TRACKING ERRORS AND SOVEREIGN DEBT CRISIS

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1 EUROPEAN BOND ETFs TRACKING ERRORS AND SOVEREIGN DEBT CRISIS Mikica Drenovak, Branko Urošević, and Ranko Jelic National Bank of Serbia National Bank of Serbia First Annual Conference of Young Serbian Economists June 2011

2 ETFs as a new asset class 753 registered European exchange traded funds (ETFs) with asset under management (AUM) of over US$ 183 billion, in 2009 The proportion of fixed income ETFs, in the total AUM, grew from 5% in 2003 to 25% in 2009 Conventional government bond ETFs remain the most popular p sub-asset class within the fixed income category with total AUM at EUR billion as of end first quarter in They account for close to 57% of overall fixed income ETFs AUM Those ETFs tracking Euro zone government bond indices account for close to 84% of AUM

3 New risk return paradigm The debt crisis ( ) has radically changed the dynamics of Euro sovereign bond markets Before the crisis, the risk of Euro sovereign bond indices was low and almost entirely attributable to yield curve risk During the crisis, the risk of Euro sovereign indices rose by approximately 30% mostly due to the increase in credit spread levels and volatility (Nomura, 2011) Some Euro sovereign bonds are more akin to corporate bonds (EU peripherals: Belgium, Greece, Italy, Ireland, Portugal, Spain)

4 Motivation ETFs are an important investment class, yet paucity of academic research The analysis of ETF tracking errors remains a widely misunderstood d and frustrating ti process (Flood 2010a) Government bonds are now seen as mixed interest rate risk and credit risk product Given the above changes in risk factors and volatility of Euro sovereign bonds, more sophisticated approach is required for assessment of ETFs tracking performance and determinants of tracking errors (TE)

5 Contributions Novel dataset; 31 Euro zone sovereign debt exchange traded d index funds (ETFs), during Examination of ETFs tracking error within cointegration framework Examination of determinants of the tracking performance panel data analysis Examination of the effects of the new risk and return paradigm in the Euro sovereign bond market on the tracking gperformance

6 Literature Amenc and Golz (2009) EU Survey - ETFs play an important role in providing exposure to various asset classes Rompotis (2008; German equity index ETFs); Milionas and Rompotis (2006; Swiss equity index ETFs); Blitz et al. (2010; EU equity index ETFs); Correlation based TE and OLS analysis ETFs underperform their benchmarks Tracking error (TE) is related to risk (volatility), bid-ask spread, expense ratio, and size

7 Literature Drenovak and Urosevic (2010): Examine tracking performance of Euro zone sovereign bond ETFs, during 2007-May 2010 Correlation-based measures Alexander (1999); Alexander and Dimitriu (2004): Two time series can be cointegrated even if static correlations between their returns are low Important to examine tracking performance based on both correlation and cointegration, especially for passive investment strategies

8 Hypotheses H1: Euro zone sovereign ETFs underperform their underlying bond indices H2: Tracking performance is negatively associated with volatility of tracked indices H3: Correlation and cointegration based TE metrics provide different assessment (ranking) of the tracking performance H4: Association between ETFs and underlying bond indices changed during financial crisis H5: Default risk has become an important determinant of H5: Default risk has become an important determinant of tracking errors

9 Sample and data Sample: 31 Euro sovereign bond indices ETFs, January 2007-December 2010: ishares (track Barclays term, Markit iboxx Liquid Sovereign Capped, eb.rexx German Government) db x-trackers (track Markit iboxx Sov) Lyxor (track EuroMTS) All sample indices are total return indices; all maturities considered Daily data on: Net Asset Values (NAV), Weights, CDS, and Bid-ask Sources: Bloomberg and official ETFs websites

