLIQ + βi DEF λ DEF where c CDS i,t denotes contract i s weekly round-trip transaction cost T t=1 Ê[ri, CDS ] = 1 CDS T Êt[ri,t+ t ] and Ê[cCDS i, ] = 1 T matched to average turnover in CDS markets T t=1 ccds i,t and ζ Ê[r CDS i, ] Ê[cCDS i, ] ζ = λ 0 + β MKT i λ MKT + β CDSILLIQ i λ CDSILLIQ + β i DEF λ DEF +u i, 7 / 14

8 Test portfolios βs at individual contract level very imprecisely estimated. 40 test portfolios, equally weighted and rebalanced quarterly Sort CDS contracts according to 1. Default risk: Five credit rating categories: AAA-AA, A, BBB, BB, and B-CCC and quintiles based on five-year EDFs (expected default frequencies) 2. Illiquidity: Quartiles based on bid-ask spreads 8 / 14

9 Expected excess returns (% p.a.) Expected Returns (% p.a.) Panel A: Realized Return Bid-Ask Spread Bid-Ask S Rating Low Q2 Q3 High Low Q2 AAA - AA [6.79] [7.53] [6.35] [6.09] [-0.97] [-0.48] A [7.75] [7.12] [5.80] [4.36] [-0.83] [-0.59] BBB [9.60] [7.16] [6.43] [5.32] [-0.74] [-0.34] BB [10.02] [9.42] [8.69] [9.26] [-0.68] [0.22] B - CCC [11.09] [13.00] [8.12] [7.17] [-0.37] [0.84] CDS Spread (% p.a.) Number of Co Bid-Ask Spread Bid-Ask S Rating Low Q2 Q3 High Low Q2 Returns computed for the party that sells protection Strongly statistically significant AAA - AA A BBB BB B - CCC Increasing along default risk and illiquidity dimensions Panel B: 9 / 14

10 Bid-Ask Spread Bid-Ask Spread Bid-Ask Spread Time-series regression Rating Low Q2 Q3 High Low Q2 Q3 High Low Q2 Q3 High AAA - AA [6.51] [3.83] [3.73] [4.83] [1.89] [0.25] [0.85] [0.79] [9.51] [10.82] [4.93] [8.11] A [7.97] [8.41] [9.22] [7.90] [2.89] [3.12] [2.69] [2.64] [5.52] [6.61] [8.73] [7.92] BBB [10.38] [9.49] [6.71] [8.01] [3.47] [3.31] [3.57] [3.65] [5.17] [7.76] [6.54] [5.64] BB [7.97] [14.23] [8.83] [7.65] [3.33] [2.87] [2.92] [4.53] [3.44] [3.83] [5.42] [5.72] B - CCC [7.19] [11.92] [11.71] [6.74] [3.39] [4.14] [5.57] [2.68] [4.64] [4.21] [4.88] [6.93] MKT CDSILLIQ DEF Bid-Ask Spread Bid-Ask Spread Bid-Ask Spread 5-year EDF Low Q2 Q3 High Low Q2 Q3 High Low Q2 Q3 High Low [7.31] [8.66] [8.01] [7.17] [2.89] [3.23] [2.86] [3.69] [5.87] [7.09] [8.00] [11.55] Q [7.44] [9.73] [9.27] [8.51] [2.84] [2.47] [3.19] [4.59] [6.85] [5.75] [9.92] [6.45] Q [10.30] [8.21] [7.05] [9.40] [2.45] [2.87] [4.32] [2.74] [6.44] [8.09] [8.81] [5.87] Q [9.89] [10.04] [7.43] [11.19] [3.15] [3.55] [3.11] [3.95] [6.70] [8.06] [6.62] [5.58] High [6.83] [8.11] [12.03] [10.60] [2.95] [3.18] [4.99] [3.47] [6.83] [3.37] [4.59] [5.41] Panel C: Adjusted R 2 Adjusted R 2 Sellers of protection realize losses when Equity market drops Market-wide CDS illiquidity increases Aggregate default risk increases Bid-Ask Spread Bid-Ask Spread Rating Low Q2 Q3 High 5-year EDF Low Q2 Q3 High AAA to AA Low A Q BBB Q BB Q B to CCC High Table 6: Results Time Series Regressions. The table displays first-step regression results at the level of individual test portfolios. Panel A provides results for single factor specifications and Panel B provides results for three-factor specifications. Panels A and B report the economic magnitudes of estimated factor loadings and their respective t-statistics, given in square brackets. Economic magnitude of a factor is the change in one-week CDS return (in basis points) 10 / 14

11 Cross-sectional regression Panel A: Full Sample Specification λ [7.90] [-1.03] [-1.10] [-1.83] [-1.33] [-1.78] [-2.70] [-1.16] [-1.31] [-1.87] [-1.50] [-1.80] [-2.79] ζ [ ] [ ] [ ] [ ] [ ] [ ] [ ] λ MKT [5.51] [4.20] [0.58] [5.19] [3.42] [0.36] λ CDSILLIQ [3.36] [3.65] [3.07] [2.67] [3.34] [3.62] [3.33] [2.76] λ DEF [3.88] [2.84] [3.86] [3.74] [2.40] [3.51] R Panel B: Non-Stress Regime Specification λ [10.11] [1.15] [0.60] [0.38] [1.74] [0.41] [1.57] [0.74] [0.23] [0.12] [1.22] [0.18] [0.90] ζ Market prices of liquidity risk and default risk are statistically [ ] [ ] [ ] [ ] [ ] [ ] [ ] λ MKT [7.97] [4.70] [1.06] [6.62] [4.49] [1.08] λ CDSILLIQ significant [3.44] [-1.88] [-1.25] [-1.25] [3.59] [-1.30] [-0.84] [-0.91] λ DEF High cross-sectional [4.60] R 2 [2.85] [3.50] [4.15] [2.67] [3.13] R Panel C: Stress Regime Specification λ [10.01] [-2.21] [-1.04] [-2.56] [-1.94] [-2.22] [-2.73] [-2.16] [-1.20] [-2.51] [-1.92] [-2.17] [-2.69] ζ [ ] [ ] [ ] [ ] [ ] [ ] [ ] λ MKT [4.77] [3.06] [-0.05] [4.50] [2.63] [-0.26] λ CDSILLIQ [3.36] [4.41] [4.51] [3.85] [3.35] [4.50] [4.55] [3.91] 11 / 14

12 Portfolio risk premia AAA-AAQ1 AAA-AAQ2 4 2 Intercept Expected illiquidity Market Liquidity risk Default risk Pricing error AAA-AAQ3 AAA-AAQ4 AQ1 AQ2 AQ3 AQ4 BBBQ1 BBBQ2 BBBQ3 BBBQ4 BBQ1 BBQ2 BBQ3 BBQ4 B-CCCQ1 B-CCCQ2 B-CCCQ3 B-CCCQ4 12 / 14

13 Decomposition of risk premia (basis points) AAA-AA/low BA B-CCC/high BA Difference Expected Illiquidity Market risk Liquidity risk Default risk Sum / 14

14 Conclusion We analyze whether liquidity risk, in addition to expected illiquidity, affects expected returns on credit default swaps We construct a market-wide CDS illiquidity measure from index-to-theoretical bases We estimate a factor pricing model, which accounts for market risk and default risk in addition to liquidity risk and expected illiquidity Liquidity risk is priced in the cross-section of single-name CDS returns and has a larger contribution to expected CDS returns than expected illiquidity A conditional analysis shows that the magnitude and price of liquidity risk were particularly high during the most intense phases of the financial crisis 14 / 14

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