## wpiea2019227-print-pdf — Sections 4.1, 4.2, 4.8, Appendix A & B

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### 4.1 Dilution Adjustment Factor across Funds and Time — Time-series patterns and determinants
- Definition:
  - Adjustment Factor = daily absolute value of swing factor for swing funds; for dual funds = 0.5*(ask-bid)/mid.
- Sample-period central tendency:
  - Adjustment Factor of funds with full swing and dual pricing is approximately 33 bps.
  - For partial swing funds, the median Adjustment Factor is zero because swinging is invoked only when daily net flows cross a threshold.
  - Most commonly used thresholds (absolute): 1 percent and 3 percent.
  - 90 percent of partial swing funds use thresholds that are less than 3 percent.
  - Average dilution adjustment factor for partial funds (restricted to days with non-zero factor values) is 57 bps.
- Time variation:
  - Outside crisis periods, average Adjustment Factor varies from 18 bps to 25 bps.
  - Adjustment Factor substantially increases in adverse market conditions:
    - Average factor nearly quadruples during the 2008 global financial crisis.
    - Adjustment factors are at relatively high levels during the European debt crisis.
  - Patterns align with prior findings: effective spreads in European corporate bonds between 12 bps and 22 bps and dramatic increases in corporate bond illiquidity in 2008.
- Regression specification (conceptual):
  - Adjustment Factori,d = α + β0 Illiquidityi,d + Day(Fund) FE + β1 Controlsi,d + εi,d
  - Illiquidity = daily value-weighted average of the bid-ask spread of fund i’s assets.
  - Day (Fund) FE = day (fund) fixed effects.
  - Controls tested: Size, Age, Expense, Inst (measured at previous month-end).
  - Alternative specification: remove day fixed effects and include Stress (VIX is above the 75th percentile).
  - Standard errors clustered by fund and day.
- Key regression findings:
  - Illiquidity is significantly positive across specifications — asset illiquidity is an important determinant of funds’ Adjustment Factors.
  - Size, Age, Expense, Inst do not appear to have important explanatory power.
  - Stress is significantly positive — Adjustment Factor significantly increases during periods of market stress.
  - Interaction Illiquidity x Stress: Adjustment Factor is particularly high for illiquid portfolios during stress periods.
- Policy-relevant implication:
  - Adjustment Factors rise notably in market stress and are larger for funds holding illiquid assets, implying that alternative pricing mechanisms that incorporate dilution adjustments are more consequential when market liquidity deteriorates.

