When Risks and Market Inefficiency Shake Hands – An Empirical Analysis of Financial CDS

This paper examines the relation between absolute CDS premium and the market efficiency of financial institutions. We test the random-walk hypothesis on 3-years CDS data set using: Q-statistics portmanteau tests by Box and Pierce, variance ratio tests by Lo and MacKinlay, variance ratio tests using ranks and signs by Wright, and wild bootstrapping variance ratio tests by Kim. We find that CDSs with the highest means and the highest standard deviations tend to fail the random-walk hypothesis. These CDSs have the highest potential to trade in an inefficient market with the highst potential for speculation and market manipulation (i.e. by hedge funds). This inefficiency negates the original function of hedging. To reconstitute the function of hedging and to overcome a CDS market that is driven by speculation our research concludes that it is necessary to adopt further regulations for the CDS market.


Introduction
Credit Default Swaps (CDS) are the most common credit derivatives and the most important risk management tools for credit risks.CDSs allow investors to insure their portfolios against pre-defined credit events.The functionality is as follows: The protection buyer makes periodic payments (in the amount of the CDS spread) and the protection seller offers to compensate the protection buyer (also periodically) if a pre-defined credit event occurs.If no credit event occurs, the CDS contract terminates without any compensation payments.The market for credit derivatives is a global, over-the-counter financial market which started in the mid-1990s and is dominated by banks, insurers, reinsurers, hedge funds, investment funds and large non-financial companies.Furthermore it is a transparent market where every market participant has the possibility to get all necessary information via information systems (e.g.Bloomberg).Most contracts are regulated by the International Swaps and Derivatives Association (ISDA).Therefore, it is to be expected that the CDS market should be an efficient market in the definition of Fama.The market reached its peak, according to the International Swaps and Derivatives Association (ISDA (2010)), right before the beginning of the financial crisis at the end of 2007 with a notional value around 62.2 Trillion USD.That value has declined continuously since the outbreak of the financial crisis.The latest estimates by the ISDA (2010) are for a notional value up to 26.3 trillion USD in 2010.Nevertheless CDS still represent a relevant factor within the financial market: (i) CDS spreads became an economic indicator for corporate credit liability.Therefore CDS spreads have a direct impact on corporate debt ratings and credit rates.(ii) For countries, CDS became the most important factor for the emission price of bonds.Corporate credit liability and sovereign debt prices play a large role in the economy.Thus, CDS spreads greatly influence our economic welfare.In this analysis we concentrate our research on CDS for banks.Investors pay credit spreads to protect them against the risk of default by the bank.In 2011/2012 CDS spreads for banks are at historic highs.This is due to the fear of contagion of the European debt crisis, disappointing earnings trends, expectations of rating downgrades and unsettling comments by politicians and international institutions.The collapse of Lehman Brothers has caused the CDS markets to become a target for speculators.The near collapse of Greece has further increased speculation.For investors hedging portfolios with CDS it is important to know if the increase in speculative activity affects market efficiency.Therefore our essay focuses on the problem of weak-form market efficiency of CDS markets.We check market efficiency by using the random-walk hypothesis.The data we use in our research is 3-years of daily and weekly CDSs on 30 international banks.We test the random-walk hypothesis by using the latest test statistics (Box & Pierce Q-statistics, variance ratio tests by Lo and MacKinlay, variance ratio tests using ranks and signs by Wright and wild bootstrapping variance ratio tests by Kim).The main interest of our research is the relation between CDS premiums and market efficiency.We support our findings with the use of the scoring model framework.

