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### Settlement risk: definition, importance, and trade-offs
- Settlement risk materializes when one counterparty delivers the currency it has sold while the other fails to deliver; risk is exacerbated by lengthy settlement cycles and time-zone differences.
- FX markets daily turnover: approximately $9.6 trillion (Bank for International Settlement, 2025).
- Documented settlement failures cited: KfW loss of $426 million in 2008; Barclays loss of $129 million in March 2020.
- Economic channels and trade-offs:
  - Settlement risk can increase counterparty exposure and liquidity risk.
  - It can constrain intermediaries’ risk-bearing capacity and require precautionary funding.
  - It can reduce intermediaries’ ability to absorb demand imbalances, leading to higher exchange rate volatility.
  - It can raise the effective cost of arbitrage across currencies, weakening no-arbitrage relationships.
  - Reducing settlement risk (e.g., shortening settlement cycles) is not costless: may increase liquidity demands, reduce netting efficiency, introduce operational costs, or compress dealers’ time to source securities for delivery.

### Quasi-natural experiment and empirical strategy
- Quasi-natural experiment: Hungary adopted Continuous Linked Settlement (CLS) PvP settlement on November 16, 2015.
  - CLS provides payment-versus-payment (PvP) settlement, ensuring both legs of an FX transaction settle simultaneously and sharply reducing settlement exposure while preserving settlement cycles and multilateral netting.
- Empirical strategy: three complementary analyses
  1. Difference-in-differences (DiD) comparing HUF with neighboring CEE currencies to estimate effects on currency excess returns and volatility.
  2. Difference-in-difference-in-differences (DiDiD) exploiting U.S.-specific holidays to assess time-zone settlement-risk mechanisms.
  3. Analysis of deviations from triangular parity to test whether CLS reduces limits to arbitrage.

### Data, measurement, and sample
- Sample: six CEE currencies against USD and EUR — HRK, CZK, HUF, PLN, RON, and RSD — from 2015 to 2016.
- Quotes: Bloomberg bid and ask quotes, timestamped in London time; midquotes computed as average of bid and ask.
- Main outcome variables:
  - Excess returns: daily log change in the exchange rate relative to the change implied by the overnight interest-rate differential, expressed in basis points.
  - Exchange rate volatility: realized volatility computed from 30-minute intraday returns, σ^2_t = 1/48 Σ_{i=1}^{48} R^2_ti.
- Bid–ask spreads used as proxy for market liquidity (control variable).
- Overnight interest rates from Bloomberg.
- Trading volume measures not comparably available across currencies at relevant frequency; focus on excess returns and volatility.

### Difference-in-differences (DiD) — design and context
- Event date: November 16, 2015 (HUF eligibility for CLS PvP settlement).
- Treatment: HUF after CLS entry; control group: HRK, CZK, PLN, RON, RSD.
- Institutional turnover context:
  - Between November 16, 2015 and March 31, 2016, daily gross turnover of HUF transactions settled in CLS averaged about 336.6 million U.S. dollars and peaked at 850.9 million U.S. dollars.
  - Total daily spot turnover in HUF was approximately 4.3 billion U.S. dollars in April 2016 (Bank for International Settlement, 2025).
- Baseline windows: symmetric ±1 month around event (also consider ±3 months).
- Baseline regression controls: bid-ask spread BAS_{c,c′,t}, currency-pair fixed effects μ_{c,c′}, currency–month–year fixed effects Γ_{c,m,y}; some specs include date fixed effects.
- Identification assumption: parallel trends between HUF and control currencies absent treatment.

