## wpiea2024168-print-pdf ## Source details **Canonical URL:** [wpiea2024168-print-pdf](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024168-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024168-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024168-print-pdf.pdf.json) --- ### Introduction — research question, data, and main contribution - Central question: When an asset is sold, what happens to its price? Relevant for asset fire sales, real effects of financial market fluctuations, and determinants of market liquidity. - Main methodological contribution: a new, general measure of selling pressure — outside selling pressure — unrelated to an asset’s fundamental value, applicable to any transactions data with identifiable counterparties. - Data and empirical setting: - Regulatory transaction-level data on trading in corporate and government bonds by financial firms in the United Kingdom from 1st January 2019 to 1st July 2020. - Coverage: dealers, non-dealer banks, hedge funds, asset managers (including mutual funds) and other firm types; British and foreign issuers; sterling and other currencies. - Key features: - Around 85% of the bonds in the sample are corporate bonds, with the remainder being government bonds. - Government bonds are traded more frequently and account for slightly over half the trades in the sample. - 80% of the instruments and over 90% of the trades are in sterling, euro or dollar instruments. - 3% of traders are dealers but they account for half of total trading. - Each trader on average trades 78 bonds a week. - Each bond is traded by 10 traders each week conditional on being traded at all that week. - Observation frequency: weekly aggregation of trade data. - Complementary data: bond-level characteristics from Eikon Fixed Income; mutual fund data (total net assets, net flows, portfolio holdings) from Morningstar for 2019 Q3 to 2020 Q2 (funds selected hold between 38-52% of bonds traded in the transaction dataset). ### Identification strategy — outside selling pressure and econometric approach - Intuition: - If an investor trading bond i at time t is simultaneously net selling many other assets unrelated to bond i, the trades are more likely driven by the investor’s condition (non-fundamental) than bond-specific fundamentals. - Conversely, idiosyncratic trading in bond i implies, on average, zero sales of other assets. - Formal measure construction: - s_{i,j,t} = net sales of bond i by trader j at time t (s_{i,j,t} > 0 indicates net selling). - z^{NS}_{i,j,t} = Σ_k 1(iss_i ≠ iss_k) s_{k,j,t} - z^{T}_{i,j,t} = Σ_k 1(iss_i ≠ iss_k) |s_{k,j,t}| - z_{i,t,J} = (Σ_{j∈J} 1(s_{i,j,t} > 0) z^{NS}_{i,j,t}) / (Σ_{j∈J} 1(s_{i,j,t} > 0) z^{T}_{i,j,t}) - J is the set of investors (initially all traders; sector-level J splits into dealers, banks, funds, hedge funds, others). - Econometric strategy: 1) Structural (2SLS): - p_{i,t} = Σ_J β_J s^{V}_{i,t,J} + X_{i,t} γ + ε_{i,t} - s^{V}_{i,t,J} = net sales of i at t by investor type J as a percentage of the average weekly trading volume in that bond. - Use z_{i,t,J} as instrument for s^{V}_{i,t,J}. β_J interpreted as marginal causal effect of sales by sector J on prices. 2) Reduced form: - p_{i,t} = Σ_J δ_J z_{i,t,J} + X_{i,t} η + ν_{i,t} - Used for aggregate selling pressure (all traders) because total net sales sum to zero by construction. - Controls and identification: - Issuer-time fixed effects (e.g., contrasting Dell Bond A vs Dell Bond B in same period), bond fixed effects, instrument fixed effects, time since issuance. - Identification assumption: cov(z_{i,t}, ε_{i,t} | X_{i,t}) = 0 after controls. - Use of notional net sales rather than value-based measures to avoid mechanical correlations. ### Empirical findings — price impact, heterogeneity, timing, and robustness - Aggregate price impact (reduced-form evidence): - Moving from the 5th to the 95th percentile of outside selling pressure is associated with a 25 basis point fall in prices. - These effects persist but halve after a couple of weeks and disappear within five weeks. - Price impacts are greater in corporate than government bonds. - Price impacts are greater during the dash-for-cash (March 2020) than in the rest of the sample period. - Sector heterogeneity (instrumenting with type-specific outside selling pressure): - Dealers’ selling has much larger price impact than any other sector. - Hedge funds are the second most impactful sector. - Asset management companies that house mutual funds have relatively minor effects, all else equal. - Robustness: - Results hold across different ways of measuring prices and selling pressure, and across different regression specifications (alternative instrument zAlt_{i,t,J}, log price specifications, inclusion of quadratic terms). - Nonlinearity checks: quadratic sales terms not statistically significant; dealers’ larger impact persists. - Selected exact empirical coefficients and statistics (preserve source values): - Table 3 summary statistics: - Prices p_{i,t}: Mean 99.82, Std. dev. 4.86, 95th-5th pctile 5.65 - Sales s^V_{i,t}: Mean 0.366, Std. dev. 7.73, 95th-5th pctile 144.06 - Pressure z_{i,t}: Mean 0.02, Std. dev. 0.22, 95th-5th pctile 0.68 - Table 5 reduced-form pressure coefficients (examples printed across specifications): - Pressurez_{i,t} coefficients: -0.3208 ∗∗, -0.2486 ∗∗∗, -0.2991 ∗∗∗, -0.3727 ∗∗∗ (standard errors (0.1366), (0.0961), (0.0552), (0.0521)) - Observations: 1,514,387 - Table 6 heterogeneity (Price (%)): - Corporate: Pressurez_{i,t} = -0.468 ∗∗∗ (0.055) - Government: Pressurez_{i,t} = -0.102 (0.114) - March 2020: Pressurez_{i,t} = -0.593 ∗∗∗ (0.176) - Rest of sample: Pressurez_{i,t} = -0.402 ∗∗∗ (0.052) - Observations: 1,193,684; 320,703; 80,541; 1,433,846 (respectively) - Appendix A1 (2SLS β estimates, Table A1): - Dealer sales: -0.1034 ∗∗∗ (0.0071) - Bank sales: -0.0305 (0.0198) - Fund sales: -0.0111 ∗∗ (0.0055) - Hedge fund sales: -0.0456 ∗∗∗ (0.0106) - Other sales: -0.0029 (0.0041) - Observations: 1,591,470 (each column) - Appendix A3 (reduced-form δ_J, Table A3): - Dealer pressure: -2.147 ∗∗∗ (0.1110) - Hedge fund pressure: -0.3509 ∗∗∗ (0.0677) - