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Defining Benchmark Status: An Application using Euro-Area Bonds Peter G. Dunne, Queen's University, Belfast Michael J. Moore, Queen's University, Belfast Richard Portes, London Business School and CEPR August 2003

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Road map Characteristics of euro-area government debt market How to define benchmark? Data set Granger-causality analysis Cointegration analysis – with a new twist Interpretation: benchmark portfolios Conclusion: German bonds do not have unambiguous benchmark status

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Structure of euro-area government debt market Size similar to US – Italy, Germany, France have largest outstanding stocks (Table 2) Turnover up dramatically (Figure 1) – e.g. turnover on Euroclear up threefold for both France and Germany, end-1997 to end-2000 On average, one-third of a country’s bonds are held by non-residents

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Source: Blanco (2001) Table 2

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Figure 1

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Integration of euro-area government debt markets Convergence among countries in debt structure and maturities Share of foreign-currency debt now negligible Almost complete reliance on marketable instruments All moving to large, liquid benchmark-size issues A dominant electronic trading platform But impediments: different tax structures, accounting rules, settlement systems, market conventions, issuing procedures

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Yield differentials Considerable convergence (Fig. 2) A major step in convergence from mid-2000 (Fig. 3) Since then, all countries have positive spreads w.r.t. Germany at all maturities Convergence was initially elimination of exchange-rate risk (Table 3) But from early 1999, spreads widened – what are they? - default risk (increase plausible) – but not for best risks (Fig. 4) - microstructure factors – esp. liquidity Interpretation problematic: spreads vary over time and along yield curve – but - ratings vary little and seldom differ across maturities - can’t identify time-varying and maturity-dependent determinants of liquidity

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Source: Galati and Tsatsaronis (2001) Figure 3

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Source: Blanco (2001) Table 3

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Source: Blanco (2001) Figure 4

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How to define benchmark? Why care? National pride (and some welfare implication)! But also information externality: benchmark reduces cost of information. Hence alternative concepts Lowest yield Most liquid Define w.r.t. price discovery

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Benchmark as information aggregator Benchmark bond is the instrument to whose price the prices of other bonds react Price discovery relates to direction of the entire market – benchmark should be highly correlated with common movements in the market. So we examine: Granger-causality between yields Patterns of cointegration among yields

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Theoretical framework Suppose the yield on a country-specific security is the country risk-free rate plus a term in euro-area-wide risk If the error terms are stationary but the area-wide-risk is I(1), then the yields are all non-stationary Yuan (2002): a benchmark security has no sensitivity to country- specific risk and has unit sensitivity to systematic risk Then we can construct a benchmark security as a basket of country securities. Its yield is the systematic risk plus a weighted average of the country risk-free rates. Thus being benchmark has nothing to do with carrying lowest yield, everything to do with the security’s information content. In practice, benchmark could be issued exogenously (as in Yuan) – but we see it as emerging endogenously.

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Key result: identifying the benchmark The variance of the residual error in the cointegrating vector between the yield on country i’s security and any other country specific security j=1…,n is always greater than the variance of the residual error in the cointegrating vector between country j’s yield and the benchmark yield. Thus we identify the benchmark in terms of this minimum variance criterion. We shall see that this maps perfectly onto our empirical treatment using irreducible cointegrating vectors.

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The analytics Country-specific security has yield Assume systematic (euro-zone-wide) risk is I(1). Then all yields are non-stationary, and all pairs of country yields are cointegrated, with variance of cointegrating residual Construct benchmark as basket of country-specific securities: So yield on benchmark is

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It is straightforward to show that all country yields r i are pairwise cointegrated with the benchmark yield r b.The variance of the cointegrating residual is We then have the main result: The variance of the residual error in the cointegrating vector between the yield on country i’s security and any other country specific security j=1…,n is always greater than the variance of the residual error in the cointegrating vector between country j’s yield and the benchmark yield. This identifies the benchmark as a basket of bonds. In our empirical analysis, a particular country’s bond emerges as benchmark at a given maturity, but we also consider the basket concept. Note again that for us, the benchmark emerges endogenously.

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Data set coverage Every transaction on Euro-MTS for November- December 2000 (44 trading days): time, volume, price, initiator (buyer or seller) Euro-MTS then handled over 40% of total volume We have all countries except Ireland but use only three: Italy (I), France (F), Germany (D) (T 4) Four maturity categories We use twice-daily observations on one security from each category for each country

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Yields and yield gaps Figs. 5-12 show yields and yield gaps (F-D, I-D, I- F) at each maturity – see e.g. Figs. 9-10 for ‘long’ German yield always lowest, then French, then Italian Looking at all countries, we find clusters – Fig. 15 – France and Italy at centres

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Figure 9

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Figure 10

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Figure 15

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Stationarity We test each yield and yield gap for stationarity (Tables 13-16) All yields are non-stationary Not clear for yield gaps – e.g. - at short end, unclear whether I-D or I-F stationary, whereas F-D seems stationary - two of three stationary at medium and long maturities - one of three stationary at very long maturity Implications to follow…