### DiD main findings: excess returns and volatility
- Excess returns — Treated × Post coefficients (Table 1):
  - ±1 month, no date FE: -0.0988*** (0.0103)
  - ±1 month, with date FE: -0.1002*** (0.0106)
  - ±3 month, no date FE: -0.1005*** (0.0115)
  - ±3 month, with date FE: -0.0979*** (0.0121)
  - Interpretation: point estimates close to −0.10, significant at 1% — reduction of about 10 basis points in daily excess returns following CLS adoption.
  - Context: average pre-event excess return for HUF ≈ 28 basis points.
- Post (aggregate effect across currencies) reported values:
  - -0.0307** (0.0111), -0.0323** (0.0100), -0.0397*** (0.0047), -0.0393*** (0.0052)
  - Interpretation: modest decline in excess returns across sample currencies after CLS entry (around −0.03).
- Excess return volatility — Treated × Post (Table 1 columns (5)–(8)):
  - -0.0321*** (0.0049)
  - -0.0326*** (0.0055)
  - -0.0320*** (0.0051)
  - -0.0326*** (0.0056)
  - Post coefficients (without date FEs) also negative and highly significant (around −0.039), indicating a common reduction in volatility with an additional HUF-specific decline.
- Inference and robustness:
  - Date fixed effects do not materially affect treatment effect estimates.
  - Currency-level clustered standard errors used; regressions allow serial correlation and heteroskedasticity within currency series.
  - Reported R-squared values vary across specifications (examples: 0.091, 0.924, 0.043, 0.897, 0.127, 0.936, 0.127, 0.894).

### Placebo, donut-hole, and randomization inference checks
- Placebo-treated-currency tests: reassigning treatment to alternative currencies yields estimates generally insignificant or opposite sign.
- Placebo-event-date tests: assigning intervention to earlier pre-treatment dates yields insignificant and substantially smaller estimates than the actual event.
- Donut-hole specification: excluding observations within ±3 trading days of the event leaves estimates negative, significant, and quantitatively similar to baseline.
- Randomization inference (RI) (Appendix Table A5):
  - Reassigned treatment across all six currencies and dates during August 15–November 15, 2015, matching ±30 and ±90 day sliding windows.
  - RI studentized t-statistics in extreme tails; RI p-values range from 0.025 to 0.066 for excess returns and 0.079 to 0.095 for volatility.
- Inference notes:
  - Wild cluster bootstrap not applicable due to single treated unit.
  - Driscoll–Kraay standard errors avoided due to potential distortions in DiD with fixed effects.

### U.S.-specific holidays, intraday identification, and DiDiD results
- Concept: U.S.-specific holidays alter settlement geography and time-zone–related settlement exposures.
- Holidays in sample: Martin Luther King Jr. Day (January 19, 2015; January 18, 2016), Presidents’ Day (February 16, 2015; February 15, 2016), Independence Day (July 3, 2015; July 4, 2016), Labor Day (September 7, 2015; September 5, 2016).
- Intraday sample and windows:
  - 30-minute intraday data focusing on 8:00 AM–1:00 PM EST.
  - Event windows: ±1, ±2, ±3 business days around each holiday.
  - Currencies: CZK, HUF, PLN, RON versus USD (HRK and RSD excluded for insufficient intraday data).
  - Sample: January 1, 2015 to November 15, 2016; European non-trading days and U.K. bank holidays excluded.
- DiDiD specification: exploits variation across treated vs control currencies, pre vs post CLS, and holiday vs non-holiday days; controls include bid-ask spread and multiple fixed effects; standard errors clustered at holiday-event level (8 clusters).
- Main DiDiD estimates (Table 2):
  - Panel A (DiDiD β2 − β3) — Excess Returns:
    - Event window [-1,1]: -0.771* (0.370)
    - Event window [-2,2]: -0.850* (0.387)
    - Event window [-3,3]: -0.726* (0.355)
  - Panel A — Excess Return Volatility:
    - [-1,1]: -0.134*** (0.033)
    - [-2,2]: -0.098*** (0.021)
    - [-3,3]: -0.100*** (0.027)
  - Panel B key interactions (selected):
    - Treated × Non-holiday (β1) — Excess Returns: 0.366 (0.244), 0.355 (0.300), 0.322 (0.285)
    - Post × Treated × Non-holiday (β2) — Excess Returns: -0.381** (0.149), -0.259* (0.111), -0.223** (0.092)
    - Post × Treated × Holiday (β3) — Excess Returns: 0.390 (0.307), 0.590* (0.307), 0.504 (0.296)
    - Treated × Non-holiday (β1) — Volatility: 0.100** (0.038), 0.077** (0.029), 0.074** (0.029)
    - Post × Treated × Non-holiday (β2) — Volatility: -0.088** (0.028), -0.044** (0.014), -0.036** (0.013)
    - Post × Treated × Holiday (β3) — Volatility: 0.046*** (0.012), 0.054*** (0.013), 0.064*** (0.018)
  - Bid-ask spread controls (selected):
    - Excess returns: -2.575** (0.862), -2.189** (0.916), -1.763** (0.684) across windows.
    - Volatility: -0.179 (0.127), 0.056 (0.092), 0.197** (0.068) across windows.
- Interpretation:
  - DiDiD estimates for excess returns are negative and statistically significant: the reduction in excess returns after CLS adoption is larger on non-holiday days than on U.S. holidays.
  - DiDiD estimates for volatility are consistently negative and significant: volatility declines more on non-holiday days than on holidays after CLS adoption.
  - Results support mechanism that PvP settlement compresses time-zone–related variation in settlement risk.

