The Cost of Unconventional Monetary Policy Measures. A Risk Manager’s Perspective

Abstract

We examine the evolution of credit risk arising from monetary policy operations and emergency liquidity assistance on the Eurosystem balance sheet over the years 2010–2022. We employ a market-driven risk model relying on the expected default frequencies for sovereigns, banks, and corporates provided by Moody’s Analytics. Dependence between defaults is modelled with a multivariate Student-t distribution with time-varying parameters. We find that at the end of August 2022, shortly after the Eurosystem ended net asset purchases under its long-standing quantitative easing and therefore the balance sheet ceased to grow, risk was approximately equal to less than half of the value measured at the peak of the sovereign debt crisis in 2012, notwithstanding the almost threefold increase in the Eurosystem monetary policy exposure occurred since then. This is due to the launch of the Outright Monetary Transactions Programme and the Pandemic Emergency Purchase Programme, which succeeded in quelling market turmoil, thereby reducing the Eurosystem’s own balance sheet risk. Our findings support the view that, in periods of severe financial distress, sovereign risk for a central bank is largely endogenous.

Appendix

1.1 A. Robustness Analysis

This section provides a robustness analysis of our results. First, we focus on the default co-dependency model. Figure 16 shows the impact on risk of different copula specifications, comparing the proposed fat-tail approach (Student-t) with the Gaussian approach. While accounting for fat tails leads to higher estimated risk (the average risk level of the Student-t copula is larger by 9% with respect to the Gaussian copula), the risk profile is basically the same under the two approaches. This is partly due to the fact that our estimates for the degrees of freedom of the Student-t are moderately high (see Fig. 5, Sect. 3.3).

Fig. 16

Risk; Student-t vs Gaussian copula (2010–2021, billion euros). This figure compares risk estimated with the fat-tail approach (Student-t) against that estimated with the Gaussian approach. Source: own calculations

Second, Fig. 17 compares our risk estimates with those obtained under the assumption of very fat tails. The latter are obtained by artificially setting the degrees of freedom to very low levels (down to 1) at all dates, rather than using our estimated values.⁴⁶ The number of degrees of freedom affects the tail behaviour: the smaller its value, the heavier the tails. Fatter tails lead to higher estimated risk; e.g. setting the degrees of freedom equal to 1 would imply an average risk level larger by 37% than in our approach. However, the risk profile over time is broadly the same.

Fig. 17

Risk; actual degrees of freedom vs very low degrees of freedom (2010–2021, billion euros). The blue line represents our estimated risk measure (based on the estimated degrees of freedom), while the other lines are obtained by setting the degrees of freedom equal to 4, 2, and 1 (constant for all dates). Source: own calculations

Figure 18 compares our risk estimates with those obtained under the assumption of very high correlations. The latter are obtained by artificially raising the correlations to very high—and rather unrealistic—levels (up to 100%) for all pairs of debtors at all dates. High correlations have a larger impact on the absolute level of risk than the degrees of freedom (a constant correlation equal to 100% implies an average risk increase by 82% with respect to our approach). Even in this case, however, the risk profile remains broadly unchanged.

Fig. 18

Risk; actual correlation vs very high correlation (2010–2021, billion euros). The blue line represents our estimated risk measure (based on the estimated correlations), while the other lines are obtained by setting all correlations equal to 75, 90, and 100% (constant for all dates and for all pairs of debtors). Source: own calculations

Next, Fig. 19 shows that the effect on the risk measure of a different rolling window for the parameter estimation, namely, the 3-year window compared with the alternative 2-year and 1-year windows. The alternative parameters do not affect our results in a significant way.

Fig. 19

Risk; different rolling window lengths (2010–2021, billion euros). The blue line represents our estimated risk measure (based on a 3-year window), while the other lines are obtained by using 2-year and 1-year windows. Source: own calculations

We then examine more closely the PDs. Since sovereign PDs are by far the most important input of our model, we have also considered as an alternative the methodology proposed by Heynderickx et al. (2016), which is also employed by Caballero et al. (2020). Even this alternative method employs physical PDs obtained from CDS quotes.

Figure 20 compares the 1-year CDS-I-EDF for Italy with the PD computed with the Heynderickx method. The latter yields a much larger volatility for the estimated PDs compared with Moody’s EDFs. We attribute this to the fact that Moody’s CDS-I-EDF involves the daily recalibration of the relevant parameters, which allows for the adjustment (from risk-neutral to physical PD) of different magnitude depending on market conditions, possibly filtering out some of the volatility in the underlying CDS quotes. The parameters proposed by Heynderickx et al. for converting risk-neutral PDs into physical PDs are constant over time, hence market noise incorporated in risk-neutral PDs is filtered out to a lesser extent.

