Online Appendix to 'Regulating the Doom Loop' · 2020. 9. 1. · “SA-IJCB-IJCB200032” —...

“SA-IJCB-IJCB200032” — 2020/8/28 — page 1 — #1

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Online Appendix to “Regulatingthe Doom Loop”∗

Spyros Alogoskoufis and Sam LangfieldEuropean Central Bank

Introduction to Appendix

This is the appendix for the paper “Regulating the Doom Loop”by Spyros Alogoskoufis and Sam Langfield. It contains the followingsections:

• Appendix A reports an illustrative application of the portfolioreallocation model to a hypothetical bank.

• Appendix B reports bank-level statistics for sovereign expo-sures as of mid-2017.

• Appendix C reproduces tables and figures from the main paperusing bank exposure data from end-2010.

• Appendix D reproduces tables and figures from the mainpaper using bank exposure data from end-2011.

• Appendix E reproduces tables and figures from the mainpaper using bank exposure data from mid-2017 and underthe assumption that an area-wide low-risk asset exists as partof the portfolio opportunity set.

• Appendix F reproduces tables and figures from the mainpaper using bank exposure data from mid-2017 and under twoassumptions: (i) an area-wide low-risk asset exists as part ofthe portfolio opportunity set and (ii) price-based regulatoryreforms also include a minimum positive risk weight for allsingle-name sovereign exposures.

∗The views expressed herein are those of the authors and do not necessarilyrepresent the views of the institutions to which they are affiliated. Author e-mails:[email protected] and [email protected].

1

“SA-IJCB-IJCB200032” — 2020/8/28 — page 2 — #2

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2 International Journal of Central Banking September 2020

Appendix A. Illustrative Application of theSimulation Model

Table A.1 provides an illustrative application of our model of endoge-nous portfolio reallocation to a hypothetical Italian bank endowedwith a sovereign portfolio of 100 units, comprising 75 units of Ital-ian, 20 units of German, and 5 units of French bonds. These assetsare funded with 30 units of equity (tier 1 capital) and 70 units ofdebt. The table shows portfolio allocations under the three reallo-cation cases applied to the four regulatory reforms. In all columns,the bank maintains its aggregate sovereign bond holdings at 100units, and it cannot reallocate those holdings to further reduce capi-tal requirements. In the regulatory status quo, these two conclusionshold by construction, since the hypothetical bank begins with a sov-ereign portfolio of 100 units to which current regulation applies nocapital charge. In subsequent columns, the bank chooses a portfo-lio under the respective reallocation rule that attracts a globallyminimal capital charge according to a given regulatory reform. Inparticular, the bank reallocates its portfolio as follows:

• Under price-based reform to target concentration, the bankdivests its single-name holdings in excess of 100 percent oftier 1 capital, i.e., 75 − 30 = 45 of its Italian bond holdings.In the prudent case, this 45-unit excess is reinvested into thelowest-risk sovereigns, i.e., Germany up to the 30-unit limitfollowed by the Netherlands, with the residual 5 units investedin Luxembourg; in the base case, the excess is invested inGerman and French bonds up to the 30-unit limit, with theresidual 10 units invested in the country with an ELRate thatmost closely matches the initial portfolio, namely Slovakia; inthe imprudent case, the excess is reinvested into the highest-risk sovereigns, i.e., Greece up to the 30-unit limit, with theresidual 15 units reinvested in Cyprus.

• Under price-based reform to target credit risk, the hypotheti-cal bank divests all 75 units of its Italian holdings, since theseattract a risk weight of 4 percent. In the prudent case, this75-unit excess is reinvested into German bonds (which are thelowest-risk securities); in the base case, the excess is dividedbetween German and French bonds in proportion to the bank’s

“SA-IJCB-IJCB200032” — 2020/8/28 — page 3 — #3

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Vol. 16 No. 4 Regulating the Doom Loop 3

initial holdings of these securities; and in the imprudent case,the excess is reinvested entirely into the highest-risk sover-eign bond with a 0 percent risk weight, which happens to beSlovenia.