Literature Review
In general, contemporary research of the CDS market consists of 2 different streams: informational efficiency in the CDS market and regulatory issues of CDS as a financial instrument.There is no research analyzing the random-walk hypothesis of CDS markets.
On the first stream, one of the findings in the empirical research of Ancharya and Johnson (2007) concluded that there is an information flow from the CDS market to the equity markets.The analysis of Jenkins et al. (2011) verified the informational efficiency of the CDS market.This is shown by the relationship between movements in subsequent CDS prices and previously announced accounting information.Hull et al. (2004) and Norden and Weber (2004) analyzed the response of stock and CDS markets to rating announcements.The empirical findings of Norden and Weber (2004) showed that the CDS and stock market anticipate rating downgrades.Anticipation starts approximately 60-90 days before the announcement day.Further findings came to the conclusion that stock and CDS markets also reviews for downgrade, and that the CDS market tends to react more quickly.Callen et al. (2009) evaluated the impact of earnings on credit risks in the CDS market.They found that a 1% increase in earnings reduces the CDS premium by 5% to 9%.Zhang (2009) showed the plausibility of the existence of informational efficiency by testing CDS prices on a variety of credit events.Furthermore his analysis showed that CDSs in comparison to stocks have more frequent large price changes.Within an empirical analysis Blanco et al. (2005) tested the theoretical equivalence of CDS prices and Investment-Grade bonds.Their results showed that first CDS prices are substantially higher than credit spreads and second the CDS market lead the bond market in the price discovery process for credit risks.Coudert and Gex (2010) analyzed the link between CDSs and bonds.They came to the conclusion that the CDS market (for corporations) leads the bond market in the price discovery process.Zhu (2006) identified that in the short run the derivatives market moves ahead of the bond market in price discovery, while in the long run credit risks are equally priced.These results imply that the CDS market needs less time to process new information.
On the second stream, Avellanda and Cont (2010) first gave an overview of existing forms of transparency in CDS markets.Second, in speaking about the importance of evaluating costs and benefits they introduced further possibilities of increasing transparency for CDSs.Duquerroy et al. (2009) showed an overview of the CDS market and pointed out challenges for regulators to improve transparency.Cont (2010) disclosed the impact of CDSs on financial stability.She argued that an unregulated market opens the possibility of contagion (especially in the case of counterparty risk) and systematic risks.Further she introduced central clearing as a method to reduce counterparty risks.

Data
Our CDS data collection consists of a set of CDS spreads of international banks provided by Bloomberg.Because CDSs are traded in the OTC market, mainly in London and New York, gaps in the data collection are unavoidable.CDS prices delivered by Bloomberg are intraday prices averaged to one daily price that represents the arithmetic mean of prices received by the agency during the previous 24 hours.We adjusted the data sample for weekends and public holidays.We considered daily observations on 3-year CDS spreads from December 14th 2007 to August 22nd 2011 for the analysis.As the data set spans the period of nearly 4 years our data has an adequate sample period to gain statistically valid evidence to address our problem statement.Every CDS spread that gets used in our sample must meet the following 2 filter criteria: (i) the observed entity has to be a system-relevant bank in its country; (ii) the entity provides a reasonable number of observations (minimum 250), as the number of observations is especially important to achieve significance in the accomplished statistical tests.The filtering yields us 30 entities (22 European banks, 6 American banks and 2 Asian-Pacific banks) and 26236 observations on CDS spreads.Additionally, in order to strengthen the comparability, we build out of the data of the daily observations a data set of weekly observations which still consists of 5373 observations.To get a better impression and for preparing the data for the test statistics we make use of descriptive statistics.Table 1 summarizes daily observations on the logarithm data set of the CDS spreads.Table 2 does the same for weekly observations.As for the necessary test statistic, we test the sample set for normality using Kolmogorov-Smirnov and Jarque-Bera test.We strongly reject the normality assumption for both the daily and weekly data set.

The Random-Walk Hypothesis
Fama (1970) defined an efficient market as one in which prices reflect all available information.In this case the prices reflect even hidden or insider information.If there is no additional data for the investors available, nobody has the ability to take advantage on the market in predicting prices.The market tends to have a semi-strong efficiency if prices already reflected all public information i.e. companies' annual reports.The weak-form market efficiency refers to the predictability in time series of prices on the basis of past information.Samuelson (1965) demonstrated that the price-generating process of a weak-form efficient market should only be affected by the arrival of new information.New information is assumed to appear at random, so prices should follow a random-walk.Price changes are not dependent on each other.A simple random-walk process can be defined as: (2) This assumption implies that absolutely no information on price changes can be obtained from the past.We applied homoscedastic variance ratio tests by Lo and MacKinlay and nonparametric variance ratio tests based on ranks by Wright to test the strong version of random-walk hypothesis.
The semi-strong form implies that the distribution of the arrival of news can change over time, but it is still independent: This form is very difficult to test because every single might come from a totally different distribution.We did not test the semi-strong version of the random-walk hypothesis.
The weak form is based on the correlation of the error terms and implies: This version is especially important, as heteroscedasticity may be a reason for rejecting the strong version of the random-walk hypothesis.
We applied Q-statistics portmanteau tests, heteroscedastic variance ratio tests by Lo and MacKinlay, nonparametric variance ratio tests based on signs by Wright and wild bootstrapping variance ratio tests by Kim to test the weak version of the random-walk hypothesis.