### Triangular arbitrage, deviations, and DiD estimation results (Section 4.2)
- Conceptual mechanism:
  - Settlement risk raises effective arbitrage costs because different legs of a triangular strategy may carry different counterparty exposures, settlement durations, and funding needs.
  - Triangular deviations capture the gap between direct and synthetic exchange rates and serve as a measure of limits to arbitrage.
- Triangular deviation definition:
  - For currency c vis-à-vis USD:
    - Dc,USD,t = |log(Sc,USD,t) − log( ̃Sc,USD,t)| × 10,000,
    - where ̃Sc,USD,t = Sc,EUR,t / SEUR,USD,t.
- DiD estimates on triangular deviations (Table 3; dependent variable measured in basis points):
  - ±1 month window:
    - Column (1): Treated × Post = -0.01950 (standard error 0.00458), ∗∗∗ (p < 0.01)
    - Column (2): Treated × Post = -0.01954 (standard error 0.00491), ∗∗∗ (p < 0.01)
    - Column (3) (with currency–month–year FE): Treated × Post = -0.00182 (standard error 0.00911), not significant
  - ±3 months window:
    - Column (4): Treated × Post = -0.01452 (standard error 0.00411), ∗∗ (p < 0.05)
    - Column (5): Treated × Post = -0.01227 (standard error 0.00394), ∗∗ (p < 0.05)
    - Column (6) (with currency–month–year FE): Treated × Post = -0.00011 (standard error 0.00874), not significant
- Standard errors clustered at currency level; specifications include currency fixed effects and control for contemporaneous liquidity via daily bid–ask spread.
- Economic magnitudes and benchmarks:
  - Pre-period treated means (Appendix Table A1):
    - One-month sample pre mean (treated HUF) = 0.0714 basis points
    - Three-month sample pre mean (treated HUF) = 0.0742 basis points
  - Scaling preferred estimates by pre mean implies:
    - About 27 percent reduction in triangular deviations in the one-month window (columns (1)–(2)): implied declines about 27.3–27.4%
    - About 17–20 percent reduction in the three-month window (columns (4)–(5)): implied declines about 16.5–19.6%
  - Distributional pre-period benchmarks (Appendix Table A2):
    - Pre-period median ≈ 0.044 basis points
    - Pre-period interquartile range ≈ 0.036–0.037 basis points
  - Note: triangular deviations are highly right-skewed; mean-based benchmarks may understate the effect for a typical observation; median/IQR benchmarks still indicate a material tightening.
- Robustness and caveats:
  - Negative Treated × Post coefficients remain robust in columns (1), (2), (4), and (5) after controlling for bid–ask spread.
  - Date fixed effects (columns (2) and (5)) indicate results are not driven by common time shocks.
  - Adding currency–month–year fixed effects (columns (3) and (6)) attenuates statistical significance though coefficients remain negative.
  - Small number of currency clusters (Currency = 7 in Table 3) implies inference should be interpreted with caution.
- Supporting statistics (Appendix Tables):
  - Table A6 (means by treatment and period) — ±1 month:
    - Control pre mean = 0.0425 bp; post mean = 0.0447 bp
    - Treated (HUF) pre mean = 0.0714 bp; post mean = 0.0546 bp
    - Unconditional DiD = -0.0190 bp
  - Table A6 — ±3 months:
    - Control pre mean = 0.0448 bp; post mean = 0.0603 bp
    - Treated (HUF) pre mean = 0.0742 bp; post mean = 0.0692 bp
    - Unconditional DiD = -0.0205 bp
  - Table A7 (pre-period distributional benchmarks):
    - ±1 month pre period (All): N = 147, Mean = 0.0466, SD = 0.0346, p25 = 0.0243, Median = 0.0436, p75 = 0.0615, IQR = 0.0372, Min–Max = 0.0021–0.2959
    - ±3 months pre period (All): N = 439, Mean = 0.0491, SD = 0.0470, p25 = 0.0267, Median = 0.0440, p75 = 0.0622, IQR = 0.0355, Min–Max = 0.0019–0.5057
  - Donut-hole, placebo tests (Appendix Tables A2–A4) and randomization inference (Table A5) provide additional robustness evidence for baseline DiD estimates on excess returns and volatility.