• Under quantity-based reform to target concentration, the bankdivests its single-name holdings in excess of 25 percent of tier 1capital, i.e., all holdings in excess of 0.25×30 = 7.5 units. Thisimplies an excess of 75−7.5 = 67.5 for its Italian holdings and20 − 7.5 = 12.5 for its German holdings, for a total excess of80 units. In the prudent case, this 80-unit excess is reinvestedinto the lowest-risk sovereigns up to the 7.5-unit limit, whichtakes the bank from the Netherlands to Latvia inclusive; inthe base case, the bank increases its holdings of French bondsby 2.5 units, and then invests the 7.5-unit maximum in coun-tries in order of their proximity to the credit risk of the initialportfolio; in the imprudent case, the excess is reinvested intothe highest-risk sovereigns from Greece to Estonia inclusive.

• Under quantity-based reform to target credit risk, the bankdivests its single-name holdings in excess of a fraction of tier 1capital given by a sovereign’s credit ratings. For the hypothet-ical bank, this constraint applies only to its Italian holdings,which have a BBB– rating and therefore a 75 percent largeexposure limit. The bank therefore divests 75 − (0.75 × 30) =52.5 of its Italian holdings. In the prudent case, this 52.5-unitexcess is reinvested into the lowest-risk sovereigns, as in theprevious reform scenario; in the base case, the excess is dividedproportionally between German and French bonds, with theresidual 17.5 units reinvested into Slovakia; in the imprudentcase, the excess is reinvested into the highest-risk sovereignsup to the respective large exposure limit, i.e., Greece, Cyprus,and Portugal (in that order).

Computing measures of portfolio concentration and credit riskprovides early intuition of the results that we obtain using data onbanks’ actual sovereign exposures. For each of the four reform sce-narios, the credit risk of the resulting portfolio is weakly lowest inthe prudent case and highest in the imprudent case, with the basecase representing an interior solution. In the case of this hypothet-ical bank, the degrees of freedom in portfolio reallocation following

“SA-IJCB-IJCB200032” — 2020/8/28 — page 4 — #4

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“SA-IJCB-IJCB200032” — 2020/8/28 — page 5 — #5

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“SA-IJCB-IJCB200032” — 2020/8/28 — page 6 — #6

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regulatory reform are such that all reform scenarios are consistentwith increased sovereign credit risk exposure in the imprudent caserelative to the status quo. Moreover, while home bias unambiguouslydecreases in all reform scenarios, price-based reform to target creditrisk is consistent with the hypothetical bank increasing its portfolioconcentration (as measured by HHI and KeyDeviation).

Appendix B. Individual Bank Sovereign Exposures(Mid-2017)

Table B.1 reports bank-level statistics on sovereign exposures asof mid-2017. The sample includes 95 banks located in 17 differentcountries. Fifty-seven of these banks have a sovereign exposure thatexceeds their tier 1 capital. Moreover, home bias is widespread: only10 banks do not exhibit any home bias. The resulting portfolio con-centration is reflected in generally high values of HHI and KeyDevi-ation. In terms of credit risk, banks exhibit significant heterogeneity.Due to home bias, the most heavily exposed bank is located in theriskiest country, namely Greece.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 7 — #7

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Vol. 16 No. 4 Regulating the Doom Loop 7Tab

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“SA-IJCB-IJCB200032” — 2020/8/28 — page 8 — #8

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8 International Journal of Central Banking September 2020Tab

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“SA-IJCB-IJCB200032” — 2020/8/28 — page 9 — #9

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“SA-IJCB-IJCB200032” — 2020/8/28 — page 12 — #12

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Appendix C. Robustness to Exposure Data from End-2010

We report simulation results using exposure data from end-2010,when the EBA publicly disclosed euro-area banks’ sovereign expo-sures for the first time. This older vintage covers 75 banks located in15 countries. Summary statistics for these older exposures data areshown in table C.1. Compared with mid-2017, bank exposures are45 percentage points higher on average, with Exp/T1 = 216 percent.Moreover, portfolios generally exhibit higher levels of concentrationand credit risk. From the perspective of the doom loop, end-2010exposure data therefore represent a more severe initial condition.