10 Table 2 Aggregate country exposure of government bond indices (in %) tracked by sample ETFs, stratified by ETF providers Germany Italy France Spain Belgium Netherlands Greece Portugal Austria Ireland Finland ishares Barclays Term Barclays Term Barclays Term Barclays Term Barclays Term Barclays Term iboxx Liq Sov Cap iboxx Liq Sov Cap iboxx Liq Sov Cap iboxx Liq Sov Cap iboxx Liq Sov Cap eb.rexx eb.rexx eb.rexx eb.rexx eb.rexx DE 100 db-trackers Short iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov Lyxor EuroMTS 1-3Y EuroMTS 3-5Y EuroMTS 5-7Y EuroMTS 7-10Y EuroMTS 10-15Y EuroMTS 15Y

11 Methodology Standard methods ( ) TE r r 1 = p b ( ) 2 2 TE2 = stdev r r = σ + σ 2σ σ ρ p b p b p b p, b

12 Methodology - OLS (TE3 = standard error of the regression) r = α + β r + ε p i i b p * Quandt-Andrews breakpoint test

13 Methodology - Cointegration framework (TE4 = residual from the cointegrating regression) m m 1 2 Δ NAVp = α + β Δ NAVp + β Δ NAVb + γ z + ε t 1 1 i t i 2 i t i 1 t 1 1 t i= 1 i= 1 m3 m4 Δ NAVb = α + β Δ NAVp + β Δ NAVb + γ z + ε t 2 3 i t i 4 i t i 2 t 1 2 t i= 1 i= 1 Here, NAVp and NAVb are daily log NAV values for ETFs and 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. The more stationary TE4 the greater the cointegration between ETF and the respective index

14 Determinants of TE Panel data analysis TE = α+ βbid ASK + βlnduration + βsynthetic + βwindex + βter + βlnsize + ε it 1 it 2 it 3 it 4 it 5 it 6 it it TE BID ASK LNDURATION SYNTHETIC WINDEX it = α + β1 it + β2 it + β3 it + β4 it β TER + β LNSIZE + β PLEHMAN + β LNWCDS + β WPCDS + ε 5 it 6 it 7 it 8 it 9 it it

15 Figure 1 Changes in volatility for sample ETFs This figure presents evolution of volatilities for the sample ETFs targeting g 10+ year maturities. Rolling 3-month standard deviation of daily returns (annualized) /1/2008 6/1/ /1/2008 4/1/2009 9/1/2009 2/1/2010 7/1/ /1/2010 ishares Bar ishares eb.rexx ishares iboxx Lyxor EuroMTS10-15 db iboxx 10-15

16 Table 5 Sample TE1, This table presents results for average (mean) TE1, based on annual returns. TE1 (annual) bps ishares Barclays Term Barclays Term Barclays Term Barclays Term Barclays Term Barclays Term Average for Barclays iboxx Liq Sov Cap iboxx Liq Sov Cap iboxx Liq Sov Cap iboxx Liq Sov Cap iboxx Liq Sov Cap Average for iboxx eb.rexx eb.rexx eb.rexx eb.rexx eb.rexx DE Average for eb.rexx

17 TE1 (annual) bps db x-trackers short iboxx iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov iboxx Sov Average for db iboxx Lyxor EuroMTS EuroMTS EuroMTS EuroMTS EuroMTS EuroMTS Average for Lyxor

18 Table 6 Sample TE2, This table presents results for average (mean) 3-month TE2 for respective ETFs, based on monthly and daily returns, in basis points. Reported levels of statistical significance are for the one sample T- test: mean=0 vs. mean not=0. *, **, and *** indicate significance at the 10%, 5%, and 1% level. TE2 (m. returns) TE2 (daily returns) ishares ETFs Barclays Term *** 0.77*** Barclays Term *** 1.53*** Barclays Term *** 2.29*** Barclays Term *** 2.33*** Barclays Term *** 2.95*** Barclays Term *** 4.08*** Average for ishares-barclays 2.73*** 2.32*** 2.05*** 4.56*** 1.65*** 0.69**** iboxx Liq Sov Cap *** 1.87*** iboxx Liq Sov Cap *** 2.52*** iboxx Liq Sov Cap *** 5.30*** iboxx Liq Sov Cap *** 12.80*** iboxx Liq Sov Cap *** 4.65*** Average for ishares-iboxx 7.03*** 5.43*** 7.40*** 4.24*** 6.48*** 1.88*** eb.rexx *** 1.89*** eb.rexx *** 2.57*** eb.rexx *** 4.84*** eb.rexx *** 11.78*** eb.rexx DE 2.77*** 2.90*** Average for ishares-eb.rexx 5.98*** 4.79*** 1.75*** 5.28*** 7.8*** 1.65***

19 TE2 (m. returns) TE2 (daily returns) db x-trackers ETFs short iboxx 4.54*** 4.38*** iboxx Sov 3.49*** 3.32*** iboxx Sov *** 1.53*** iboxx Sov *** 3.07*** iboxx Sov *** 5.03*** iboxx Sov *** 3.81*** iboxx Sov *** 4.34*** iboxx Sov *** 6.40*** iboxx Sov *** 9.42*** Average for db x-trackers 4.97*** 4.59*** 4.33*** 6.88*** 4.02*** 0.65*** Lyxor ETFs EuroMTS **** 9.54*** EuroMTS *** 19.34*** EuroMTS *** 26.94*** EuroMTS *** 32.65*** EuroMTS *** 40.72*** EuroMTS *** 12.87*** Average for Lyxor 25.66*** 23.68*** 22.30*** 29.12*** 23.42*** 17.03***

20 Figure 2 Patterns of sample TE2 This figure presents the patterns of average three month TE2 based on daily returns (in bps) for the sample ETFs targeting 10+ year maturities. TE2 based on daily returns /1/2008 6/1/ /1/2008 4/1/2009 9/1/2009 2/1/2010 7/1/ /1/2010 ishares Bar ishares eb.rexx ishares iboxx Lyxor EuroMTS db iboxx

21 Table 7 OLS model: Sample TE3 and break points, 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 the regression model in basis points. Presented averages are mean values. T-tests statistics is for the two tail tests: i) alpha =0 vs. alpha not = 0 (column 3); ii) beta=1 vs. beta not = 1 (column 5). Results in column (8) are identified break points in the relationship between ETF and index returns, together with levels of statistical significance for the Quandt-Andrews (Q-A) test. *, **, and *** indicate significance at the 10%, 5%, and 1% level. Alpha T-test Beta T-test R 2 TE3 Q-A N ishares ETFs Barclays Term ** /08/08*** 1037 Barclays Term /08/08*** 1037 Barclays Term ** Barclays Term ** /08/08*** 1037 Barclays Term /09/09** 439 Barclays Term ** /08/08*** 1037 Average for ishares-barclays *** ** iboxx Liq Sov Cap *** /04/10*** 1037 iboxx Liq Sov Cap *** /10/08* 1037 iboxx Liq Sov Cap *** /10/08*** 1037 iboxx Liq Sov Cap *** /10/07*** 1037 iboxx Liq Sov Cap ** /10/07*** 1037 Average for ishares-iboxx ib ** 410** eb.rexx *** /10/08* 1037 eb.rexx *** /10/08* 1037 eb.rexx *** /08/08** 1037 eb.rexx *** /01/09*** 1037 eb.rexx DE *** /08/08** 1037 Average for ishares-eb.rexx ***

22 Alpha T-test Beta T-test R 2 TE3 Q-A N db x-trackers ETFs short iboxx *** /12/ iboxx Sov ** /04/09** 937 iboxx Sov ** /05/09*** 934 iboxx Sov ** /06/08** 934 iboxx Sov *** /06/08** 931 iboxx Sov ** /06/ iboxx Sov ** /08/08* 929 iboxx Sov ** /05/09*** 929 iboxx Sov ** /05/09** 927 Average for db x-trackers *** *** Lyxor ETFs EuroMTS ** *** EuroMTS * *** EuroMTS *** EuroMTS *** EuroMTS *** EuroMTS *** /06/08*** 911 Average for Lyxor *** ***

