EUROPEAN SOVEREIGN BOND ETFs – TRACKING ERRORS AND SOVEREIGN DEBT CRISIS

1. EUROPEAN SOVEREIGN BOND ETFs – TRACKING ERRORS AND SOVEREIGN DEBT CRISIS Branko Urošević, Faculty of Economics, University of Belgrade and National Bank of Serbia First Moscow Finance Conference November 2011

2. Outline • Background, motivation, contributions • Literature and hypotheses • Data and methodology • Results • Conclusions

3. Motivation • Market for sovereign bonds of the Euro zone in the forefront of interest of investors, politicians, … • Fundamental shift in perception: from virtually riskless to much more akin to corporates (some of them with a junk bond status) • Diverging performance across countries • EFTs: new, liquid and relatively transparent way to get exposure to that market • While many asset classes are severely impacted by the crisis, ETFs steadily grow in importance

5. Literature and motivation • Amenc and Golz (2009) – EU Survey - ETFs play an increasingly important role in providing exposure to various asset classes • Rompotis (2008; German equity index ETFs); Milionas and Rompotis (2006; Swiss equity index ETFs); Gallagher and Segara (2005; Australian equity index ETFs); Blitz et al. (2010; EU equity index ETFs); • Drenovak and Urosevic (2010), Houweling (2011) analyse corporate (European and US) and sovereign (US) bond ETFs. Performance measured using correlation-based tracking error. • Alexander (1999); Alexander and Dimitriu (2004): • Two time series can be cointegrated even if static correlations between them are low • Important to examine tracking performance based on both correlation and cointegration, especially for passive investment strategies.

6. Literature and motivation • Norden and Weber (2009) • CDS market reflects information earlier than bond market • Bond spreads adjust to CDS spreads. • The dynamics of spread volatility are driven by those of spread levels (Nomura, 2011). They may influence tracking performance after the crisis commenced. • Composition of ETFs may also play an important role now (and did not play much of a role before)

7. Contributions • Study tracking performance of the most important families of ETF funds that track indexes of euro zone sovereign bonds using a novel data set • Compare performance using 4 types of tracking errors: active return (TE1), two short-term correlation based measures (TE2 and TE3) and a cointegration-based tracking error measure (TE4) • Synthetic versus physical replication • Preliminary study of determinants of tracking errors including how crisis influenced them

8. Hypothesis • H1: Euro zone sovereign ETFs underperform their underlying bond indexes, regardless of the replication method. • H2: ETFs’ tracking errors are positively associated with the volatility of target indices. • H3: ETFs’ tracking errors are positively associated with the maturity of underlying indexes.

9. Hypotheses • H4: Tracking performance of EU sovereign debt ETFs deteriorated during the post Lehman period. • H5: CDS spreads for index constituents are an important determinant of tracking performance of EU sovereign debt ETFs in a post-Lehman period • H6: Synthetic ETFs perform better measured by TE1 and TE4, and worse measured by correlation based measures (TE2 and TE3), compared to full replication physically-based ETFs.

10. Sample and data • Sample: 31 Euro sovereign bond indices ETFs, January 2007-December 2010 (captures more than 90% of the market):  • iShares (track Barclays term, Markit iBoxx Liquid Capped, eb.rexx German Government). Physical replication. • db x-trackers (track Markit iBoxx Sov). Synthetic replication • Lyxor (track EuroMTS). Synthetic replication • All indices tracked by sample ETFs are total return indices (all interest payments are reinvested); all maturities considered • Daily data on: Net Asset Values (NAV), Weights, CDS, and Bid-ask. Data on NAV from Frankfurt (for consistency) •  Sources: Bloomberg, index providers, Morningstar

11. Aggregate country exposure of government bond indices tracked by sample ETFs, stratified by ETF providers

12. Summary statistic (average values)

13. Methodology – Standard methods

14. Methodology - OLS (TE3 = standard error of the regression)

15. Methodology - Cointegration framework (TE4 = autocorrelaton of the residual from the cointegrating regression) Here, NAVp and NAVb are daily log NAV values for ETFs and underlying indices, z is the cointegrating vector NAVpt - αNAVbt, Δ is the first difference operator, and the lags, lengths and coefficients are determined by OLS regression.

16. Tracking error and replication methods • Previous studies did not examine tracking errors in the context of different replication methods adopted by ETFs. • Replication methods should be taken into consideration when selecting an appropriate measure of tracking errors. • A full physical replication of indexes with strict inclusion criteria would, for example, lead to a very high correlation of ETF and tracking index returns and, therefore, low TE2 and TE3. • This can come at the expense of long term co-movement (TE4, for example).