Subsequent tables and figures reproduce the standard set of simu-lation results for each of the four regulatory reform scenarios. Despitethe aggravated initial condition as of end-2010, the prudent case gen-erates outcomes in terms of concentration and credit risk that arecomparable to those obtained using mid-2017 data. By contrast, thebase case and in particular the imprudent case demonstrate higherlevels of concentration and credit risk. Consequently, greater severityin initial conditions widens the range of outcomes associated withthe prudent and imprudent cases, exacerbating uncertainty regard-ing banks’ portfolio reallocation decisions. In turn, this implies moreambiguity regarding equilibrium outcomes for the doom loop.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 13 — #13

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Table C.1. Summary Statistics on Bank SovereignExposures (end-2010)

Mean St. Dev. p10 p25 p50 p75 p90

Exp/T1 216 206 79 107 159 240 392HomeBias 76 27 30 60 88 98 100HHI 72 27 28 45 81 97 100KeyDeviation 18 5 9 14 20 22 23ELRate 8.4 9.0 1.7 3.7 6.8 7.2 26.3VaR 69 18 40 55 79 80 90ExpectedLoss 19.4 44.2 2.7 5.3 8.9 14.3 33.1UnexpectedLoss 139 126 55 84 112 168 238

Notes: This table reports summary statistics on banks’ sovereign bond hold-ings as of end-2010 according to the EBA. Exp/T1 refers to a bank’s sover-eign exposure as a percentage of its tier 1 capital. HomeBias is defined as

Max

[0, 100 × (hi=d/

∑19i=1 hi)−CKi=d

1−CKi=d

], where hi=d is the bank’s holdings of bonds

issued by its domestic sovereign d,∑19

i=1 hi is the bank’s sovereign exposures summedacross all 19 euro-area countries, and CKi=d is the ECB capital key share ofdomestic country d. HHI refers to the Herfindahl-Hirschman index of concentra-

tion, defined as∑19

i=1(hi/∑19

i=1 hi)2

100 . KeyDeviation measures the extent to whicha bank’s portfolio deviates from ECB capital key weights, and is calculated as√ ∑19

i=1((hi/∑19

i=1 hi)−CKi)219 . ELRate refers to a bank’s five-year expected loss rate

(expressed as a percentage) on its sovereign portfolio, and VaR refers to the mini-mum percentage reduction in portfolio value that occurs over five years with 1 percentprobability. ExpectedLoss and UnexpectedLoss are calculated by multiplying Exp/T1by ELRate and VaR, respectively.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 14 — #14

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Table C.2. Price-Based Reform to TargetConcentration (end-2010)


A. Prudent Case


B. Base Case

Exp/T1 216 206 79 107 159 240 392HomeBias 49 31 7 25 45 73 99HHI 49 26 21 28 44 64 98KeyDeviation 14 5 7 9 14 18 22ELRate 7.9 6 3.5 4.6 6.6 8.2 15.2VaR 71 12 53 62 73 80 83ExpectedLoss 17.1 19.8 3.7 6.7 9.5 20.3 37.5UnexpectedLoss 149 139 55 85 112 161 267

C. Imprudent Case


Notes: Using exposures data from end-2010, this table shows the simulation resultsfor price-based reform to target concentration in the limiting case of full reinvest-ment. In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B,banks reinvest into a portfolio that is similar to their existing portfolio; in panel C,banks reinvest into the highest-risk sovereign bond. The summary statistics corre-spond to the case of 100 percent reinvestment shown in figure C.1. Variables aredefined in the notes to table C.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 15 — #15

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Table C.3. Price-Based Reform to TargetCredit Risk (end-2010)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: Using exposures data from end-2010, this table shows the simulation resultsfor price-based reform to target credit risk in the limiting case of full reinvestment.In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B, banksreinvest into a portfolio that is similar to their existing portfolio; in panel C, banksreinvest into the highest-risk sovereign bond. The summary statistics correspond tothe case of 100 percent reinvestment shown in figure C.2. Variables are defined in thenotes to table C.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 16 — #16

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Table C.4. Quantity-Based Reform to TargetConcentration (end-2010)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: Using exposures data from end-2010, this table shows the simulation resultsfor quantity-based reform to target concentration. In panel A, banks reinvest into thelowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similarto their existing portfolio; in panel C, banks reinvest into the highest-risk sovereignbond. The summary statistics correspond to the case of a 25 percent large exposurelimit shown in figure C.3. Variables are defined in the notes to table C.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 17 — #17