### 4.2 The coefficient ββ — Investor behavior, flow-performance sensitivity, and costs/benefits of alternative pricing
- Investor-level sample and trading patterns:
  - Average (median) fund in investor-level sample has 596 (85) investors.
  - 13percent of investors are institutional clients.
  - Individual investor participation (value of holding / total fund size):
    - Retail: mean 0.005, median 0.003.
    - Institutional: mean 0.17, median 0.006.
    - Maximum individual ownership in overall sample: 2.3 percent.
  - Total observed investor trades in event window: about 120K.
  - Trading frequency: cross-sectional average (median) 0.33 (0.16); 25th and 75th percentiles 0 and 0.5.
  - Institutional investors: mean (median) frequency 0.44 (0.3).
  - Average flow volatility (standard deviation of investor-level flows during event period): Institutional 3.9; Retail 0.78.
- Trade sizes and patterns:
  - Conditional on selling, mean and median end-investors’ outflows are 50 percent and 38 percent (of their total positions).
  - About 40 percent of sales are full-position sales.
  - Among purchases, 10 percent are new positions.
  - Median (mean) value of purchases that adjust existing positions: 0.7 percent (5 percent).
  - Analogous numbers for exits: 5 percent (median) and 16 percent (mean).
  - Purchases more frequent but smaller: 18 percent versus 82 percent (purchases versus sales frequency).
- Investor-level regression evidence (Flow EndInv dependent; investor fixed effects):
  - Investors in switching (treated) funds react less to stressed market conditions in withdrawals after the switch; control-group investors do not change significantly.
  - Triple-difference regressions: investors in funds with alternative pricing withdraw relatively less during periods of high market stress and put less money into alternative funds in periods of no stress.
  - Identification caveat: assumes investors differ only by time-invariant characteristics; staggered switches make time-varying preference confounding unlikely.
  - Conclusion: the same investor is significantly less likely to redeem shares during a stress period if the fund uses alternative pricing than if it uses traditional pricing.
- Flow-performance sensitivity (fund-level, Equation (5)):
  - Flow in month t+1 regressed on Alpha, NegAlpha, NegAlpha x Alternative, and controls: Size, Age, Expense, Illiquidity, Inst; year-month fixed effects.
  - Key coefficients (Panel A, Table 7):
    - NegAlpha = 5.8227 (significant at the 1percent level).
    - NegAlpha x Alternative = -4.0730 (significant at the 1percent level).
    - Interpretation: sensitivity to negative performance is significantly lower for funds with alternative pricing; no significant difference for positive performance.
  - End-investor level (Panel B, Table 7):
    - NegAlpha x Treated x Post = -1.5247 (significant at 10 percent).
    - Extreme negative performance (NegAlpha defined as Alpha below 25th percentile): NegAlpha x Treated x Post = -4.5641 (significant at 5 percent).
  - Interpretation: alternative pricing primarily reduces sensitivity to poor performance and does not increase upside sensitivity.
- Volatility of end-investor flows (Equation (7), Table 8):
  - Following a fund’s change to alternative pricing, investors in treatment funds exhibit fewer volatile flows than investors in funds that do not change pricing.
- Cross-sectional heterogeneity — when alternative pricing matters more (Table 9):
  - The effect of alternative pricing is significantly greater for funds with:
    - More illiquid assets.
    - More dispersed ownership (lower Herfindahl–Hirschman Index).
    - More retail investors (Retail = 1 - Inst).
- Do alternative pricing rules affect fund performance? (Equation (9), Table 10)
  - AbReturn t+1 regressed on Net Flow / Net Outflow / Net Inflow interactions with Alternative and controls; AbReturn = fund return net of exposures to global bond and global stock market returns.
  - Key findings:
    - Column (1), full sample: higher outflows deteriorate subsequent fund performance for funds with traditional pricing; the negative impact of outflows on fund performance is almost fully eliminated for funds with alternative pricing.
    - Column (2), funds with highly illiquid portfolios: unconditional effect amplified; magnitude almost twice that in the unconditional sample.
    - Columns (3)-(4), funds with inflows: results statistically insignificant.
- Costs of alternative pricing (tracking error and new investor growth; Table 11):
  - Observed tradeoff: alternative pricing mitigates redemption risk during stress but reduces inflows outside stress periods.
  - Tracking Error = -1 times R-squared from 12-month rolling factor model of fund returns on global bond and stock excess returns (higher value = higher tracking error).
  - Regressions show:
    - Alternative → Tracking Error 0.0989*** (0.0306).
    - Alternative’s coefficient on flows is negative but borderline insignificant.
    - Including Tracking Error explains much of Alternative’s negative effect on flows: Tracking Error is negative and statistically highly significant for flows, and Alternative’s coefficient becomes nearly zero when Tracking Error included.
  - New Investor growth:
    - New Investor = number of new investors entering a fund in a month divided by fund’s total number of investors as of previous month-end.
    - Alternative → New Investors -0.8640** (0.4247) during non-stress periods — funds with alternative pricing attract significantly fewer new investors outside periods of high market stress.

### 4.8 Do Fund Companies Internalize their Investors’ Decisions? — Hedging behavior and substitution
- Hedging instruments examined:
  - Cash (Cash): fund’s total cash holdings (including cash equivalents) divided by the fund’s total assets.
  - Asset concentration (Asset Conc): Herfindahl–Hirschman Index of a fund’s asset holdings in each month.
- Regression (equation (10)):
  - Hedging Instrumenti,t+1 = f(Alternative, lagged Hedging Instrument, lagged Alpha, Size, Age, Expense, Inst, time/fund FEs).
- Main empirical findings (Table 12):
  - Alternative → Cash: -3.2586** (standard error 1.2938).
    - Observations: 9,158; R-squared: 0.278; Controls: Y; Time FE: Y.
    - Interpretation: funds with alternative pricing hold less cash on average — consistent with cash and alternative pricing acting as substitutes.
  - Alternative → Asset Conc: -0.0051 (standard error 0.0123) — coefficient negative but statistically insignificant.
    - Observations: 10,563; R-squared: 0.039; Controls: Y; Time FE: Y.
  - Other noted coefficients:
    - Alpha → Cash: -0.1688 (0.5638).
    - Illiquidity → Asset Conc: -1.1383** (0.4474).
- Interpretation and mechanism:
  - Evidence indicates alternative pricing rules act as substitutes for cash hoarding.
  - No robust evidence that alternative pricing is associated with reduced asset concentration.
  - Implication: fund companies internalize investors’ run-risk via pricing rules rather than increasing cash buffers in the observed UK corporate bond fund sample.
- Broader V. CONCLUSION highlights:
  - Open-end mutual funds manage tens of trillion of dollars globally; liquidity mismatch and first-mover advantages create run risk.
  - Swing pricing effects: change fund operations to better manage liquidity risk and reduce redemptions during high market stress.
  - Associated costs: funds with alternative pricing have greater tracking errors and attract fewer new investors outside crisis periods.
  - Policy context: regulators concerned about illiquidity mismatch; U.S. regulation permitting alternative pricing became effective in November 2018.
  - Research recommendation: evaluate swing pricing relative to alternatives, weighing stress-mitigation benefits against costs in reduced attractiveness to new investors.