Fig. 20

1-year probability of default of Italy and Italy’s CDS (2010–2021, basis points). This figure compares the 1-year probability of default of Italy retrieved from the Credit Edge platform provided by Moody’s Analytics (CDS-I-EDF, blue line) with that obtained with an alternative method also based on CDS (red line). For comparison, the yellow line represents the Italian CDS (right y-axis). Source: Moody’s Credit Edge, CMA, own calculations

Figure 21 shows the impact on risk of these two different PD specifications for the sovereign. The volatility of the PD with the alternative method affects the volatility of the corresponding risk estimate, which shows a larger peak-to-trough difference.

Fig. 21

Risk; Moody’s EDFs vs alternative PDs (2010–2021, billion euros). This figure compares the risk estimates based on Moody’s EDF (blue line) with those obtained using for all sovereigns the alternative specification based on Heynderickx et al. (2016) (red line). Source: own calculations

Our interpretation of this check is that, while alternative parameter choices may affect the absolute level of the risk estimates, the evolution of risk over time looks broadly similar in all cases. This supports our general conclusion, namely, that at the end of August 2022 financial risk is broadly equivalent to the average level observed in 2011 and corresponds to less than half of the risk measured at the peak of the sovereign debt crisis in 2012, despite monetary policy and ELA exposure have grown by almost a factor of four during the entire period.

1.2 B. Further Methodology Details

1.2.1 Simulation of Collateral

While risk on purchase programme holdings and counterparties is simulated over a 1-year horizon, collateral is simulated over a much shorter horizon, since collateral is assumed to be swiftly liquidated by the Eurosystem in the event of a counterparty default. More specifically, collateral is simulated over the time horizon that is deemed necessary for its smooth liquidation (time-to-liquidation, T2L). Table 5 reports the T2Ls used in our exercise, which are based on expert judgement. In most cases, a few weeks are considered sufficient to liquidate collateral. Noticeable exceptions are own-used assets,⁴⁷ simulated over a 1-year horizon to align their outcome to that of the counterparty, and credit claims, simulated over a 1-year horizon as well, to take into account their non-marketable nature and possible operational hurdles.

Table 5 Assumed time-to-liquidation for collateral (number of weeks)

In order to simulate collateral over a time horizon equal to the assumed T2L, the default thresholds (T_i, see Sect. 3.2) must be calculated on the T2L PDs (e.g. the default threshold of a government bond pledged as collateral is given by the Student-t quantile of the 1-week PD). We inferred T2L PDs from 1-year PDs with the following formula, which assumes constant conditional default probabilities:

$$ {\mathrm{PD}}_{\mathrm{T}2\mathrm{L}}=1-{\left(1-{\mathrm{PD}}_{1-\mathrm{year}}\right)}^{\mathrm{T}2\mathrm{L}} $$

We note that the same asset might be included in the purchase programme holdings as well as in the collateral pool. In such cases, two different thresholds are considered: one for the purchase programme holdings (based on the 1-year PD of the issuer) and one for the collateral (based on the T2L PD of the issuer).

Finally, we aggregate credit claims pledged as collateral in order to reduce the computational burden. For each counterparty, we aggregate all credit claims into two different groups: one containing credit claims with a quality comparable to investment grade, and one containing the remaining credit claims.⁴⁸ These two groups are simulated as if they were a single instrument (i.e. as if they had the same debtor), with a PD equal to the weighted average of the individual PDs. By doing so, the number of credit claim debtors shrinks from hundreds of thousands (the actual number of distinct debtors) to below 1000. The approximation leans on the conservative side, since it reduces the degree of diversification within the collateral pool.

1.2.2 ELA Operations

In theory, losses arising from ELA operations could be calculated with the same formula employed for monetary policy credit operations (see Sect. 3). In practice, however, risks from ELA exposures should be modelled with some suitable assumptions, as the data regarding the amount and composition of collateral are not available and the potential role of the government as the ultimate guarantor in case of a systemic crisis, or ELA granted to systemic banks, should be taken into account.