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Table C.5. Quantity-Based Reform to TargetCredit Risk (end-2010)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: Using exposures data from end-2010, this table shows the simulation resultsfor quantity-based reform to target credit risk. In panel A, banks reinvest into thelowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similarto their existing portfolio; in panel C, banks reinvest into the highest-risk sovereignbond. The summary statistics correspond to the case of a 25 percent large exposurelimit for the lowest rating bucket shown in figure C.4. Variables are defined in thenotes to table C.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 18 — #18

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Figure C.1. Price-Based Reform to Target Concentration(end-2010)

Notes: Using exposures data from end-2010, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table C.1, as afunction of the percentage of banks’ sovereign bond portfolios that is reinvested.Zero percent reinvestment corresponds to table C.1 and 100 percent reinvestmentcorresponds to table C.2. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 19 — #19

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Figure C.2. Price-Based Reform to Target Credit Risk(end-2010)

Notes: Using exposures data from end-2010, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table C.1, as afunction of the percentage of banks’ sovereign bond portfolios that is reinvested.Zero percent reinvestment corresponds to table C.1 and 100 percent reinvestmentcorresponds to table C.3. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 20 — #20

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Figure C.3. Quantity-Based Reform to TargetConcentration (end-2010)

Notes: Using exposures data from end-2010, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table C.1, as afunction of the large exposure limit (expressed as a percentage of tier 1 capital),where a 25 percent limit corresponds to the summary statistics reported in tableC.4. In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B,banks reinvest into a portfolio that is similar to their existing portfolio; in panelC, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 21 — #21

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Figure C.4. Quantity-Based Reform to Target Credit Risk(end-2010)

Notes: Using exposures data from end-2010, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table C.1, as afunction of the large exposure limit (expressed as a percentage of tier 1 capital)for the lowest sovereign credit rating bucket (CCC+ to D), where a 25 percentlimit corresponds to the summary statistics reported in table C.5. In panel A,banks reinvest into the lowest-risk sovereign bond; in panel B, banks reinvest intoa portfolio that is similar to their existing portfolio; in panel C, banks reinvestinto the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 22 — #22

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Appendix D. Robustness to Exposure Data from End-2011

We report simulation results using exposure data from end-2011,when the EBA ran an ad hoc recapitalization exercise designed torestore confidence in the European banking sector. This data vin-tage covers a smaller sample, with 46 banks located in 14 countries.Summary statistics are shown in table D.1. Compared with end-2010 data, banks generally have larger sovereign exposures relativeto capital but maintain a portfolio allocation with lower concentra-tion and credit risk. This is primarily due to sample selection: inthe end-2011 sample, the median bank in terms of ELRate residesin Germany, whereas the median bank in the end-2010 sample isfrom Spain. Consequently, post-reform portfolios appear somewhatmore benign in terms of concentration and credit risk using end-2011 data, although outcomes remain heterogeneous across banks.Compared with mid-2017 data, however, outcomes are more severe,particularly in the imprudent case. This reflects reductions in banks’sovereign exposures between 2011 and 2017.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 23 — #23

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Table D.1. Summary Statistics on Bank SovereignExposures (end-2011)



Notes: This table reports summary statistics on banks’ sovereign bond hold-ings as of end-2011 according to the EBA. Exp/T1 refers to a bank’s sover-eign exposure as a percentage of its tier 1 capital. HomeBias is defined as

Max

[0, 100 × (hi=d/

∑19i=1 hi)−CKi=d

1−CKi=d

], where hi=d is the bank’s holdings of bonds

issued by its domestic sovereign d,∑19

i=1 hi is the bank’s sovereign exposures summedacross all 19 euro-area countries, and CKi=d is the ECB capital key share ofdomestic country d. HHI refers to the Herfindahl-Hirschman index of concentra-

tion, defined as∑19

i=1(hi/∑19

i=1 hi)2

100 . KeyDeviation measures the extent to whicha bank’s portfolio deviates from ECB capital key weights, and is calculated as√ ∑19

i=1((hi/∑19

i=1 hi)−CKi)219 . ELRate refers to a bank’s five-year expected loss rate

(expressed as a percentage) on its sovereign portfolio, and VaR refers to the mini-mum percentage reduction in value that would occur over five years with 1 percentprobability. ExpectedLoss and UnexpectedLoss are calculated by multiplying Exp/T1by ELRate and VaR, respectively.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 24 — #24