Box-Pierce Q-Statistics
The Q-statistics portmanteau test developed by Box and Pierce (1970) is a possible method for testing a time series for white noise, an uncorrelated sequence of errors, which is also a definition for a weak-form random-walk.We used the relative future price change as a sequence for the sample basis.The Box-Pierce Q-Statistics are calculated as a linear operation of various squared autocorrelations with different time lags, all weighted equally.It can be defined as: To test the validity of the random-walk hypothesis, the Q-statistic is computed for various values of m.For large sample sizes n, Campbell et al. (1997) showed that the sample autocorrelation coefficients are asymptotically independent and normally distributed.
Thus if the price change series is Gaussian distributed, then the Q-statistic is distributed like the sum of squares of m Gaussian random variables.So this statistic is asymptotically distributed as the chi-square distribution with m degrees of freedom.
The null hypothesis can be defined as: Q-statistics points out any deviation from the null hypothesis of no autocorrelation in any direction, and at all considered time lags depending on the value of m.The selection of m is critical for the statistical power of the test, as too small values of m would disregard possible higher order autocorrelation, and too high values of m would reduce statistical significance.We tried to avoid this problem by calculating all Q-statistics for m = 1 to m = 10, for both daily and weekly observations.

Variance Ratio Tests by Lo and MacKinlay
The variance ratio tests by Lo and MacKinlay (1988) were first proposed to test for a random-walk in case of homoscedasticity and later extended to the more general case of an uncorrelated random-walk in case of heteroscedasticity.This test utilises data sampled at various frequencies.Lo and MacKinlay (1989) demonstrated that variance ratio tests are statistically more powerful than the Box-Pierce Q-statistics.As an important property of a random-walk, the variance of its increments is linear in the observed period.Specifically, the variance estimated from the q-periods returns should be q times as large as the variance estimated from one-period returns, or: where t q r = Returns of a sample t for a the period with a length of q t r = Returns of a sample t with one-period length The variance ratio VR(q) can be defined as: The null hypothesis is therefore: Lo and MacKinlay derived asymptotic standard normal test statistics for their variance ratios.We used two different test statistics: z(q) in case of homoscedasticity, and z*(q) in case of heteroscedasticity.The first statistic z(q) assumes an i.i.d.error term.The standard normal z(q) test statistic can be computed as: The heteroscedastic test statistic z*(q) allowed us to relax the requirements of i.i.d.increments.Despite the presence of heteroscedasticity, the test statistic z*(q) is still asymptotically standard normal in case of a random-walk.It can be defined as: where We used both homoscedastic and heteroscedastic test statistics for aggregation values q of 2, 4, 8 and 16.Wright (2000) introduced alternative variance ratio tests based on ranks and signs.He showed that for some processes his nonparametric variance ratio tests are performing better in rejecting violations of the random-walk hypothesis than the tests recommended by Lo and MacKinlay.He explained the outperformance of ranks-and signs-based tests by the mention of two potential advantages.First, his tests often allow for computing the exact distribution.As it is not necessary to appeal to any asymptotic approximation, size distortions can be neglected.Second, if the sample data is highly nonnormal, tests based on ranks and signs may be more powerful than other variance ratio tests.Formally for the ranks-based tests, let ) ( t r r be the rank of the difference of the futures

