**1. Introduction**

Considerable ambiguity exists regarding the likely liquidity effects of introducing Sovereign Bond-Backed Securities, as proposed by Brunnermeier et al. (2017). The competing forces are (i) a reduced supply of the underlying asset and (ii) improved prospects for the more efficient managemen<sup>t</sup> of inventory risks. This paper argues that trading costs in country-specific European sovereign bond markets would be constrained by an arbitrage relation as a result of the existence of liquid Sovereign Bond-Backed Securities (SBBS) and this would dominate any negative supply effects.<sup>1</sup> This outcome relies on sufficient diversification and hedging by dealers in a truly European-wide context. In this sense, and in some other respects to be discussed below, the outcome envisaged is a deeply integrated market in which SBBS become the primary focus for price discovery while trading costs in most national markets shrink to within tight bounds of those in SBBS markets.

Brunnermeier et al. (2016) and Brunnermeier et al. (2017) propose the issuance of sovereign bond-backed securities (SBBS) in the euro area with tranches that would be sequentially exposed to losses arising from defaults on any of the underlying individual sovereign securities. The senior tranche would make up the majority of the securitisation and be extremely low risk. The junior tranches would be more sensitive to early signs of defaults, but, at the same time, maintain some of the risk reducing benefits of diversification. In theory, this proposal has the potential to induce bond holders to diversify beyond their national sovereign markets and this could substantially weaken the sovereign-bank

<sup>1</sup> A wider range of potential effects are considered in the report by the ESRB High-Level Task Force on Safe Assets (2018).

doom-loop that was prevalent during the Sovereign Debt Crisis in Europe. The question remains whether it would work in practice.

Traditionally, banks hold sovereign bonds as collateral for use in short-term treasury managemen<sup>t</sup> and in official monetary policy operations. This is encouraged by the fact that such assets are zero risk weighted for capital adequacy purposes. During the Great Recession and euro area Sovereign Debt Crisis, many European banks experienced widespread defaults on their loan portfolios and they required recapitalisation from their governments. Sovereigns simultaneously experienced severe current account deficits and expected imminent high bank bail-out costs which drove their yields to record levels. The higher risk of sovereign default fed back into credit and counter-party risks for the linked banks and this exacerbated the expected bail-out costs for sovereigns. These linked risk exposures generated what was referred to as a "vicious circle" at a euro area summit of heads of governments in 2012. It was also referred to as the "doom loop" by Farhi and Tirole (2018) or as the "diabolic loop" by Brunnermeier et al. (2016).

Proposals to break the bank-sovereign vicious circle have been debated as part of a two-year reassessment by the Basel Committee on Banking Supervision of the Regulatory Treatment of Sovereign Exposures (RTSE) (see Basel Committee on Banking Supervision 2017). The Committee decided to retain zero risk weights on domestic sovereign exposures acknowledging that there was no consensus among supervisors, experts, and economists on alternative policy options to amend the framework. Alternative approaches to breaking the doom loop have therefore appeared and the Sovereign Bond Backed Securitisation proposal by Brunnermeier et al. (2016) is just one of these. Several related proposals are assessed by Leandro and Zettelmeyer (2018) and the analysis below would have some relevance for the 'Blue bond' proposal discussed there since that proposal gives rise to a similarly liquid low risk bond that could be used in hedging by dealers.

An apparent drawback of the SBBS proposal is that it would leave already small and illiquid sovereign bond markets with reduced free float and this would do further harm to liquidity and raise issuance costs. If orders arrive infrequently in smaller sovereign bond markets—and if orders of a type needed to reduce inventories are inelastic with respect to dealer pricing—then inventory positions will be held for longer and providing continuous liquidity would be costly. It is frequently argued that such costs would rise if the national free float is reduced by absorption into a securitisation.

The analysis below suggests that such a conclusion arises only when national markets are considered in isolation. A wider perspective introduces the potential for liquidity spillovers due to hedging and diversification in market making. Rather than reducing liquidity, the effects of SBBS on sovereign bond markets should have more in common with how opportunities to trade 'To-Be-Announced' US Agency Mortgage Backed Securities contracts (TBA-MBS) affect trading costs in Specific-Pools of Mortgage Backed Securities, even those that are not cheapest to deliver.<sup>2</sup>

If SBBS are very liquid, they present dealers with instantaneous access to offsetting positions following trades in any given sovereign market and this would established a valid arbitrage relation to constrain trading costs in those markets. SBBS markets (particularly for the senior tranche) are likely to be deeper and more liquid than smaller euro area sovereign bond markets due mainly to the greater amounts of SBBS in issue relative to what is typical for any individual sovereign. However, this is also thought likely because SBBS markets (having factor-like properties) would acquire benchmark status. Yuan (2005) shows that the presence of benchmarks gives rise to liquidity in related markets.<sup>3</sup>

<sup>2</sup> Gao et al. (2017) describe how, in that market, dealers typically hedge inventory risk in their Specific-Pool exposures with offsetting TBA trades and they show that impediments to hedging can reduce such liquidity. More interestingly, they conclude that the presence of TBA markets has very widespread beneficial effects on liquidity significantly beyond the mortgage pools that are cheapest to deliver. This is also traced to the ability to hedge inventory holding risk.

<sup>3</sup> In a related paper, the acquisition of benchmark status in pre-crisis European sovereign bond markets is examined in Dunne et al. (2007). Benchmarks tend to become liquid as they are the location for discovery of the systematic component of the risk premium (in this case, it is envisaged that the different tranches of SBBS would be benchmarks for credit risks within different categories of the market).