### Interpretation and implications
- Settlement risk is priced in FX markets and has economically meaningful effects:
  - CLS PvP adoption for HUF is associated with a roughly 10 basis point decline in daily excess returns and an approximate 0.032 decline in excess return volatility in baseline DiD specifications.
  - Triangular deviations decline materially (estimated 16.5–27.4 percent depending on window and specification), consistent with reduced limits to arbitrage.
- Mechanism consistent with PvP reducing counterparty exposure, relaxing intermediaries’ balance-sheet constraints, lowering the shadow cost of arbitrage, and tightening no-arbitrage relationships.
- Empirical evidence from U.S.-specific holiday DiDiD analysis supports that PvP operates through time-zone exposure channels.

*Source: 4.2 Estimation results (Working Paper No. WP/2026/156).*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Settlement risk: definition and importance
- Settlement risk materializes when one counterparty delivers the currency it has sold while the other fails to deliver, a risk exacerbated by lengthy settlement cycles and time-zone differences.
- FX markets have large notional amounts, with daily turnover of approximately $9.6 trillion (Bank for International Settlement, 2025); even a premium of a few basis points would imply aggregate transaction costs of several billion dollars per day.
- Settlement failures continue to occur (examples cited in the source: KfW loss of $426 million in 2008; Barclays loss of $129 million in March 2020).

### Economic channels and trade-offs
- If market participants require compensation for bearing settlement exposure, exchange rates should embed a settlement risk premium.
- Settlement risk can:
  - Increase counterparty exposure and liquidity risk;
  - Constrain intermediaries’ risk-bearing capacity and require precautionary funding;
  - Reduce intermediaries’ ability to absorb demand imbalances, leading to higher exchange rate volatility;
  - Raise the effective cost of arbitrage across currencies, weakening no-arbitrage relationships.
- Reducing settlement risk is not costless: shortening settlement cycles or changing infrastructure may increase liquidity demands, reduce netting efficiency, introduce operational costs, or compress the time dealers have to source securities for delivery (Rochet and Tirole, 1996; Capponi and Chang, 2025; Mattille, 2026).

### Quasi-natural experiment: Hungary’s CLS adoption
- Hungary adopted Continuous Linked Settlement (CLS) PvP settlement in November 2015.
- CLS introduces payment-versus-payment (PvP) settlement, ensuring both legs of an FX transaction settle simultaneously and sharply reducing settlement exposure while preserving settlement cycles and multilateral netting.
- CLS adoption provides a setting to isolate the effect of settlement risk from confounding changes in liquidity demand or market structure.

### Empirical strategy (overview)
- Three complementary empirical analyses:
  1. Difference-in-differences (DiD) comparing Hungary with neighboring central and eastern European (CEE) currencies to estimate effects on currency excess returns and volatility.
  2. Difference-in-difference-in-differences (DiDiD) exploiting variation from U.S.-specific holidays (reducing time-zone settlement risk for CEE trades more likely within Europe) to assess whether CLS altered holiday exchange rate dynamics.
  3. Analysis of deviations from triangular parity to test whether CLS reduces limits to arbitrage induced by settlement risk.

