Summary CDS systematic moment statistics

Summary statistics for beta, systematic skewness and systematic kurtosis can be seen in table 2.2 . The systematic variance values are negative demonstrating negative co- variance between CDS prices and the equity market. The average mean beta is -0.0632 with a standard deviation of 0.0344. The magnitude of the CDS systematic variance is in line with expectation and ranges from a minimum of -0.3979 and a maximum of 0.2179. Calculated CDS beta values were expected to be of similar magnitude as corporate bond betas calculated in previous studies looking at systematic risk but to be of opposite sign (See Friend et al. (1978), Weinstein (1981), Cornell and Green (1991) and De Jong and Driessen (2012)). As the CDS names are of investment grade, small values for the systematic variance are to be expected, however lower grade CDS do exhibit higher systematic variance.

In table 2.2 are additional historical beta credit rating statistics. The CDS returns are binned by credit rating and the systematic variance and statistics calculated. The trend in the mean average systematic variance is as expected, with lower rated CDSs exhibiting greater systematic variance than higher rated CDSs. Exceptions to this are in AA, A, A- and BBB+ rated CDSs, where their systematic variance is lower than higher rated CDSs. This can also be seen in the beta standard deviation of the CDS bins with the AA, AA- and BBB+ rated CDSs also exhibiting a lower standard deviation.

This is of interest as mean returns belonging to BBB+ rated CDSs for example are not lower than AA-, A+ or A rated bins as would be expected in line with their lower standard deviation and average mean betas. This may demonstrate that some higher rated CDS names may not be compensating the holder for the higher level of

Table 2.2: Summary statistics for systematic variance, skewness and kurtosis 2007-2010

β γ δ

Mean SD Max Min Mean Mean N Obs.

All Returns -0.063 0.034 0.218 -0.398 -0.272 -0.064 128 744 Credit Rating AA+ -0.044 0.025 0.006 -0.152 -0.027 -0.045 2 744 AA -0.030 0.017 0.029 -0.130 -0.029 -0.032 5 744 AA- -0.052 0.027 0.008 -0.216 -0.003 -0.056 11 744 A+ -0.051 0.029 0.070 -0.289 0.016 -0.055 13 744 A -0.051 0.029 0.195 -0.212 -0.085 -0.053 9 744 A- -0.048 0.025 0.224 -0.255 -0.035 -0.049 29 744 BBB+ -0.051 0.026 0.024 -0.207 -0.075 -0.052 32 744 BBB -0.072 0.038 0.039 -0.320 -0.100 -0.072 20 744 BBB- -0.109 0.050 -0.006 -0.327 -0.193 -0.112 6 744 Sector Auto -0.061 0.031 0.224 -0.327 -0.098 -0.062 31 744 Consumer -0.058 0.033 0.195 -0.288 -0.117 -0.060 31 744 Energy -0.038 0.019 0.010 -0.211 -0.010 -0.039 20 744 Financial -0.062 0.034 0.070 -0.289 -0.002 -0.067 26 744 TMT -0.054 0.025 0.015 -0.189 -0.054 -0.053 20 744

Note: Summary statistics for systematic variance β, systematic skewness γ and systematic kurtosis δ for the period 2007-2010 binned by credit rating, sector and all 128 CDS entities.

systematic risk present in the bin. The credit bins AA-, A+ and A all share a common characteristic in that the majority of the 26 financial sector entities are located in one of these three bins. Financial entities make up 82%, 54% and 45% of the AA-, A+ and A credit rating bins respectively. As such it suggests that during the sample period 2007-2010 that market risk in the financial sector was underestimated by the credit markets.

A graphical representation of the mean beta estimates can be seen in figure 2.2. Fur- thermore, there is a large increase in the systematic variance in the lower rated BBB and BBB- rated bonds.

2.4 Data

Jan07 Apr07 Jul07 Oct07 Jan08 Apr08 Jul08 Oct08 Jan09 Apr09 Jul09 Oct09 Jan10 Apr10 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 Date

CDS average systematic variance

iTraxx 5 year CDS systematic variance

Figure 2.2: CDS Systematic Variance March 2007-2010

systematic kurtosis statistic is negative for the bin holding all 128 CDS names and across all credit rating and sector bins. The systematic skewness statistic is also negative for the all-inclusive bin, the sector bins and all credit rating bins bar one. Investors will dislike the negative systematic skewness and will require a reward of excess returns for accepting this risk. Adding an asset with negative systematic skewness to a portfolio will decrease the overall positive skewness and so will be unattractive to an investor and so should be commensurate with higher returns.

Lastly the systematic risk sensitivity parameters by sector are provided. The systematic variance and systematic kurtosis are the largest for the financial sector demonstrating the interconnectedness of this sector with the equity market during this time period. Interestingly looking at the mean return for this sector in table 2.1, the sector has the second lowest return of the five sectors suggesting that the level of risk was not fully recognised in the market.

Table 2.3: Regression between credit ratings and systematic risk sensitivity parameters

Systematic Variance Systematic Skewness Systematic Kurtosis

α0 α1 α0 α1 α0 α1 Credit Rating -0.333 -94.362*** (-0.189) (-3.222) Credit Rating 3.017*** -33.720*** (3.489) (-3.262) Credit Rating -0.308 -90.723*** (-0.167) (-3.060)

Regression coefficients and t-statistics below for regression between credit ratings and sys- tematic risk sensitivity parameters where credit ratings have been assigned numerical values from 1 through to 9 for AA+ to BBB- respectively. (***, **, * = 1%, 5% and 10% sig- nificance respectively) Systematic variance regression : cri = α0+ α1βi+ i, Systematic

skewness regression: cri= α0+α1γi+i, Systematic kurtosis regression: cri= α0+α1δi+i

Where cri is the assigned numerical value assigned to the credit rating bin. β, γ and δ

refer to the bin systematic variance, skewness and kurtosis respectively. i represents the

residuals of the equation

sensitivity parameters and credit rating. Numerical values are assigned to each credit rating from 9 for BBB- to 1 for AA+ and cross sectional regressions are run between the credit rating and sensitivity parameter to determine if there is a significant relationship. It is expected that entities with a lower credit rating have larger systematic variance, systematic skewness and systematic kurtosis values. The methodology of assigning numerical values to credit ratings is commonly used in the literature (for example Cantor and Packer (1996)) when running regression analysis. Regression results are provided in table 2.3. Coefficients from the analysis show a positive significant (at 1% level) relationship between each risk factor and credit rating. It is evident that generally as credit rating decreases the magnitude of each systemic risk factor, variance, skewness and kurtosis increase and lower rated reference entities have higher systematic risk.