### Appendix A — Variable definitions (selected)
- Adjustment Factor: Equals the absolute value of swing factor for swing funds; equals half-spread, (0.5*(ask-bid)/mid, for dual funds — percent
- Age: Natural logarithm of fund age in years (using the age of the oldest class share)
- Alpha: Estimated using rolling-window time-series regression for each fund using the past 12 months data. Alpha is the intercept from a regression of excess fund returns on excess global bond market and global stock market returns. Indices obtained from Barclays — percent
- Alternative: An indicator variable that equals one if the fund is using one of the alternative pricing rules
- Asset Conc: Herfindahl–Hirschman Index of fund’s asset holdings in each month
- Asset Illiquidity: Bid-ask spread; end of day bid and ask prices obtained from Thomson Reuters Datastream in order of availability: Thomson Reuters composite price, Thomson Reuters Pricing Service evaluated price, iBOXX, and ICMA
- Cash: Fund’s total cash holding (cash plus cash equivalents including cash deposits, money market funds, Treasury Bills, commercial paper, short term bonds, repos and currency holdings) divided by total assets — percent
- Dual: Indicator = 1 if fund is a dual fund
- Expense: Fund’s annual total expense ratio — percent
- Flow: Monthly capital flows into a fund divided by fund’s total net assets in t — percent
- Flow EndInv: Change in each investor’s holding (in number of shares) from previous month — percent
- Illiquidity: Value-weighted average of Asset Illiquidity of fund’s assets
- Inst: Fraction of fund’s total net assets held by institutional investors — percent
- NegAlpha: Equals Alpha if the fund’s Alpha is negative (or below the 25th percentile); set to zero otherwise — percent
- Net Outflow / Net Inflow: Net monthly outflows/inflows definitions based on Flow sign
- New Investor: Number of new investors divided by the fund’s total number of investors in each month — percent
- Size: Natural logarithm of fund’s total net assets — £
- Stress: Indicator = 1 if monthly VIX index is above the 75th percentile of the sample
- Tracking Error: -1 times R-squared from the alpha regression described above

### Appendix B — Selected summary tables and findings
- Table B.1 — Swing Thresholds of Partial Swing Funds (frequency distribution):
  - Threshold: 0.01 percent — Frequency: 4.59
  - Threshold: 0.50 percent — Frequency: 3.1
  - Threshold: 1 percent — Frequency: 40.36
  - Threshold: 1.50 percent — Frequency: 1.17
  - Threshold: 2 percent — Frequency: 4.05
  - Threshold: 2.50 percent — Frequency: 2.29
  - Threshold: 3 percent — Frequency: 34.39
  - Threshold: 4 percent — Frequency: 1.2
  - Threshold: 5 percent — Frequency: 6.92
  - Threshold: 6 percent — Frequency: 0.22
  - Note: For funds with multiple thresholds (around 1 percent of partial swing funds), the minimum is reported.
- Table B.2 — Full vs Partial vs Dual (selected coefficients; dependent variable Flow):
  - Full x Stress: 1.0782** (0.5301); matched sample reports 1.3324* (0.7819)
  - Partial x Stress: 0.8211* (0.4969); matched sample reports 1.3070** (0.5507)
  - Dual x Stress: 1.9450** (0.9662); matched sample reports 2.1814 (1.6003)
  - Full: -1.1169** (0.5308); matched sample reports -0.8210 (0.5649)
  - Dual: -1.9327** (0.8517); matched sample reports -2.4882** (1.0934)
  - Stress: -0.9890*** (0.2776) in columns (1)-(4); matched sample reports -1.2943*** (0.3905)
  - Observations and R-squared vary by column (e.g., Observations column (1) 6,552; R-squared column (1) 0.008).
- Table B.3 — Extended robustness tests (matched sample; Alternative x Stress significant across stress measures):
  - Alternative x Stress examples:
    - TED: 1.1808** (0.5446)
    - Libor: 1.3295** (0.5744)
    - MOVE: 1.1951** (0.5319)
    - P90: 1.2982** (0.5489)
    - Other columns show significance at ** or *** for Alternative x Stress with reported standard errors.
  - Stress coefficients are consistently negative and significant (e.g., TED: -1.2712*** (0.3809); Libor: -1.3592*** (0.3795)).
  - Observations typically around 9,670; R-squared ranges from 0.025 to 0.040 depending on specification.