23 Table 8 Cointegrated vector error-correction (VEC) model and TE4 This table presents results of Johansen test (JT) for cointegration between daily log NAV values for ETFs and relevant indices. Estimations are made assuming a constant trend. Critical value for JT trace statistics for rejecting a null (at 5% level of significance) that there is zero cointegrating vector is Number of lags (NL) is determined based on unreported results of Hannan-Quin information criterion (HQIC), Schwartz Bayesian information criterion (SBIC) and sequential Likelihood Ratio (LR) methods. Log likelihood is for the overall model. Estimated parameters of the cointegrating vector are normalised cointegrating vector coefficients for ETFs and indices. The coefficient on ETF is restricted to unity by the Johansen normalization. DF is Dickey-Fuller test statistics from unit root tests for the cointegrating regressions residuals (TE4). NL JT trace Normalised coefficients DF Log lik. N ETF Index ishares ETFs Barclays Term Barclays Term Barclays Term ** *** , Barclays Term Barclays Term ** *** , Barclays Term Average for ishares-barclays iboxx Liq Sov Cap ** *** , iboxx Liq Sov Cap ** *** , iboxx Liq Sov Cap ** *** , iboxx Liq Sov Cap ** *** , iboxx Liq Sov Cap ** *** , Average for ishares-iboxx eb.rexx ** *** , eb.rexx ** *** , eb.rexx ** *** , eb.rexx ** *** , eb.rexx DE ** *** , Average for ishares-eb.rexx

24 NL JT trace Normalised coefficients DF Log lik. N ETF Index db x-trackers ETFs short iboxx ** *** , iboxx Sov ** *** , iboxx Sov iboxx Sov ** *** , iboxx Sov ** *** , iboxx Sov ** *** , iboxx Sov ** *** , iboxx Sov ** *** , iboxx Sov ** *** , Average for db x-trackers Lyxor ETFs EuroMTS ** *** , EuroMTS ** *** , EuroMTS ** *** , EuroMTS ** *** , EuroMTS ** *** , EuroMTS ** *** , Average for Lyxor

25 Table 10 Panel data analysis of sample tracking errors (TE2), This table presents results of the random effects GLS regression with a robust estimator of variance adjusted for clustering on fund. Panel A presents estimates of equations 7, 8, 9, and 10 (Models 1, 2, 3, and 4, respecively). TE2 is dependent variable in all models. BKW condition number is the ratio of largest to smallest eigenvalue, representing an unbounded measure of the regression collinearity, The condition number larger than 30 indicates collinearity problems. AIC is the Akaike Information Criteria used for model selection. *, **, and *** indicate significance at the 10%, 5%, and 1% level. Panel A Model 1 Model 2 Model 3 Model 4 BID-ASK *** ** LNDURATION ** ** ** *** SYNTHETIC ** * ** * PLEHMAN *** *** WINDEX *** *** *** *** TER *** *** *** *** LNSIZE *** *** LNWCDS *** 00030*** *** 00027*** WPCDS *** LNWCDS*WPCDS WINDEX*WPCDS WINDEX*LNWCDS Constant *** *** *** *** Wald Chi *** *** *** *** R 2 (overall) BKW AIC N (obs.) N (groups)

26 Conclusions ETFs underperform their respective indices Consistency of TE2 and TE3 tracking measures; both measures provide the same ranking and suggest superior tracking performance of physically-based ETFs. Consistency of TE1 tracking measure and cointegration based metric for the sample funds Cointegration based TE4 provides different ranking compared to TE2 Results highlight the importance of using both metrics for proper assessment of tracking quality and ranking of ETFs which employ different replication strategies

27 Conclusions Association of ETFs and indices changed during the crisis, resulting in changes of tracking performance (TE2) Variables associated with the credit risk in Euro zone sovereign bond market significantly increase explanatory power of our models for determinants of TE

KEY WORDS: exchange-traded funds, tracking errors, fixed-income, sovereign debt JEL CLASSIFICATION: D81, E43, G15, G24

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