As a first assumption, we set the EAD equal to the current exposure. This makes sense since in the ELA operations the exposure is decided by the NCB and cannot be arbitrarily increased by the counterparty, even if abundant collateral is available. In addition, we conservatively assume no over-collateralization:

$$ \mathrm{EAD}={\sum}_{a\ \mathrm{in}\ \mathrm{collateral}}{\mathrm{AH}}_a=\mathrm{actual}\ \mathrm{exposure} $$

With regard to the composition of collateral, we distinguish between idiosyncratic ELA, where a single non-systemic bank is involved, and systemic ELA, where a relevant bank and/or a number of banks in the same jurisdiction resort to ELA. Both types are in turn divided into two different subtypes. More specifically we consider:

• 1. Idiosyncratic ELA—suspension. This is the case of a bank that relies on ELA after having been suspended from the monetary policy operations because of financial soundness issues. In this case, we use for ELA the same collateral composition as that observed in the monetary policy operations right before the suspension;

• 2. Idiosyncratic ELA—liquidity crisis. This is the case of a bank facing liquidity problems that resorts to ELA as an additional financing source while not being suspended from monetary policy operations. In this case, we assume that ELA collateral entirely consists of credit claims, assuming that the most liquid assets—such as investment grade debt securities—are already pledged as collateral for the monetary policy operations;

• 3. Systemic ELA—government support. This is the case of ELA granted to a systemic relevant bank or to a large number of banks in a jurisdiction, where an explicit support of the government is present, for example in the form of promissory notes and/or guarantees. In this case, we assume that collateral consists of a government guarantee, which covers the entire ELA exposure. For the calculation of risk, we only simulate the counterparty and the government: if they both default, then a loss is realized; otherwise, the loss is zero;

• 4. Systemic ELA—government crisis. This is the case of ELA granted to an entire banking system, which is facing a severe crisis because of a simultaneous sovereign debt crisis. In this case, we only simulate the sovereign: if it defaults, we assume that both the counterparty and the collateral automatically default, generating a loss in the ELA operations; otherwise, the loss is zero.

In the case of systemic ELA (type 3 and 4 above), where the collateral composition is not considered, the loss (if any) is computed as:

$$ L=\mathrm{EXP}\bullet \left(1-\frac{30\%}{1-H}\right) $$

where EXP is the actual exposure, 30% is the recovery rate, and H is the average haircut.

1.2.3 Probability of Default for Covered Bonds and ABS

For covered bonds and ABS,⁴⁹ an adjustment is required to account for the fact that they exhibit a higher credit quality than their issuers. Since they are the least risky among the Eurosystem exposures,⁵⁰ we apply a simplified approach and divide the issuer’s EDF by a predefined number, equal to 8.07 for covered bonds and 3.06 for ABS. These numbers are obtained by comparing the long-term default rates implied in the rating of these assets (as reported by rating agencies in their annual Default Studies)⁵¹ with those implied by the rating of their issuers. In spite of the same average level of rating, we estimate a lower divisor (3.06) for ABS than for covered bonds since ABS default rates are generally higher than non-ABS default rates, for any given rating level.

1.3 C. Dataset and Software

We build a unique dataset for this study. It is made up of four tables:

• 1. purchase programme holdings table: each record contains the face and book value for any given combination of date/portfolio/issuer. The number of dates is 661, the number of portfolios ranges from 0 to 9 depending on the date,⁵² and the average number of issuers for any portfolio is 120, yielding a total number of records approximately equal to 360,000;

• 2. monetary policy credit operations table: each record contains the face value, before haircut and after haircut, for any given combination of date/counterparty/collateral issuer/collateral type. The number of dates is 661, the average number of counterparties by date is 1500, and the average number of collateral issuers for any date/counterparty is 15. Collateral type is a categorical variable that depends on the type of instrument, required for the assumptions on the recovery rates (e.g. covered bonds vs uncovered bank bonds) and time-to-liquidation (e.g. market-placed covered bonds vs retained covered bonds). The total number of records is around 13 million;

• 3. ELA operations table: each record contains the face value, before haircut and after haircut, for any given combination of date/counterparty/collateral issuer/collateral type. The total number of records is around 8000;

• 4. probability of default table: each record contains the PD for any given combination of date/debtor. The number of dates is 661, the number of debtors (either issuers or monetary policy counterparties) is approximately 9000, yielding a total number of records around six million.

Risk estimates are obtained with a C++ object-oriented program, while the calibration of the multivariate Student-t parameters is performed with a Matlab script.