*Source: wpiea2019227-print-pdf — Sections 4.1, 4.2, 4.8, Appendix A & B*

### 4.1 Dilution Adjustment Factor across Funds and Time

### 4.1 Dilution Adjustment Factor across Funds and Time

### Time-series patterns in Adjustment Factor
- Definition: Adjustment Factor = daily absolute value of swing factor for swing funds; for dual funds = 0.5*(ask-bid)/mid.
- Sample-period central tendency:
  - Adjustment Factor of funds with full swing and dual pricing is approximately 33 bps.
  - For partial swing funds, the median Adjustment Factor is zero because swinging is invoked only when daily net flows cross a threshold.
  - Most commonly used thresholds (absolute): 1 percent and 3 percent.
  - 90 percent of partial swing funds use thresholds that are less than 3 percent.
  - Average dilution adjustment factor for partial funds (restricted to days with non-zero factor values) is 57 bps.
- Time variation:
  - Outside crisis periods, average Adjustment Factor varies from 18 bps to 25 bps.
  - Adjustment Factor substantially increases in adverse market conditions:
    - Average factor nearly quadruples during the 2008 global financial crisis.
    - Adjustment factors are at relatively high levels during the European debt crisis.
  - Patterns align with prior findings: e.g., effective spreads in European corporate bonds between 12 bps and 22 bps (Biais and Declerck (2013)); dramatic increases in corporate bond illiquidity measures during 2008 (Dick-Nielsen, Feldhutter, and Lando (2011)).

### Determinants of Adjustment Factor (regression evidence)
- Regression specification (conceptual): Adjustment Factori,d = α + β0 Illiquidityi,d + Day(Fund) FE + β1 Controlsi,d + εi,d, where:
  - Illiquidity = daily value-weighted average of the bid-ask spread of fund i’s assets.
  - Day (Fund) FE = day (fund) fixed effects.
  - Additional fund characteristics tested: Size, Age, Expense, Inst (measured at previous month-end).
  - Alternative specification: remove day fixed effects and include Stress (VIX is above the 75th percentile of the sample).
  - Standard errors clustered by fund and day.
- Key empirical findings:
  - Illiquidity is significantly positive across specifications — asset illiquidity is an important determinant of funds’ Adjustment Factors.
  - Other fund characteristics (Size, Age, Expense, Inst) do not appear to have important explanatory power.
  - Stress is significantly positive — Adjustment Factor significantly increases during periods of market stress.
  - Interaction Illiquidity x Stress: Adjustment Factor is particularly high for illiquid portfolios during stress periods.

### Policy-relevant implication from Section 4.1
- Adjustment Factors rise notably in market stress and are larger for funds holding illiquid assets, implying that alternative pricing mechanisms that incorporate dilution adjustments are more consequential when market liquidity deteriorates.

*Source: wpiea2019227-print-pdf - 4.1 Dilution Adjustment Factor across Funds and Time*