### Data and measurement (summary)
- Sample: six CEE currencies against USD and EUR — HRK, CZK, HUF, PLN, RON, and RSD — from 2015 to 2016.
- Quotes: Bloomberg bid and ask quotes, timestamped in London time, available at daily and 30-minute frequencies; midquotes computed as average of bid and ask.
- Main outcome variables:
  - Excess returns: daily log change in the exchange rate relative to the change implied by the overnight interest-rate differential, expressed in basis points.
  - Exchange rate volatility: realized volatility computed from 30-minute intraday returns.
    - Specifically, if R_ti denotes the 30-minute return within day t, realized volatility is computed as σ^2_t = 1/48 Σ_{i=1}^{48} R^2_ti.
- Bid–ask spreads constructed as a proxy for market liquidity and used as a control variable.
- Overnight interest rates collected from Bloomberg.
- Note: comparable trading volume measures were not available across all currencies at the relevant frequency, so the focus is on excess returns and volatility.

### Difference-in-differences (DiD) design (key elements)
- Event date: November 16, 2015, the first day HUF became eligible for CLS PvP settlement.
- Treatment: HUF (Hungarian forint) after CLS entry; control group: HRK, CZK, PLN, RON, RSD.
- Institutional context: between November 16, 2015 and March 31, 2016, daily gross turnover of HUF transactions settled in CLS averaged about 336.6 million U.S. dollars and peaked at 850.9 million U.S. dollars.
- Additional benchmark: total daily spot turnover in HUF was approximately 4.3 billion U.S. dollars in April 2016 (Bank for International Settlement, 2025).
- Baseline window: symmetric one month before and after the event (also consider three-month window for robustness).
- Baseline regression specification (informal description retained from source):
  - Outcome Y_{c,c′,t} for currency pair (c,c′) with c ∈ CEE and c′ = USD.
  - Post_t indicator equals one after November 16, 2015.
  - Treated_{c,c′} equals one for HUF/USD.
  - Controls include bid-ask spread BAS_{c,c′,t}, currency-pair fixed effects μ_{c,c′}, and currency–month–year fixed effects Γ_{c,m,y}; some specifications include date fixed effects.
- Identification relies on parallel trends: absent treatment, HUF and control currencies would have followed similar short-run dynamics.

### Main findings (summary)
- Settlement risk is priced and has economically meaningful effects on FX markets:
  - Currency excess returns decline by about ten basis points following CLS adoption, consistent with reduced compensation for bearing settlement risk.
  - Exchange rate volatility also falls, indicating improved risk-bearing capacity of intermediaries and a relaxation of balance sheet constraints.
- Evidence from U.S.-specific holiday analysis supports a mechanism operating through time-zone exposure.
- Deviations from triangular arbitrage conditions narrow after CLS entry, suggesting settlement risk raises arbitrage costs and limits market integration.

### Contributions and implications
- Establishes settlement risk as both a priced friction in currency markets and a source of limits to arbitrage.
- By isolating the PvP channel (CLS adoption), provides a benchmark for evaluating alternative settlement design approaches.
- Bridges literature on institutional settlement arrangements affecting prices and risk with literature on deviations from no-arbitrage conditions in FX markets by identifying settlement risk as a distinct source of these frictions.

*Source: IMF working paper — 1. Introduction (extracted content).*

### Appendix Table A1 shows no evidence of differential pre-trends between HUF and the control currencies.

### wpiea2026156-source-pdf - Appendix Table A1 shows no evidence of differential pre-trends between HUF and the control currencies.