17. Ranking Based on TE1 • Consistent with our hypothesis 1, sample ETFs underperformed their respective indexes during the sample period • The average underperformance for the total sample is similar to the underperformance reported in previous studies on bond ETFs (Drenovak and Urosevic, 2010; Houweling, 2011). • The average annual TE1, however, varies significantly from 0.53 (LyxorMTS+15) bps to 27.38 bps (iShares-BarclaysTerm10-15). • Overall, the iShares–BarclaysTerm family exhibits largest whilst Lyxor ETFs exhibit the smallest average TE1s. • Lyxor ETFs actually over-performed relevant indices in 2007 and 2009. • db x-trackers exhibited the most consistent performance during the sample period. • While iShares-Barclays family continues to exhibit similar TE1s, the rest of the ETF families exhibited a sharp drop in the TE1 levels in 2009. • In 2010, iShares-eb.rexx and Lyxor’s were the only ETFs with a sharp increase in average TE1.

18. Performance and sample TE1 This table represents ETFs annual returns (%) and TE1 presented in basis points [in brackets]. Positive basis points indicate undeperformance of the ETFs.

19. Ranking of funds based on TE2 • All sample ETFs have statistically significant average (mean) tracking errors at the 1% level of significance. • This result is robust to the use of weekly or monthly instead of daily price series. • Overall, iShares funds which replicate Barclays Term indices exhibit the smallest while Lyxor ETFs exhibit the largest values of TE2. • TE2 (based on monthly returns) range from 1.1 basis points (iShares-BarclaysTerm1-3) to 43.83 (LyxorMTS10-15). • The results also suggest that ETFs tracking higher maturity indices have typically higher levels of tracking error. This is the case for all sample ETFs except for db iBoxx Sov 5-7. • There are also some differences in the way TE2s changed during the sample period. iBoxx Liquidity and eb.rexx, for example, exhibited the highest TE2 in 2009. • This is consistent with high weightings for Greece (in iBoxx liquidity) and Germany (in eb.rexx), the two countries with extremely volatile interest rates during 2009. • Barclays, db, and Lyxor indices, however, exhibited the highest TE2 during 2008. • Lyxor funds have particularly high TE2.

20. Sample TE2 This table presents results for average (mean) 3 month TE2 for respective ETFs, based on monthly and daily NAV series. N is the number of bonds in the portfolio – calculated by authors based on the data from ETFs’ prospectuses as in May 2010. P-values for one sample T-test for mean=0 vs. mean#0 in brackets. Unreported results for one sample Wilcoxon test for median=0 vs. median#0 are economically and statistically consistent with the reported results for the T-test.

23. Figure 2 Evolution patterns of sample TE2 This figure presents the patterns of average three month TE2 (in bps) for the sample ETFs targeting 10+ year maturities. TE2 based on daily returns.

24. Ranking based on TE3 • The results presented in the following table suggest that only 3 out of 31 sample ETFs have alphas statistically different from zero. • The estimations for all beta coefficients are statistically different from 1 for all but 3 sample funds. • Lyxor family is a clear outlier with an average beta of 0.53 confirming that ETFs from this family depart from full replicating strategy. • The coefficient beta is below 1 for all but two sample funds, indicating that the sample’s ETFs may be more conservative than their respective benchmarks.

25. Ranking based on TE3 • Regarding R2, the Lyxor family is again a clear outlier with an average of only 30%. • For all other sample ETFs, ranges between 93% and 99%, indicating a very good regression fit. • The iShares family exhibits the highest average of 98%. • Reported values for TE3, measured by standard deviation of residuals, indicate the same ranking of sample funds as is it was case when we employed TE2 measure.

26. OLS Regression model for ETFs’ returns and TE3 This table presents results of the OLS model for ETFs daily returns as dependent variable and daily returns of the underlying indices as explanatory variable. TE3 is standard error of regression (i.e. standard deviation of residuals) in basic points.

29. Cointegration-based measure TE4 • Based on the results of the JT test for cointegration, we strongly reject the null hypothesis of no cointegration in all but five ETFs. • Four out of the five ETFs are from the iShares–Barclays Term family (1-3, 3-5, 7-10, and 15-30). In contrast, the log likelihoods, JT test statistics, and DF test statistics indicate a very good model fit for iShares - iBoxx€LiqSovCap and Lyxor ETFs, followed by the iShares - eb.rexx and the db x-trackers funds. • Based on TE4, Lyxor ETFs are the best and iShares – Barclays Term the worst performers. Overall, swap-based ETFs perform better than physically-based ETFs measured by TE4.