### Section 4.2. The coefficient 훽훽

### Section 4.2. The coefficient 훽훽

### Investor-level evidence on pricing changes and flows
- Sample and investor composition
  - The average (median) fund in the investor-level sample has 596 (85) investors.
  - 13percent of investors are institutional clients.
  - Individual investor participation in a given fund (value of holding divided by total fund size):
    - Retail clients: mean 0.005, median 0.003.
    - Institutional clients: mean 0.17, median 0.006.
    - Maximum individual ownership in the overall sample is 2.3 percent.
  - Total observed investor trades in the event window: about 120K.
- Trading frequency and volatility
  - Cross-sectional average (median) trading frequency is 0.33 (0.16).
  - 25th and 75th percentiles for trading frequency are 0 and 0.5.
  - Institutional investors are more active: mean (median) frequency 0.44 (0.3).
  - Average flow volatility (standard deviation of investor-level flows during the event period):
    - Institutional clients: 3.9.
    - Retail clients: 0.78.
- Trade sizes and patterns
  - Conditional on selling, mean and median end-investors’ outflows are 50 percent and 38 percent (of their total positions), respectively.
  - About 40 percent of sales are full-position sales.
  - Among purchases, 10 percent of purchases are new positions.
  - Median (mean) value of purchases that are adjustments on existing positions is 0.7 percent (5 percent).
  - Analogous numbers for exits are 5 percent and 16 percent.
  - Purchases are more frequent but smaller: 18 percent versus 82 percent (purchases versus sales frequency).
- Regression evidence at investor level (Flow EndInv dependent variable; investor fixed effects)
  - Investors in switching (treated) funds react less to stressed market conditions in terms of withdrawals after the switch; control-group investors do not change significantly.
  - Triple-difference regressions show qualitatively similar results to fund-level estimations: investors in funds with alternative pricing withdraw relatively less during periods of high market stress and put less money into alternative funds in periods of no stress.
  - Identification caveat: tests assume investors differ only by time-invariant characteristics; time-varying investor preferences coinciding with switch dates could alter interpretation, but this is considered unlikely given staggered switches.
- Conclusion from investor-level analysis
  - The same investor is significantly less likely to redeem shares during a stress period if the fund uses alternative pricing than if the fund uses traditional pricing, providing strong evidence that alternative pricing structures affect investor decisions and mitigate runs on funds.

### Investment stability and alternative pricing — flow-performance sensitivity
- Background and hypothesis
  - Prior literature: fund flows are associated with past performance; corporate bond funds show a concave flow-performance relationship (Goldstein et al., 2017).
  - Theory: traditional pricing induces strategic complementarities and first-mover advantage; alternative pricing should lessen concavity for swing funds by removing first-mover advantage.
- Fund-level specification (Equation (5)) controls and estimation details
  - Flow in month t+1 regressed on Alpha, NegAlpha, interactions with Alternative, and controls: Size, Age, Expense, Illiquidity, Inst; year-month fixed effects; clustered standard errors by fund and time.
- Key coefficients and findings (Panel A, Table 7)
  - NegAlpha coefficient: 5.8227 (statistically significant at the 1percent level).
  - NegAlpha x Alternative coefficient: -4.0730 (statistically significant at the 1percent level).
  - Interpretation: sensitivity to negative performance is significantly lower for funds with alternative pricing; no significant difference found for sensitivity to positive performance.
  - Results robust in matched-sample (column (3)).
- End-investor level flow-performance sensitivity (Panel B, Table 7)
  - Regress Flow EndInv on NegAlpha x Treated x Post and Alpha x Treated x Post with end-investor fixed effects using 24-month pre/post switch window.
  - Column (1): overall sensitivity to performance (positive and negative) — no significant effects.
  - Column (2): asymmetry with NegAlpha — NegAlpha x Treated x Post = -1.5247 (significant at 10 percent).
  - Column (3): extreme negative performance (NegAlpha defined as Alpha below 25th percentile) — NegAlpha x Treated x Post = -4.5641 (significant at 5 percent).
- Interpretation
  - Alternative pricing primarily reduces sensitivity to poor performance (mitigates run incentives on the downside) and does not increase sensitivity on the upside.

### Investment stability and alternative pricing — volatility of end-investor flows
- Volatility test specification (Equation (7))
  - For each investor, Vol of Flow EndInv calculated before and after switch; regressions include treatment indicator, post indicator, investor fixed effects, and controls.
- Finding (Table 8)
  - Following a fund’s change to alternative pricing, investors in treatment funds exhibit fewer volatile flows than investors in funds that do not change pricing.

### When do alternative pricing rules matter more?
- Theoretical channels linked to strategic complementarities and run risk:
  - Greater portfolio illiquidity increases run sensitivity because liquidation takes longer and is costlier → pricing structure should matter more.
  - More dispersed ownership (many small investors) increases run risk because large investors can internalize price impact; pricing should matter more for dispersed ownership.
  - Higher fraction of retail investors (Retail = 1 - Inst) implies more dispersed ownership and higher run risk.
- Empirical test (Table 9, matched sample; full sample used for cross-sectional variation)
  - Interaction specifications appended to baseline show:
    - Effect of alternative pricing significantly greater for funds with more illiquid assets.
    - Effect significantly greater for funds with more dispersed ownership (lower Herfindahl–Hirschman Index).
    - Effect significantly greater for funds with more retail investors.