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Granger-causality tests 3-variable VAR on yields, each maturity separately T 17-20 select lag length, T 21-24 give GC results Results - at short end, no benchmark: non-causality rejected in all cases (lagged yields of each country affect yields of one or both other country) - at medium end, rule out D as benchmark – but both I and F yields have predictive power for others - at long end, I is benchmark - very long maturity similar to medium: only D can be ruled out as benchmark Counter-intuitive – but this is only short-run dynamics

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Longer-run perspective: cointegration LR structure of price discovery process should appear from analysis of cointegration of yield series If (say) Germany provides benchmark at a given maturity, then cointegrating vectors could be Italian yield = German yield + nuisance parameters French yield = German yield + nuisance parameters If constant in each cointegrating vector is unity, we have 2 stationary yield gaps (note: tests suggested that wasn’t always true)

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Puzzle and resolution But any linear combination of multiple cointegrating vectors is itself one – e.g. Italian yield = ( / )French yield + nuisance parameters What to do? Test for irreducibility of cointegrating vectors and rank by min variance We thereby get structural relationship linking cointegrated series (the benchmark) from the data

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How to do it? Davidson and Barassi-Caporale-Hall Davidson: A set of I(1) variables is ‘irreducibly cointegrated’ (IC) if they are cointegrated but dropping any of them leaves a set that is not cointegrated ‘Structural’ and ‘solved’ IC vectors: An IC relation is structural if it contains a variable that appears in no other IC relation. A solved vector is a linear combination of structural IC vectors. Our system has 3 I(1) variables (yields). Suppose (D,F) and (D,I) both cointegrated. Then (F,I) also cointegrated. All 3 are IC vectors. Which of cointegrating relations is ‘solved’, which ‘structural’? If there is a single benchmark that provides structure for IC relations, then one of the IC vectors must be solved – and benchmark is common component in structural relations. BCH: Rank cointegrating vectors according to size of their variance. Why?

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Minimum variance criterion Suppose x, y, z are cointegrated: y - βx = e1, y - z = e2, x - z = e3 are 3 irreducible cointegrating relations Suppose the first 2 are ‘structural’, with e1 and e2 distributed independently N(0, i 2 ), i=1,2 Then e3 is a function of e1 and e2, distributed N[0, ( 1 2 + 2 2 )/β 2 ]. If β 1, then 3 2 max ( 1 2, 2 2 ) The condition β 1 holds in all our estimates. So the minimum-variance cointegrating relations are the structural ones – the one with largest residual variance must be the solved IC vector. Criterion implements theory above (Sec 2 of paper).

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Empirical strategy Johansen procedure identifies the number of cointegrating vectors at each maturity Phillips-Hansen FMOLS estimates irreducible cointegrating vectors BCH variance ranking criterion ranks them – the structural vectors are those with minimum residual variance, the benchmark is the common yield in the two structural irreducible cointegrating vectors. Short: I-D, I-F I (liquidity?) Medium: F-D, F-I F (liquidity and ‘quality’?) Long and Very Long: D-I and D-F D (‘quality’ – lowest yield)

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Results on this criterion contrast sharply with the GC results

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Benchmark as basket Canonical case If (say) Germany provides benchmark at a given maturity, we should find - stationary yield gap between D and each of F and I - two cointegrating vectors Italian yield = 0 + 1 German yield + stationary error ( 1 = 1) French yield = 0 + 1 German yield + stationary error ( 1 = 1) with error correction representation Italian yield = 0 + 1 (German/Italian yield gap) + 2 (German/French yield gap) + nuisance lags + noise This suggests benchmark portfolios

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Benchmark portfolios Two ‘canonical’ benchmark portfolios - long position in D bonds, equal short position in I bonds (return = D-I yield gap) - long position in D, equal short position in F Loading sensitivities and But these are not in fact what the data yield

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Estimated benchmark portfolios at short maturity (for example) benchmark portfolios are - a portfolio long in F bond and (equally) short in the D bond – this is one of the canonical portfolios above, loading sensitivities differ only by sign changes - a portfolio long in I bond with an equal short position which is itself equally weighted D and F Benchmark as a basket (interpretation as in Sec 2 of paper)

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A new and only partially integrated market German securities have lowest yield at all maturities But German bond yields don’t Granger-cause I or F at any of the 4 maturities And cointegration tests suggest I as benchmark at short end, F at medium term, D at long and very long end Alternatively we could interpret cointegration results as implying basket portfolios as benchmarks, especially at shorter maturities Thus no clear dominance for Germany

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What do the markets say? German government bonds, long the unrivalled royalty of the European debt market, now find pretenders to the throne. The German government is careful…to protect the benchmark status of its bonds…But all the good intentions…are nothing in the face of the inexorable march of European monetary union. The euro-driven integration of European financial markets is creating vigorous competition to Germany’s long reign as king of the region’s bond markets. “Benchmark status is more contended now than it ever was,” said Adolf Rosenstock, European economist in Frankfurt at Nomura Research… (International Herald Tribune, 21 March 2002)

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