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Table D.2. Price-Based Reform to TargetConcentration (end-2011)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: Using exposures data from end-2011, this table shows the simulation resultsfor price-based reform to target concentration in the limiting case of full reinvest-ment. In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B,banks reinvest into a portfolio that is similar to their existing portfolio; in panel C,banks reinvest into the highest-risk sovereign bond. The summary statistics corre-spond to the case of 100 percent reinvestment shown in figure D.1. Variables aredefined in the notes to table D.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 25 — #25

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Table D.3. Price-Based Reform to TargetCredit Risk (end-2011)


A. Prudent Case


B. Base Case


C. Imprudent Case

Exp/T1 238 228 59 119 175 286 502HomeBias 44 36 0 0 51 74 93HHI 67 25 35 42 72 92 99KeyDeviation 18 5 11 15 17 23 25ELRate 4.4 2.8 1 1.7 3.4 7.8 8.2VaR 60 17 36 43 61 78 80ExpectedLoss 8.8 8.9 1.8 3.1 5.9 11.7 17.5UnexpectedLoss 129 107 37 67 99 146 211

Notes: Using exposures data from end-2011, this table shows the simulation resultsfor price-based reform to target credit risk in the limiting case of full reinvestment.In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B, banksreinvest into a portfolio that is similar to their existing portfolio; in panel C, banksreinvest into the highest-risk sovereign bond. The summary statistics correspond tothe case of 100 percent reinvestment shown in figure D.2. Variables are defined in thenotes to table D.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 26 — #26

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Table D.4. Quantity-Based Reform to TargetConcentration (end-2011)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: Using exposures data from end-2011, this table shows the simulation resultsfor quantity-based reform to target concentration. In panel A, banks reinvest into thelowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similarto their existing portfolio; in panel C, banks reinvest into the highest-risk sovereignbond. The summary statistics correspond to the case of a 25 percent large exposurelimit shown in figure D.3. Variables are defined in the notes to table D.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 27 — #27

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Table D.5. Quantity-Based Reform to TargetCredit Risk (end-2011)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: Using exposures data from end-2011, this table shows the simulation resultsfor quantity-based reform to target credit risk. In panel A, banks reinvest into thelowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similarto their existing portfolio; in panel C, banks reinvest into the highest-risk sovereignbond. The summary statistics correspond to the case of a 25 percent large exposureomit for the lowest rating bucket shown in figure D.4. Variables are defined in thenotes to table D.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 28 — #28

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Figure D.1. Price-Based Reform to Target Concentration(end-2011)

Notes: Using exposures data from end-2011, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table D.1, as afunction of the percentage of banks’ sovereign bond portfolios that is reinvested.Zero percent reinvestment corresponds to table D.1 and 100 percent reinvestmentcorresponds to table D.2. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 29 — #29

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Figure D.2. Price-Based Reform to Target Credit Risk(end-2011)

Notes: Using exposures data from end-2011, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table D.1, as afunction of the percentage of banks’ sovereign bond portfolios that is reinvested.Zero percent reinvestment corresponds to table D.1 and 100 percent reinvestmentcorresponds to table D.3. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 30 — #30

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Figure D.3. Quantity-Based Reform to TargetConcentration (end-2011)

Notes: Using exposures data from end-2011, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table D.1, as afunction of the large exposure limit (expressed as a percentage of tier 1 capital),where a 25 percent limit corresponds to the summary statistics reported in tableD.4. In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B,banks reinvest into a portfolio that is similar to their existing portfolio; in panelC, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 31 — #31

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Figure D.4. Quantity-Based Reform to Target CreditRisk (end-2011)

Notes: Using exposures data from end-2011, this figure plots HomeBias, Key-Deviation, ELRate, and ExpectedLoss, as defined in the note to table D.1, as afunction of the large exposure limit (expressed as a percentage of tier 1 capital)for the lowest sovereign credit rating bucket (CCC+ to D), where a 25 percentlimit corresponds to the summary statistics reported in table D.5. In panel A,banks reinvest into the lowest-risk sovereign bond; in panel B, banks reinvest intoa portfolio that is similar to their existing portfolio; in panel C, banks reinvestinto the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 32 — #32

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Appendix E. Endogenizing an Area-Wide Low-Risk Asset

We repeat the simulation exercise using mid-2017 data with oneinnovation: an area-wide low-risk asset exists alongside national sov-ereign bonds in the portfolio opportunity set.