### Do alternative pricing rules affect fund performance?
- Motivation
  - Traditional pricing can induce dilution from flow-induced costly trades, worsening subsequent fund performance.
  - Hypothesis: alternative pricing reduces dilution; effect should be stronger for illiquid portfolios and mainly for outflows.
- Specification (Equation (9))
  - AbReturn in month t+1 regressed on interactions of Net Flow / Net Outflow / Net Inflow with Alternative and controls; AbReturn computed as fund return net of exposures to global bond and global stock market returns; betas from 12-month rolling regressions; clustered standard errors by fund and month.
- Key findings (Table 10)
  - Column (1), full sample: higher outflows deteriorate subsequent fund performance for funds with traditional pricing; the negative impact of outflows on fund performance is almost fully eliminated for funds with alternative pricing.
  - Column (2), funds with highly illiquid portfolios: unconditional effect amplified; magnitude is almost twice as large as in the unconditional sample.
  - Columns (3) and (4), funds with inflows: results statistically insignificant, consistent with inflows being less distortionary because managers can deploy new capital flexibly.

### The costs of alternative pricing
- Observed tradeoff
  - Funds with alternative pricing mitigate redemption risk during stress periods but receive less inflows outside periods of market stress.
- Proposed channels
  - Investor concern that managers’ discretion in setting adjustment factors may hurt performance.
  - Increased tracking errors for funds that move prices in response to flows, potentially raising investors’ cost in good market conditions when run-mitigating benefits are smaller.
- Tracking Error measure and tests (Table 11)
  - Tracking Error defined as -1 times the R-squared from rolling 12-month factor model of fund returns on global bond and stock excess returns (so higher value = higher tracking error).
  - Regressions show:
    - Alternative has a positive and statistically significant coefficient in the Tracking Error regression (funds with alternative pricing generate higher tracking errors).
    - Alternative’s coefficient on flows is negative but borderline insignificant (column (2)).
    - When Tracking Error is included as explanatory variable (column (3)), Tracking Error is negative and statistically highly significant for flows, and the coefficient of Alternative becomes nearly zero — implying an important part of Alternative’s negative effect on flows operates through higher tracking error.
- New investor growth
  - New investor defined as number of new investors entering a fund in a month divided by fund’s total number of investors as of previous month-end.
  - Regression of New investor on Alternative (column (4) of Table 11) shows funds with alternative pricing attract significantly fewer new investors outside periods of high market stress.

*Source: wpiea2019227-print-pdf — Section 4.2. The coefficient 훽훽*

### 4.8 Do Fund Companies Internalize their Investors’ Decisions?

### 4.8 Do Fund Companies Internalize their Investors’ Decisions?

### Hedging instruments considered
- Hedging Instrument variables examined:
  - Cash (Cash): fund’s total cash holdings (including cash equivalents) divided by the fund’s total assets.
  - Asset concentration (Asset Conc): Herfindahl–Hirschman Index of a fund’s asset holdings in each month.
- Empirical specification: regression of Hedging Instrument at i,t+1 on Alternative Pricing indicator (Alternative), lagged Hedging Instrument, controls (lagged Alpha, Size, Age, Expense, Inst), and time/fund fixed effects (see equation (10) in source).

### Main empirical findings (Table 12)
- Effect of alternative pricing rules on cash holdings:
  - Alternative → Cash: -3.2586** (standard error 1.2938)
  - Interpretation: funds with alternative pricing rules hold less cash, on average, consistent with cash and alternative pricing rule being substitutes.
  - Observations: 9,158; R-squared: 0.278; Controls: Y; Time FE: Y.
- Effect of alternative pricing rules on asset concentration:
  - Alternative → Asset Conc: -0.0051 (standard error 0.0123) — coefficient negative but statistically insignificant.
  - Observations: 10,563; R-squared: 0.039; Controls: Y; Time FE: Y.
- Other coefficient notes from Table 12:
  - Alpha → Cash: -0.1688 (0.5638)
  - Illiquidity → Asset Conc: -1.1383** (0.4474)

### Interpretation and mechanism
- Substitution behavior:
  - Evidence indicates alternative pricing rules (e.g., swing pricing, dual pricing) act as substitutes for cash hoarding—funds using alternative pricing hold less cash.
  - No robust evidence that alternative pricing is associated with reduced asset concentration; the asset concentration coefficient is statistically insignificant.
- Implication: fund companies internalize investors’ run-risk via pricing rules rather than increasing cash buffers, at least in the observed UK corporate bond fund sample.

### Broader results and policy-relevant conclusions (from V. CONCLUSION)
- Aggregate context:
  - Open-end mutual funds globally manage tens of trillion of dollars in assets; liquidity mismatch and first-mover advantages create run risk.
- Swing pricing effects documented:
  - Alternative pricing rules change fund operations to better manage liquidity risk.
  - They reduce the degree of redemptions during periods of high market stress.
- Associated costs:
  - Funds with alternative pricing rules have difficulty attracting new investor capital outside crisis periods.
  - Primary reason: their portfolios exhibit greater tracking errors, which reduces new investor inflows (see Table 11: Alternative → Tracking Error 0.0989*** (0.0306); Alternative → New Investors -0.8640** (0.4247) during non-stress periods).
- Policy implications and context:
  - Regulators and policy makers have expressed concerns about growing illiquidity mismatch in asset management.
  - Example cited: policy speech on June 26, 2019 by Mark Carney (Governor of the Bank of England) calling for actions to prevent systemic runs arising from illiquidity mismatch.
  - U.S. regulation permitting alternative pricing rules became effective in November 2018; given market similarities, the UK evidence may inform expectations for U.S. effects.
- Research recommendation:
  - Future research should evaluate swing pricing relative to potential alternatives, weighing benefits in stress mitigation against costs in reduced attractiveness to new investors.

*Italic: Source — wpiea2019227-print-pdf - 4.8 Do Fund Companies Internalize their Investors’ Decisions?*

### Appendix A. Variable Definitions

### Appendix A. Variable Definitions

### Variable definitions and units
- Adjustment Factor: Equals the absolute value of swing factor for swing funds; equals half-spread, (0.5*(ask-bid)/mid, for dual funds — percent
- Age: Natural logarithm of fund age in years (using the age of the oldest class share)
- Alpha: Estimated using rolling-window time-series regression for each fund using the past 12 months data. Alpha is the intercept from a regression of excess fund returns on excess global bond market and global stock market returns. Indices obtained from Barclays — percent
- Alternative: An indicator variable that equals one if the fund is using one of the alternative pricing rules
- Asset Conc: Herfindahl–Hirschman Index of fund’s asset holdings in each month
- Asset Illiquidity: Bid-ask spread; end of day bid and ask prices are obtained from Thomson Reuters Datastream and used in the following order depending on availability: Thomson Reuters composite price, Thomson Reuters Pricing Service evaluated price, iBOXX, and ICMA
- Cash: Fund’s total cash holding – defined as cash plus cash equivalents including cash deposits, money market funds, Treasury Bills, commercial paper, short term bonds, repos and currency holdings – divided by the value of total assets — percent
- Dual: An indicator variable that equals one if the fund is a dual fund
- Expense: Fund’s annual total expense ratio — percent
- Flow: Monthly capital flows into a fund divided by fund’s total net assets in t — percent
- Flow EndInv: Change in each investor’s holding (in number of shares) from previous month — percent
- Full: An indicator variable that equals one if the fund is a full swing fund
- Illiquidity: Value-weighted average of Asset Illiquidity of fund’s assets
- Inst: Fraction of fund’s total net assets held by institutional investors — percent
- Investor Horizon: Number of months the investor holds his shares after an initial purchase. We use purchases before December 2014
- N of Inv: Natural logarithm of total number of investors in a given fund
- NegAlpha: Equals Alpha if the fund’s Alpha is negative (or below the 25th percentile); set to zero otherwise — percent
- Net Inflow: Net monthly inflows. Equal to Flow if Flow>0; equal to 0 if Flow<=0
- Net Outflow: Net monthly outflows. Equal to Flow if Flow<0; equal to 0 if Flow>=0
- New Investor: Number of new investors divided by the fund’s total number of investors in each month — percent
- Ownership Concentration: Herfindahl–Hirschman Index calculated using each end-investors’ ownership in each month
- Partial: An indicator variable that equals one if the fund is a partial swing fund
- Retail 1-Inst: percent
- Return: Fund’s monthly raw return — percent
- Size: Natural logarithm of fund’s total net assets — £
- Stress: An indicator variable that equals one if monthly VIX index is above the 75th percentile of the sample
- Tracking Error: -1 times R-squared from the alpha regression described above

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### Appendix B. Summary Tables and Findings

### Table B.1 — Swing Thresholds of Partial Swing Funds (frequency distribution)
- Threshold: 0.01 percent — Frequency: 4.59
- Threshold: 0.50 percent — Frequency: 3.1
- Threshold: 1 percent — Frequency: 40.36
- Threshold: 1.50 percent — Frequency: 1.17
- Threshold: 2 percent — Frequency: 4.05
- Threshold: 2.50 percent — Frequency: 2.29
- Threshold: 3 percent — Frequency: 34.39
- Threshold: 4 percent — Frequency: 1.2
- Threshold: 5 percent — Frequency: 6.92
- Threshold: 6 percent — Frequency: 0.22
- Note: For funds with multiple thresholds (around 1 percent of partial swing funds), the minimum is reported.