### Difference-in-Differences estimates: Excess returns and volatility
- Main finding: Across all specifications, the estimated Treated × Post coefficient for excess returns is negative and statistically significant, indicating a decline in excess returns for HUF following CLS adoption.
- Key coefficient estimates (Table 1):
  - Treated × Post (Excess Returns)
    - ±1 month, no date FE: -0.0988*** (0.0103)
    - ±1 month, with date FE: -0.1002*** (0.0106)
    - ±3 month, no date FE: -0.1005*** (0.0115)
    - ±3 month, with date FE: -0.0979*** (0.0121)
  - Interpretation: Point estimates close to −0.10 and significant at the 1% level, implying a reduction of about 10 basis points in daily excess returns following CLS adoption.
  - Contextual statistic: The average pre-event excess return for HUF is approximately 28 basis points.
- Post (aggregate effect across currencies)
  - Post coefficient (where reported): -0.0307** (0.0111), -0.0323** (0.0100), -0.0397*** (0.0047), -0.0393*** (0.0052)
  - Note: The coefficient on Post is also negative and statistically significant (around −0.03), suggesting a modest decline in excess returns across all sample currencies after CLS entry.
- Treated × Post (Excess Return Volatility) (Table 1 columns (5)–(8))
  - Estimates centered around −0.032 with statistical significance:
    - -0.0321*** (0.0049)
    - -0.0326*** (0.0055)
    - -0.0320*** (0.0051)
    - -0.0326*** (0.0056)
  - In specifications without date fixed effects, Post is also negative and highly significant (around −0.039), suggesting a common reduction in volatility across currencies, with HUF exhibiting an additional decline captured by the interaction term.
- Robustness to fixed effects and serial correlation:
  - Inclusion of date fixed effects does not materially affect the estimated treatment effect.
  - Regressions use currency-level clustered standard errors (matching level of treatment assignment) and allowance for serial correlation and heteroskedasticity within currency series.
  - R-squared reported vary widely across specifications (e.g., 0.091, 0.924, 0.043, 0.897, 0.127, 0.936, 0.127, 0.894).

### Placebo evidence and randomization inference
- Placebo exercises:
  - Placebo-treated-currency tests: reassign treatment to alternative currencies — estimates generally statistically insignificant or opposite sign.
  - Placebo-event-date tests: assign intervention to earlier pre-treatment dates — estimates insignificant and substantially smaller than those for the actual event date of November 16, 2015.
- Donut-hole specification:
  - Excluding observations within ±3 trading days of the event yields estimates that remain negative and statistically significant and quantitatively similar to baseline (Appendix Table A2).
- Randomization inference (RI) results (Appendix Table A5):
  - Expanded placebo distribution by reassigning treatment across all six currencies and dates during the 90-day pre-event period (August 15 to November 15, 2015), matching baseline sliding windows (±30 days and ±90 days).
  - RI studentized t-statistics fall in extreme tails; RI p-values range from 0.025 to 0.066 for excess returns and 0.079 to 0.095 for volatility, supporting robustness of baseline estimates.
- Inference choices:
  - Wild cluster bootstrap not applicable because of single treated unit (MacKinnon and Webb, 2020).
  - Avoid Driscoll–Kraay standard errors due to potential distortions in DiD with fixed effects (references to Sun and Yan, 2019; Liu and Sun, 2019).