As explained in the main paper, most outcomes under the twoprice-based approaches—shown in tables E.1 and E.2 and the cor-responding figures E.1 and E.2—are similar to those that obtain inthe absence of an area-wide low-risk asset. Neither of the two price-based reforms embeds strong incentives for banks to reinvest intoan area-wide low-risk asset, since other portfolio allocations can beequally effective at minimizing capital requirements. Consequently,banks reinvest into an area-wide low-risk asset only in the prudentcase; in the other cases, banks generally prefer a different portfolioallocation.

Under the two quantity-based approaches—reported in tablesE.3 and E.4 and figures E.3 and E.4—banks reliably reallocate theirportfolios in favor of an area-wide low-risk asset only when largeexposure limits are very restrictive. This is because an area-widelow-risk asset allows banks to maintain the aggregate value of theirsovereign portfolio while respecting binding large exposure limitsand avoiding the need for additional capital. However, when largeexposure limits are not restrictive, banks have no regulatory incen-tive to reallocate their portfolios, regardless of the existence of anarea-wide low-risk asset.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 33 — #33

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Table E.1. Price-Based Reform to Target Concentration(with an area-wide low-risk asset)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: This table shows the simulation results for price-based reform to target con-centration in the limiting case of full reinvestment. In panel A, banks reinvest into thelowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similarto their existing portfolio; in panel C, banks reinvest into the highest-risk sovereignbond. The summary statistics correspond to the case of 100 percent reinvestmentshown in figure E.1. Variables are defined in the notes to table A.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 34 — #34

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Table E.2. Price-Based Reform to Target Credit Risk(with an area-wide low-risk asset)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: This table shows the simulation results for price-based reform to target creditrisk in the limiting case of full reinvestment. In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similar to theirexisting portfolio; in panel C, banks reinvest into the highest-risk sovereign bond.The summary statistics correspond to the case of 100 percent reinvestment shown infigure E.2. Variables are defined in the notes to table A.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 35 — #35

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Figure E.1. Price-Based Reform to Target Concentration(with an area-wide low-risk asset)

Notes: This figure plots HomeBias, KeyDeviation, ELRate, and ExpectedLoss,as defined in the note to table A.1, as a function of the percentage of banks’sovereign bond portfolios that is reinvested. One-hundred percent reinvestmentcorresponds to table E.1. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 36 — #36

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Figure E.2. Price-Based Reform to Target Credit Risk(with an area-wide low-risk asset)

Notes: This figure plots HomeBias, KeyDeviation, ELRate, and ExpectedLoss,as defined in the note to table A.1, as a function of the percentage of banks’sovereign bond portfolios that is reinvested. One-hundred percent reinvestmentcorresponds to table E.2. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 37 — #37

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Table E.3. Quantity-Based Reform to TargetConcentration (with an area-wide low-risk asset)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: This table shows the simulation results for quantity-based reform to targetconcentration. In panel A, banks reinvest into the lowest-risk sovereign bond; in panelB, banks reinvest into a portfolio that is similar to their existing portfolio; in panelC, banks reinvest into the highest-risk sovereign bond. The summary statistics corre-spond to the case of a 25 percent large exposure limit shown in figure E.3. Variablesare defined in the notes to table A.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 38 — #38

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Table E.4. Quantity-Based Reform to Target Credit Risk(with an area-wide low-risk asset)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: This table shows the simulation results for quantity-based reform to targetcredit risk. In panel A, banks reinvest into the lowest-risk sovereign bond; in panelB, banks reinvest into a portfolio that is similar to their existing portfolio; in panelC, banks reinvest into the highest-risk sovereign bond. The summary statistics cor-respond to the case of a 25 percent large exposure limit for the lowest rating bucketshown in figure E.4. Variables are defined in the notes to table A.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 39 — #39

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Figure E.3. Quantity-Based Reform to TargetConcentration (with an area-wide low-risk asset)

Notes: This figure plots HomeBias, KeyDeviation, ELRate, and ExpectedLoss,as defined in the note to table A.1, as a function of the large exposure limit(expressed as a percentage of tier 1 capital), where a 25 percent limit correspondsto the summary statistics reported in table E.3. In panel A, banks reinvest intothe lowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that issimilar to their existing portfolio; in panel C, banks reinvest into the highest-risksovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 40 — #40