33. Overall ranking

34. Determinants of TE1 and TE2 • STDEV3: rolling 3 month standard deviation of underlying indexes. • LNDURATION: log of index duration. Proxy for maturity of bonds and their sensitivity to changes in interest rates. • PLEHMAN: 1 for observations post 1st September 2008, and zero otherwise. • SYNTHETIC*PLEHMAN: examine differences in the tracking performance of swap and physically-based ETFs during the credit crisis. • TER: portion of management fees deducted on a daily basis. • BID-ASK: daily bid-ask spread for ETFs. • LNSIZE: is a natural logarithm of daily AUM values.

35. Determinants of TE1 and TE2 • LNWCDS: log of of weighted averages indexes’ CDS. Calculate that using daily weights and CDS spreads for the index constituents. • WPCDS: weekly percentage change of the weighted average CDS spread.

36. Determinants of TE – Panel data analysis

37. Findings from the panel regressions • The results for model 1 indicate a positive and statistically significant association of tracking errors with STDEV3 and LNDURATION (hypotheses 2 and 3). • The coefficient for LNSIZE negative and statistically significant suggesting that larger funds tend to exhibit better tracking performance. • Tracking errors have increased since the sovereign crisis, resulting in a positive and statistically significant coefficient for PLEHMAN, as predicted by our hypothesis 4.

38. Findings from the panel regressions • Positive and statistically significant variable SYNTHETIC suggest worse overall performance of sample synthetic ETFs. This is consistent with Hypothesis 6 for TE2 but not for TE1. • To study TE1 further examine possible differences between sample synthetic funds we introduce LYXOR and DBX categorical variables. The results highlight the differences between Lyxor and db x-trackers. • For example, the coefficient for LYXOR is negative while the coefficient for DBX is positive and highly statistically significant. • The results for SYNTHETIC were, therefore, driven by the performance of db x-trackers.

39. Findings from the panel regression • Coefficient for SYNTHETIC*PLEHMAN significant. This confirms a different tracking performance of synthetic and physically-based ETFs during the sovereign debt crisis. • The results suggest a better performance of synthetic funds during the crisis measured by TE2 and worse performance measured by TE1. • First of these results in part related to higher correlation of returns for different asset classes during the crisis. The increase in correlation was particularly evident for corporate and government bonds (Nomura, 2011).

40. Findings from the panel regression • Proxies related to the sovereign credit risk show importance of CDS spreads for the tracking performance lending support to hypothesis 5. • The coefficients for credit spread levels (LNWCDS) are, however, positive and statistically significant only in models for TE2. • Similarly, the coefficients for volatility of spreads (WPCDS) and interaction variables (LNWCDS*WPCDS) are statistically significant only in models for TE2 and not for TE1. • Overall, the results confirm that variations in credit risk of index constituents tend to be more relevant for TE2 than for TE1.

41. Conclusions • ETFs underperform their respective benchmarks. Large discrepancy across types of tracking errors and funds. • Deterioration of the sample ETFs’ TE2 tracking performance during the crisis period. Credit risk considerations are increasingly important. Not so much for TE1. • Evidence for the importance of volatility of underlying indices, duration, the replication method, bid-ask spreads, management fees and ETFs’ size to the tracking performance. • To compare across families of ETFs adopting different replication methods caution is needed. • When TE2 and TE3 are used, physically-based ETFs show superior performance • Opposite is true if TE1 and, especially, TE4 are used. • Lyxor ETFs tend to improve the performance during the more volatile market conditions, measured by TE2.

42. Conclusions • Edhec, 2009 survey suggests that European investors prefer to use ETFs passively and favour ETFs that adopt a full replication. • At the same time, more than 70% of the investors use TE1 as the measure of the tracking performance. Half of them see ETFs tracking quality as fairly good • Our results suggest that a great deal of the investors’ dissatisfaction with the ETFs tracking performance could be due to a mismatch between the tracking performance measures used by investors and the characteristics of selected ETFs. • According to our findings, each ETF family should be assessed on its own merits and the choice of the error metric should be based on characteristics of ETFs, investment strategies and the underlying indexes they seek to replicate.