### U.S.-specific holidays, intraday identification, and DiDiD results
- Rationale: Settlement risk varies with counterparties’ locations and payment-system operating hours; U.S.-specific holidays change the geography of trading and thus settlement exposures.
- U.S.-specific holidays in sample:
  - Martin Luther King Jr. Day (January 19, 2015; January 18, 2016)
  - Presidents’ Day (February 16, 2015; February 15, 2016)
  - Independence Day (July 3, 2015; July 4, 2016)
  - Labor Day (September 7, 2015; September 5, 2016)
- Intraday window and sample:
  - Use 30-minute intraday data focusing on 8:00 AM–1:00 PM EST (corresponding to 12:00 PM–5:00 PM or 1:00 PM–6:00 PM GMT depending on DST).
  - Event windows considered: ±1, ±2, and ±3 business days around each holiday.
  - Currencies: CZK, HUF, PLN, and RON versus USD.
  - Sample spans January 1, 2015 to November 15, 2016.
  - Exclusions: HRK and RSD excluded due to insufficient intraday data; European non-trading days and U.K. bank holidays excluded.
- Triple-difference (DiDiD) specification:
  - Exploits variation across (i) treated vs control currencies, (ii) pre- vs post-CLS periods, and (iii) holiday vs non-holiday days within event windows.
  - Controls: bid-ask spread and fixed effects for currency-pair, time-of-day (30-minute bin), holiday, event-time (relative-day), and year.
  - Standard errors clustered at holiday-event level (8 clusters).
- Main DiDiD findings (Table 2):
  - Panel A (DiDiD estimate β2 − β3):
    - Excess Returns: -0.771* (0.370), -0.850* (0.387), -0.726* (0.355) for event windows [-1,1], [-2,2], [-3,3].
    - Excess Return Volatility: -0.134*** (0.033), -0.098*** (0.021), -0.100*** (0.027) for event windows [-1,1], [-2,2], [-3,3].
  - Panel B key interactions:
    - Treated × Non-holiday (β1): 0.366 (0.244), 0.355 (0.300), 0.322 (0.285) for excess returns; 0.100** (0.038), 0.077** (0.029), 0.074** (0.029) for volatility.
    - Post × Treated × Non-holiday (β2): -0.381** (0.149), -0.259* (0.111), -0.223** (0.092) for excess returns; -0.088** (0.028), -0.044** (0.014), -0.036** (0.013) for volatility.
    - Post × Treated × Holiday (β3): 0.390 (0.307), 0.590* (0.307), 0.504 (0.296) for excess returns; 0.046*** (0.012), 0.054*** (0.013), 0.064*** (0.018) for volatility.
  - Bid-ask spread controls:
    - For excess returns: -2.575** (0.862), -2.189** (0.916), -1.763** (0.684) across windows.
    - For volatility: -0.179 (0.127), 0.056 (0.092), 0.197** (0.068) across windows.
- Interpretation:
  - DiDiD estimates for excess returns are negative and statistically significant, indicating the reduction in excess returns after CLS adoption is larger on non-holiday days than on U.S. holidays.
  - DiDiD estimates for excess return volatility are consistently negative and statistically significant across all event windows, indicating volatility declines more on non-holiday days than on holidays after CLS adoption.
  - Results support interpretation that PvP settlement compresses time-zone–related variation in settlement risk, leading to more stable exchange rate dynamics outside holiday periods.

### Settlement risk, triangular arbitrage, and implications
- Conceptual mechanism:
  - Settlement risk can limit arbitrage because different legs of a triangular strategy may carry different counterparty exposures, settlement durations, and funding needs, raising the effective cost of arbitrage.
  - Triangular deviations measure the gap between direct and synthetic exchange rates, capturing the effective cost of arbitrage under intermediary constraints.
- Triangular deviation definition:
  - For currency c vis-à-vis USD:
    - Dc,USD,t = |log(Sc,USD,t) − log( ̃Sc,USD,t)| × 10,000,
    - where ̃Sc,USD,t = Sc,EUR,t / SEUR,USD,t is the synthetic exchange rate implied by the euro cross rate.
- Empirical approach:
  - Apply a DiD specification analogous to Section 2, adapted to the triangular deviation outcome, to assess whether CLS adoption affects limits-to-arbitrage as measured by triangular deviations.

*Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026156-source-pdf.pdf*

### 4.2    Estimation results

### 4.2    Estimation results

### Difference-in-differences (DiD) findings on triangular deviations
- The DiD coefficient on Treated × Post, δ, captures the change in triangular deviations for HUF relative to the control CEE currencies after Hungary’s entry into CLS.
- Main estimated Treated × Post coefficients from Table 3 (dependent variable: triangular deviation measured in basis points):
  - ±1 month window:
    - Column (1): Treated × Post = -0.01950 (standard error 0.00458), significance: ∗∗∗ (p < 0.01)
    - Column (2): Treated × Post = -0.01954 (standard error 0.00491), significance: ∗∗∗ (p < 0.01)
    - Column (3) (with currency–month–year FE): Treated × Post = -0.00182 (standard error 0.00911), not significant
  - ±3 months window:
    - Column (4): Treated × Post = -0.01452 (standard error 0.00411), significance: ∗∗ (p < 0.05)
    - Column (5): Treated × Post = -0.01227 (standard error 0.00394), significance: ∗∗ (p < 0.05)
    - Column (6) (with currency–month–year FE): Treated × Post = -0.00011 (standard error 0.00874), not significant
- Standard errors are clustered at the currency level; specifications include currency fixed effects and control for contemporaneous liquidity via the daily bid–ask spread.
- Columns (2) and (5) include date fixed effects, implying identification comes from within-date cross-currency differentials in deviations between HUF and control currencies before versus after CLS adoption.