Variance Ratio Tests Using Ranks and Signs by Wright
. Then, t r 1 and t r 2 are the ranks of the futures price differences, defined as: where 1   is the inverse of the standard normal cumulative distribution function.
The series t r 1 is a simple linear transformation of the ranks, standardised to have a sample mean 0 and a sample variance 1.The series t r 2 , known as the inverse normal or van der Warden score, has a sample mean 0 and a sample variance approximately equal to 1.The rank series t r 1 and t r 2 substitute the difference in futures prices ) ( in the definition of the variance ratio test statistic by Lo and MacKinlay z(q) in equation ( 11), which is written as 1 R and 2 R : where   q  is defined in equation ( 12).Wright (2000) demonstrated that under the assumption that the rank   t r r is an unbiased, random permutation of the numbers T ,..., 2 , 1 , the test statistics' distribution can be provided.So the exact sampling distribution of 1 R and 2 R may easily be simulated to an arbitrary degree of accuracy, for a given choice of T and q .Therefore, the distribution does not suffer from disturbance parameters and the test can be used to construct a test with exact power.
By using the signs of the differences instead of the ranks, it may be possible to apply a variance ratio test that is exact in case of conditional heteroscedasticity.Formally, for a time series . Clearly, t s is an i.i.d.series with zero mean and variance equal to one.Each t s is equal to 1 with a probability 0.5 and is equal to -1 otherwise.The test statistic based on signs 1 S is given by: In Monte Carlo experiments and empirical tests, Wright showed that this test could be exact and more powerful than other variance ratio tests under both homoscedastic and heteroscedastic conditions.Kim (2006) proposed variance ratio tests based on wild bootstrapping -a re-sampling method that approximates the sampling distribution of the test statistic.The main advantage of this finite sample test is the fact that it does not rely on asymptotic approximations.Therefore, it is robust to nonnormality.Wu (1986) and Mammen (1993) demonstrated that wild bootstrapping should be a natural choice in case of conditional and unconditional heteroscedasticity.The test is based on a Chow and Denning (1992) joint version of the Lo and MacKinlay test statistic   q z * , as provided in equation ( 13), selecting the maximum absolute value from a set of l test statistics.The test statistic can be written as:

Wild Bootstrapping Variance Ratio Tests by Kim
The wild bootstrap variance ratio test can be conducted in three stages, as below: given in equation ( 13).The p-value of the test is calculated as the proportion of In Monte Carlo simulations, Kim demonstrated that wild bootstrapping variance ratio tests are powerful and robust alternatives for testing the random-walk hypothesis.

Scoring Model
For a classification and to strengthen our results of the test statistics we made use of scoring model framework.
In the building process of the scoring model our criteria to be considered is the likelihood of the CDSs following a random-walk by using the findings of the statistical tests discussed previously.We grouped the daily and weekly data by mean and standard deviation into groups of 2, 3, 5, 6, 10, and 15 (by beginning with the highest value).Tables 3 and 4 give an overview of the mean and standard deviation by each CDS premium for daily and weekly observations on the whole sample period.

Table 3. 3-years-daily CDSs hierarchy criterion Table 4. 3-years-weekly CDSs hierarchy criterion
To determine how well each group member m satisfies the criterion, we assigned a scoring paradigm tmi r by alternative i for every statistical test t in terms of how well it satisfies the criterion.The scoring paradigm has the following structure: 7 Scores: 0% significance within the comprehensive survey 6 Scores: up to 100% significance in the first quarter and 0% significance in the other three quarters within the comprehensive survey 5 Scores: up to 50% significance in the first two quarters and 0% significance in the last 2 quarters within the comprehensive survey 4 Scores: up to 33.33% significance in the first three quarters and 0% significance in the last quarter within the comprehensive survey 3 Scores: up to 100 % significance in the first two quarters and 0% significance in the last two quarters within the comprehensive survey 2 Scores: up to 66.66% significance in the first three quarters and 0% significance in the last quarter within the comprehensive survey 1 Score: up to 100% significance in the first three quarters and 0% significance in the last quarter within the comprehensive survey 0 Scores: exceed 0 % significance in the last quarter within the comprehensive survey In the next step we chose the relative importance of each statistical test by matching weights t w .We assigned the Box-Pierce Q-Statistics the weight w=1, Variance Ratio Test by Lo and Mac Kinlay the weight w=1, Variance Ratio Test using Ranks and Signs by Wright the weight w=2 and Wild Bootstrapping Variance Ratio Tests by Kim the weight w=2.
In the following step we computed the aggregated score for each group member: In the final step we ranked every group by its achieved scores starting by the highest score result.