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Figure E.4. Quantity-Based Reform to Target Credit Risk(with an area-wide low-risk asset)

Notes: This figure plots HomeBias, KeyDeviation, ELRate, and ExpectedLoss,as defined in the note to table A.1, as a function of the large exposure limit(expressed as a percentage of tier 1 capital) for the lowest sovereign credit rat-ing bucket (CCC+ to D), where a 25 percent limit corresponds to the summarystatistics reported in table E.4. In panel A, banks reinvest into the lowest-risksovereign bond; in panel B, banks reinvest into a portfolio that is similar to theirexisting portfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 41 — #41

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Appendix F. Area-Wide Low-Risk Asset with aRisk-Weight Floor

We repeat the simulation exercise for price-based reforms using mid-2017 data with two innovations: (i) an area-wide low-risk asset existsalongside national sovereign bonds in the portfolio opportunity setand (ii) a minimum positive risk weight is imposed on all single-namesovereign exposures. Under these conditions, the results reported intables F.1 and F.2 and figures F.1 and F.2 indicate that the prudent,base, and imprudent cases generate identical outcomes, with banksreallocating their portfolios in favor of the area-wide low-risk asset.With 100 percent reallocation, sovereign portfolios consist exclu-sively of the area-wide low-risk asset, which is characterized by lowconcentration and low credit risk. The explanation for this find-ing is that a sovereign portfolio comprised of an area-wide low-riskasset always represents the unique solution to banks’ constrainedoptimization problem, regardless of the reallocation rule that theyadopt.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 42 — #42

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Table F.1. Price-Based Reform to Target Concentration(with an area-wide low-risk asset and

positive risk-weight floor)


A. Prudent Case


B. Base Case


C. Imprudent Case


Notes: This table shows the simulation results for price-based reform to target con-centration in the limiting case of full reallocation. In panel A, banks reinvest into thelowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similarto their existing portfolio; in panel C, banks reinvest into the highest-risk sovereignbond. The summary statistics correspond to the case of 100 percent reallocationshown in figure F.1. Variables are defined in the notes to table A.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 43 — #43

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Table F.2. Price-Based Reform to Target Credit Risk(with an area-wide low-risk asset and

positive risk-weight floor)


A. Prudent Case

Exp/T1 171 224 41 80 123 194 324HomeBias 0 0 0 0 0 1 1HHI 17 0 17 17 17 17 17KeyDeviation 0 0 0 0 0 0 0ELRate 0.4 0.0 0.4 0.4 0.4 0.4 0.4VaR 18 0 18 18 18 18 18UnexpectedLoss 31 41 8 15 23 36 60

B. Base Case


C. Imprudent Case


Notes: This table shows the simulation results for price-based reform to target creditrisk in the limiting case of full reallocation. In panel A, banks reinvest into the lowest-risk sovereign bond; in panel B, banks reinvest into a portfolio that is similar to theirexisting portfolio; in panel C, banks reinvest into the highest-risk sovereign bond.The summary statistics correspond to the case of 100 percent reallocation shown infigure F.2. Variables are defined in the notes to table A.1.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 44 — #44

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Figure F.1. Price-Based Reform to Target Concentration(with an area-wide low-risk asset and positive

risk-weight floor)

Notes: This figure plots HomeBias, KeyDeviation, ELRate, and ExpectedLoss,as defined in the note to table A.1, as a function of the percentage of banks’sovereign bond portfolios that is reinvested. One-hundred percent reinvestmentcorresponds to table F.1. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio that is similar to their existingportfolio; in panel C, banks reinvest into the highest-risk sovereign bond.

“SA-IJCB-IJCB200032” — 2020/8/28 — page 45 — #45

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Figure F.2. Price-Based Reform to Target Credit Risk(with an area-wide low-risk asset and positive

risk-weight floor)

Notes: This figure plots HomeBias, KeyDeviation, ELRate, and ExpectedLoss,as defined in the note to table A.1, as a function of the percentage of banks’sovereign bond portfolios that is reinvested. One-hundred percent reinvestmentcorresponds to table F.2. In panel A, banks reinvest into the lowest-risk sovereignbond; in panel B, banks reinvest into a portfolio

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