### Economic magnitude and benchmarks
- Pre-period treated means used for scaling (Appendix Table A1):
  - One-month sample pre mean (treated HUF) = 0.0714 basis points
  - Three-month sample pre mean (treated HUF) = 0.0742 basis points
- Scaling preferred estimates by the treated pre-period mean implies:
  - About 27 percent reduction in triangular deviations in the one-month window (columns (1)–(2)): implied declines about 27.3–27.4%
  - About 17–20 percent reduction in the three-month window (columns (4)–(5)): implied declines about 16.5–19.6%
- Distributional (robust) pre-period benchmarks (Appendix Table A2):
  - Pre-period median ≈ 0.044 basis points
  - Pre-period interquartile range ≈ 0.036–0.037 basis points
- Because triangular deviations are highly right-skewed, mean-based benchmarks may understate the effect for a typical observation; under median/IQR benchmarks, estimated effects still represent a material tightening relative to the central mass of the distribution.

### Robustness checks and inference caveats
- Inclusion of bid–ask spread controls:
  - The negative Treated × Post coefficient remains robust in columns (1), (2), (4), and (5), supporting interpretation that CLS eligibility improves triangular parity beyond contemporaneous liquidity conditions.
- Fixed-effects structure and alternative specifications:
  - Date FEs (columns (2) and (5)) show results are not driven by common time shocks.
  - Adding currency–month–year fixed effects (columns (3) and (6)) causes the estimated coefficients to lose statistical significance but retain negative sign.
- Inference caution:
  - Small number of currency clusters (reported clusters (Currency) = 7 in Table 3) implies inference should be interpreted with caution.

### Interpretation and mechanism
- The evidence in columns (1), (2), (4), and (5) indicates CLS introduction is associated with a statistically and economically meaningful reduction in triangular deviations.
- Interpreting triangular deviations as a measure of arbitrage frictions, the results imply:
  - Settlement risk raises the effective cost of arbitrage by increasing counterparty exposure, tying up balance sheet capacity, and requiring precautionary funding.
  - These effects tighten intermediaries’ risk constraints (e.g., value-at-risk limits) and reduce the ability to deploy capital to arbitrage trades.
  - PvP settlement via CLS reduces these exposures, relaxes intermediary constraints, lowers the shadow cost of arbitrage, and leads to tighter no-arbitrage relationships in FX markets.

### Key supporting statistics from appendices and robustness tables
- Table A6 (Triangular Deviations: Means by Treatment and Period):
  - ±1 month window:
    - Control pre mean = 0.0425 bp; post mean = 0.0447 bp
    - Treated (HUF) pre mean = 0.0714 bp; post mean = 0.0546 bp
    - Unconditional DiD = -0.0190 bp
  - ±3 months window:
    - Control pre mean = 0.0448 bp; post mean = 0.0603 bp
    - Treated (HUF) pre mean = 0.0742 bp; post mean = 0.0692 bp
    - Unconditional DiD = -0.0205 bp
- Table A7 (Pre-period distributional benchmarks):
  - ±1 month pre period (All): N = 147, Mean = 0.0466, SD = 0.0346, p25 = 0.0243, Median = 0.0436, p75 = 0.0615, IQR = 0.0372, Min–Max = 0.0021–0.2959
  - ±3 months pre period (All): N = 439, Mean = 0.0491, SD = 0.0470, p25 = 0.0267, Median = 0.0440, p75 = 0.0622, IQR = 0.0355, Min–Max = 0.0019–0.5057
- Donut-hole and placebo tests (Appendix Tables A2–A4) and randomization inference (Table A5) provide additional robustness evidence for baseline DiD estimates on excess returns and volatility (statistical significance reported as in-source p-value notations).

*Source: 4.2 Estimation results (Working Paper No. WP/2026/156).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026156-source-pdf.pdf_