Results from the Box-Pierce Q-Statistics
We used a chi-square distribution on 5 per cent level with m degrees of freedom to test the validity of the random-walk null hypothesis of all 30 CDS for daily and weekly observations.We tested for the existence of autocorrelations by logarithmic means of Q-statistics within the limits of m=1 to 10.
For the daily observations only the CDS of Natixis shows no significance at the 5 per cent level, for all values of m. 9 CDS show a pattern of significances at the first lags (Erste Bank, Rabobank), or at the last lags (Credit Mutual, Credit Suisse, LBHT, Nomura) or at the beginning and at the end of the lags (HSBC, JP Morgan, Macquarie).Furthermore 20 CDS are significant at the 5 per cent level, for all values of m.The value of each CDS increases as m is raised for daily and weekly observations.There is a large difference in the autocorrelation values of Q-Statistics which ranges from 0.0165 (Credit Mutual, m=1) to 78.9984 (RBS, m=10).
For the weekly observations 9 CDS (Credit Mutual, Deutsche Bank, Erste Bank, Goldman Sachs, ING, LBBW, Merill Lynch, Natixis, Macquarie) show no significances at the 5 per cent level, for all values of m.This result conforms only to the daily findings of Natixis.7 CDS (Barclays, BNP, Commerzbank, JP Morgan, Nomura, NordLB, Rabobank) can be identified to be significant at the 5 per cent level for all values of m.As a comparison only Barclays, BNP, Commerzbank and NordLB conform to the daily observations.Parallel to the findings above there are identified patterns within the remaining 14 CDS.These patterns can be found in no significance at the first lags, at the last lags or at the beginning and at the end of the lags.
As an intermediate result of the daily and weekly findings from the Box-Pierce Q-Statistics it can be ascertained that null hypothesis of a random-walk existing for all values of m is highly possible within the time series of the Natixis CDS.

Results from the Variance Ratio Tests by Lo and MacKinlay
The variance ratio tests by Lo and MacKinlay check for homoscedasticity and heteroscedasticity to test the existence of a random-walk within the CDS data basis.We compared the results of the Variance Ratio Test with the random-walk null hypothesis at a level of 5 %.For this purpose we made use of a two-sided standardized normal distribution.Furthermore test statistics used aggregation values of q = 2, 4, 8, and 16.
For the daily observations with low values only Credit Mutual, Credit Suisse, Macquarie and Natixis exhibit signs of a random-walk within their time series under homoscedasticity and heteroscedasticity at the significance of 5%.Further, 10 CDSs show no significance at the 5% level under heteroscedasticity at all aggregation levels.Bank of America, Barclays, BayernLB and Erste Bank are significant under homoscedasticity and heteroscedasticity at the aggregation level 2 and 4. Unicredit is significant under heteroscedasticity and homoscedasticity at the aggregation levels 2, 4 and 8. LBBW shows no existence of a random-walk under the assumption of homoscedastic at all aggregation levels.NordLB shows fully significance at all aggregate levels for both homoscedasticity and heteroscedasticity, providing no indication of a random-walk.The rest show differences in rejection and compliance to the random-walk hypothesis.There is a predominant diminishment of positive initial values between q=2 to q=16.Negative initial values don't change in a clear pattern from q=2 to q=16.The highest value of homoscedasticity is for Bank of America (5.0926851 at level 2) and the lowest for NordLB (-5.516824 at level 2).The highest value of heteroscedasticity is for Unicredit (3.270464 at level 4) and the lowest for NordLB (-3.371303 at level 2).
For the weekly observations 20 CDSs are not significantly homoscedastic or heteroscedastic at all aggregation levels.Out of these 20 CDSs only the CDSs of Credit Mutual, Credit Suisse and Macquarie confirm the findings of daily observations.Nomura is significantly homoscedastic at all aggregation levels.Within the daily observations only Nomura is significant on the level 8 and 16.Most of the remaining CDSs are significantly homoscedastic and heteroscedastic at the aggregation level of 2 and/or 4.There is a predominant advancement of negative initial values between the levels of 2 and 16.In comparison to the daily observations Nomura shows the highest value of homoscedasticity (3.275605 in level 4).But as in the daily observations NordLB has the lowest value in the weekly observations (-4.298436 in level 2) as well.The highest value of heteroscedesticity is for Nomura (2.765704 in level 4) and the lowest JP Morgan (-3.006155 in level 2).
As an intermediate result of the daily and weekly findings from the variance ratio tests by Lo and MacKinlay it can be pointed out that only Credit Mutual, Credit Suisse, and Macquarie exhibit no evidence of homo-and heteroscedasticity.Therefore, a random-walk is highly probable only for these 3 CDSs.The remaining 27 CDS likely do not follow a random-walk.