An important difference between the SBBS proposal and the situation discussed in Yuan (2005) is that increased supply of SBBS directly implies a reduction in the supply of individual sovereign bonds outstanding. Yuan assumes, in contrast, that benchmarks enhance the likelihood of issuance of corporate bonds and more issuance improves liquidity. However, a positive externality that Yuan's analysis does not take into account is the hedging benefits that dealers can avail of in the presence of liquid benchmarks. It also leaves out post-hedging diversification benefits. These externalities are worthy of further examination.

Although we lack actual evidence of the characteristics of SBBS, it is possible to assess their likely behaviour (or how they would have behaved in the past) through a simulation approach. The present analysis derives SBBS yield estimates using the simulation approach of Schönbucher (2003). This permits an assessment of hedge effectiveness and it shows that dealer inventory positions in most national markets can be, to some extent, hedged by using one or more of the tranches of the sovereign bond-backed securitisation. More importantly, it turns out that what cannot be hedged is largely idiosyncratic and diversifiable by dealers who are active in many markets. Since inventory risk only requires compensation for its systematic component, the liquidity benefits of SBBS are enhanced by diversification.

Hedge effectiveness is assessed by measuring the risk of the optimally-hedged position relative to the unhedged portfolio, as in Bessler et al. (2016). The additional diversification benefits are assessed by assuming that dealers typically have positions in all sovereigns (with both equal weights on individual sovereigns and market-size based weights). A core result from the analysis is that trading costs in SBBS markets would determine limits on the size of trading costs in national sovereign bonds.<sup>4</sup>

The following section outlines the type of hedging behaviour by dealers that is deemed likely when sovereign bond-backed securities exist. The relevant literature is then surveyed. Methodologies used to estimate SBBS yields, to measure time-varying hedge ratios and to assess diversification benefits, are then explained. The discussion of results from the application of these methods follows. The conclusion gives some indication of overall liquidity benefits that would flow from the existence of SBBS based on the recent history.

### **2. Hedging, Arbitrage and Diversification**

The benefit of hedging with a highly-liquid, contemporaneously correlated, asset is clear-cut in the extreme case of perfect correlation. Let ask and bid prices in the bond market be denoted (**a**) and (**b**) and those in the SBBS market be ( **A**) and ( **B**), respectively. Assuming no frictions (i.e., no basis, coordination, execution or timing risks and no variability in market making risks or risk aversion), then arbitrage and competition between dealers should keep the two bid–ask spreads close to each other.<sup>5</sup> Perfect correlation in the underlying values of the two securities and the assumption of instantaneous availability of trading opportunities in the highly liquid asset allow us to subtract the common underlying value changes, **V**(**t**), from all bid and ask prices in each period **t**, leaving **a\*, A\*, b\*** and **B\*** as timeless (where starred variables are deviations from the relevant common **V**(**t**)).

A dealer who acquires a long position at a price (**b**) can immediately sell an equal amount in the SBBS market at price ( **B**). This leaves the position hedged against movements in **V** until the bond is sold again at a price (**a**) and the SBBS is simultaneously bought at ( **A**). Regardless of common movements in **V**, there is a profit for the dealer of **B\*** − **b\* + a\*** − **A\***. This profit is trivially increasing in the difference between the spreads **s-S**. In a competitive market, we would expect such differences in spreads to be competed away (excluding any extra costs associated with operating in the more

<sup>4</sup> Whether these bounds are sufficient to improve on current trading costs is moot. Even if the costs of hedging with SBBS were to exceed current trading costs in national markets, their use in this way would still be relevant in minimising the extent of any deterioration in trading costs due directly to reductions in the free float as a result of the securitisation.

<sup>5</sup> This also relies, for simplicity, on the assumption that there is symmetry in the positioning of spreads relative to the underlying value. If not, then the proposition that follows applies on average across many trades.

general environment). The spread in the bond market will, in this case, be primarily determined by the required bid–ask spread in the SBBS market.

If there is only a partial correlation between the value of the SBBS and that of the bond then the remaining risk must be managed somehow. In this case, a diversification strategy should be very effective since remaining risks would largely be idiosyncratic. The finding of a substantial reduction in risk due to diversification can be regarded as indirect evidence that SBBS behave like systematic risk factors.

Since only the non-diversifiable component of the unhedged risk will require compensation, the link between the size of the spread in the hedge instrument and that in the asset being hedged is relatively unaffected relative to the case of a perfectly correlated hedge. Standard diversification arithmetic implies that, increasing the extent of diversification from one sovereign market to 11 uncorrelated markets with similar-sized risks and activity, would produce more than a 70% reduction in risk exposure. Hence, if dealers are active in providing liquidity across all European sovereign markets that contribute to the securitisation, then any unhedged risks will largely average-ou<sup>t</sup> in their trading portfolios.<sup>6</sup>

It is important to draw a distinction between hedging with offsetting positions in an asset possessing highly correlated contemporaneous price movements and the alternative of hedging with a futures contract on the underlying. Futures contracts involve risk premiums that impose direct cost on dealers. There is also a considerable difficulty in correctly matching the expected duration of inventory holding with the expiry time of the associated futures contract.<sup>7</sup> Matching the size of an inventory position with standardized sizes in the futures market may also be an issue. Hedging with CDS contracts is similar to the use of a correlated asset but this analogy is also incomplete. The CDS premium will only be highly correlated with the credit risk of the underlying security. The disadvantage of the CDS when compared with a factor-like hedge is that it does not hedge systematic interest rate risk. CDS trading also tends to be less liquid than the underlying.