### Table B.2 — Full Swing versus Partial Swing versus Dual Priced (regression summaries)
- Dependent variable: Flow (net monthly capital flows into a fund divided by fund’s total net assets)
- Stress: indicator = 1 if monthly VIX is above the 75th percentile of the sample
- Baseline category: funds which use the traditional pricing rule
- Standard errors clustered by fund and time; *, **, *** indicate 10 percent, 5 percent, and 1 percent significance levels

Key coefficient estimates (with standard errors in parentheses):
- Full x Stress: 1.0782** (0.5301) — columns (1) and (4) report 1.0782** (0.5285); matched sample (5) reports 1.3324* (0.7819)
- Partial x Stress: 0.8211* (0.4969); matched sample (5) reports 1.3070** (0.5507)
- Dual x Stress: 1.9450** (0.9662); matched sample (5) reports 2.1814 (1.6003)
- Full: -1.1169** (0.5308); matched sample (5) reports -0.8210 (0.5649)
- Partial: -0.4036 (0.5419); matched sample (5) reports -0.7123 (0.5724)
- Dual: -1.9327** (0.8517); matched sample (5) reports -2.4882** (1.0934)
- Stress: -0.9890*** (0.2776) in columns (1)-(4); matched sample (5) reports -1.2943*** (0.3905)
- Constant: 1.5715*** (0.5075) in columns (1)-(4); matched sample (5) reports 1.3470** (0.5443)

Model statistics:
- Observations: column (1) 6,552; column (2) 11,729; column (3) 5,468; column (4) 16,693; column (5) 10,069
- R-squared: column (1) 0.008; column (2) 0.002; column (3) 0.009; column (4) 0.006; column (5) 0.008

### Table B.3 — Extended Robustness Tests (matched sample; controls included)
- Dependent variable: Flow (net monthly capital flows into a fund divided by the fund’s total net assets)
- Alternative: indicator = 1 if fund is using one of the alternative pricing mechanisms
- Stress definitions:
  - Columns (1)-(5): Stress = 1 if monthly VIX is above the 75th percentile
  - Columns (6)-(8): Stress defined according to the 75th percentile of TED spread, LIBOR, and Merrill Lynch’s MOVE index, respectively
  - Column (9): Stress defined using the 90th percentile cut-off
- Regressions use the matched sample including controls: lagged Alpha, Size, Age, Expense, Illiquidity, and Inst
- Unit of observation: fund-month
- Standard errors clustered by fund and month; *, **, *** indicate 10 percent, 5 percent, and 1 percent significance levels

Selected coefficient estimates (with standard errors in parentheses):
- Alternative:
  - Column (1) TED: -0.2480 (0.5619)
  - Column (2) Libor: -0.1044 (0.6332)
  - Column (3) MOVE: -0.5181 (0.5482)
  - Column (4) P90: -0.8621* (0.5157)
  - Columns (6)-(9): -0.6912 (0.5189), -0.6779 (0.5113), -0.7053 (0.5770), -0.6494 (0.5529)
- Alternative x Stress:
  - Column (1) TED: 1.1808** (0.5446)
  - Column (2) Libor: 1.3295** (0.5744)
  - Column (3) MOVE: 1.1951** (0.5319)
  - Column (4) P90: 1.2982** (0.5489)
  - Columns (6)-(9): 1.7446*** (0.6415), 1.9577*** (0.7220), 1.2229* (0.6540), 1.6387** (0.7516)
- Stress:
  - Column (1) TED: -1.2712*** (0.3809)
  - Column (2) Libor: -1.3592*** (0.3795)
  - Column (3) MOVE: -1.2335*** (0.3565)
  - Column (4) P90: -1.3075*** (0.3884)
  - Columns (6)-(9): -1.0096** (0.5134), -1.0631* (0.5629), -1.0970** (0.4866), -1.1284* (0.5832)

Model statistics and controls:
- Observations: columns generally report 9,670 (column (3) 9,510)
- R-squared: column (1) 0.035; column (2) 0.030; column (3) 0.028; column (4) 0.040; columns (6)-(9) 0.026, 0.026, 0.025, 0.026 respectively
- Controls: Y (lagged Alpha, Size, Age, Expense, Illiquidity, Inst)
- Fixed effects included in specified columns: Region of Sale FE (column noted), Domicile FE (column noted), Global Category FE (column noted), Investment Area FE (column noted)

*Source: Appendix A and Appendix B of the provided content unit.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019227-print-pdf.pdf_