Results from the Variance Ratio Test Using Ranks and Signs by Wright
The variance ratio tests by Wright analyze the existing of a random-walk with ranks (R1, R2) under homoscedasticity and signs (S1) under heteroscedasticity.The results of the tests have to be transferred to value systems conceived by Wright.The range of numbers that belongs to each value system depends on the number of observations and on the chosen quantile.To determine the existence of a random-walk within the data we compared the results of the Variance Ratio Test with the random-walk null hypothesis at a level of 5%.Further we used aggregation values of q = 2, 4, 8, and 16 for the variance ratio tests.
For the daily observations 11 CDSs do not exhibit signs of a random-walk within their time series for both R1 and R2.Moreover 4 Banks show no significances at all aggregation levels under the 5 % hypothesis in R1 (Bank of America, Citigroup, Credit Suisse) or R2 (Rabobank).BayernLB has no significance at the rank R2, but shows significance under R1 at lag 4. Most of the remaining 14 CDS are not significant at the aggregation level 2 and 4 or level 2, 4 and 8.The highest value for the test on homoscedasticity can be seen in Credit Mutual (12.643859 in lag 16/R1) and the lowest in NordLB (-3.961521 in lag 2/R2).Under heteroscedasticity (S1) we find significant results on all lags for 24 CDS.The other 6 CDS are significant at lag 2 and 4 (BNP, Deutsche Bank, Morgan Stanley) or at lag 2, 4 and 8 (Barclays, Commerzbank, Societe General).For daily and weekly observations there is a predominant diminishment of positive initial values between q=2 to q=16.Contrary to positive initial values, negative initial values change from q=2 to q=16 by raising values.
For the weekly observations 13 CDS are insignificant under both R1 and R2 for all levels of aggregation.But these findings are in contrast to 0 CDS that are insignificant under both R1 and R2 for daily observations.Further 5 CDS are insignificant at R1 (Morgan Stanley, Rabobank) or R2 (Erste Bank, LBBW, LBHT).Nomura and Macquarie show significance for all aggregation levels under R1 and R2.The other 10 CDS mostly are insignificant for lag 2. On the test for heteroscedasticity (S1) we find fully significant results by the CDS of Credit Mutual, HSBC, HSH, LBBW, LBHT, Macquarie and Nomura.These 7 CDS are also fully significant under daily observations.Further 12 CDS are fully insignificant, but have no accordance on daily observations.The other 11 CDS are very unspecific regarding their significance to the four chosen lags.This means that there are no specific patterns that can be identified.
As an intermediate result we find no evidence of a random-walk at any of the tested levels for both daily and weekly data.

Results from the Wild Bootstrapping Variance Ratio Tests by Kim
The variance ratio tests by Kim analyze the existing of a random-walk on a 5 percent level of significance.We use aggregation values of q = 2, 4, 8, and 16.
For daily observations 13 CDS show no significant results for lags of 2, 4, 8, and 16.By contrast, the CDS of NordLB shows significant results for all investigated lags.Most of the other 16 CDS are significant for just q=2 or q=2 and q=4.The highest value within the test statistics is for Barclays (0.991082 in q=16) the lowest value belongs to NordLB (0.000006 in q=2).Noticeable is an increasing value of the test statistic for the most CDSs by raising m's for daily and weekly observations.
For weekly observations 21 CDS are not significant for all of the chosen aggregation levels, while 11 CDS are also not significant under the daily observations.For Nomura we find significant results on all levels, which is in contrast to the results for Nomura in the daily observation (significant for lag 16 only).The remaining 8 CDS are mostly significant on all levels except on lag 2.
As an intermediate result of the daily and weekly findings from the Wild Bootstrapping Variance Ratio Tests by Kim it can be ascertained that a random-walk under all investigated levels within the time series is possible for the following 11 CDS: Bayern LB, Credit Mutual, Credit Suisse, Deutsche Bank, HSBC, ING, LBHT, Macquarie, Morgan Stanley, Natixis and Nomura.

Results Scoring Model
The results of the scoring models for 3-years-daily mean-ranked, 3-years-weekly mean-ranked, 3-years-daily standard-deviation-ranked, 3-years-weekly standard-deviation-ranked are as follows (see Table 5 to 8): It appears that subgroups (and their consisting entities) with low values for mean or standard deviation has higher scores and a better rank within the scoring model.This can be tested by dividing the number of subgroups in each group by 2 and adding the sums of the first half and the last half of the subgroups separately.An efficient market implies a high probability for the existence of a random-walk, otherwise it would be an inefficient market.Our findings for the daily and weekly data sorted by mean shows that CDSs with the lowest means have the highest total scores.This implies a high probability for the existence of a random-walk and consequently the highest market efficiency, the lowest speculation and the lowest market manipulation.The same results can be found for the daily and weekly data sorted by standard deviation as low volatilities (as the prices of the derivatives) have the highest market efficiency, the lowest speculation and the lowest market manipulation.
In contrast to this result, companies with a low value for mean or standard deviation are often victims of market manipulation and organized speculations (i.e. by Hedge Funds) as they seem to be traded in an inefficient market with a low probability of a random-walk.Taken as a whole our results show that a company's CDS with a low absolute risk (mean) and a low volatility has higher market efficiency and less market manipulation as compared to companies with high values.
A closer look at the results discloses spikes within the subgroups.In the first moment these spikes seem to weaken our results but as we see the results as a whole these spikes get moderated by the value of the other subgroup members i.e.Table 5: G2_6 (ranked 8th by its mean) achieved with the other 4 by its mean worst-ranked subgroups (G2_7 -G2_10) a total value of 262.63 scores in comparison to 218.482 scores for the 5 best-ranked subgroups (G2_1 -G2_5).
Furthermore our results for daily observations consist of higher scores in comparison to weekly observations.The crucial factor for the different high values for daily and weekly observations depends on the much better performances on Box-Pierce Q-Statistics and Variance Ratio Test Using Ranks and Signs by Wright.
If it comes to the point to choose the scoring model that fits best to the assumption presented above, it can be asserted that for 3-years-daily mean-ranked CDSs groups of 6, for 3-years-weekly mean-ranked CDSs groups of 6, for 3-years-daily standard-deviation-ranked CDSs groups of 15 and for 3-years-weekly standard-deviation-ranked CDSs groups of 3 are the best choices.These scoring models represents best the findings of CDSs with the lowest mean and standard deviation have the highest market efficiency and CDSs with the highest mean and standard deviation have the highest market inefficiency.

Conclusion
Investors hedging portfolios with CDSs need information on the question of whether the increase in speculation affects market efficiency or not.To answer this question our research has examined the relation between the absolute CDS premium and market efficiency.We focused on CDSs for international banks.We find that for daily and weekly data CDSs with the lowest mean and the lowest standard deviation have the highest probabilities for the existence of a random-walk.Consequently these CDSs are affected by the highest market efficiency, the lowest speculation and the lowest market manipulation.This finding is consistent as CDSs with the highest means and the highest standard deviations have the lowest probabilities for the existence of a random-walk.Therefore these CDSs have the highest potential to trade in an inefficient market with the highest potential for speculation and market manipulation.The results of our analysis show that the CDS market of financial institutions is already a target for market manipulation and speculation.Many of these financial institutions are global players and have become "too big to fail".Their insolvency would affect other financial institutions, the financial system and the global economy.To reduce speculation we support new regulations on the CDS market.These regulations should safeguard against dangerous speculation and market manipulation in order to protect our quality of life.
where m Q = Box-Pierce Q-statistic for m time lags m = number of coefficients n = number of observations k r = autocorrelation coefficient for time lag k

Bank of Am erica Barclays BayernLB BNP Citigroup Com m erzbank Credit Mutual Credit Suisse Deutsche Bank Erste Bank
Campbell et al. (1997)7)stated, there are three different versions of the random-walk hypothesis, each of them being slightly more stringent.The strongest assumption implies that all error terms t

Table 5
Table 7. 3-years-daily CDSs standard-deviation-ranked Table 8. 3-years-weekly CDSs standard-deviation-ranked To check market efficiency we tested the random-walk hypothesis by different test statistics.The strongest version of the randomwalk hypothesis was tested by homoscedastic variance ratio tests by Lo and MacKinlay and by nonparametric variance ratio test based on ranks by Wright.The weak form gets tested by Q-statistics portmanteau tests by Box and Pierce, heteroscedastic variance ratio tests by Lo and MacKinlay, nonparametric variance ratio tests based on signs by Wright and wild bootstrapping variance ratio tests by Kim.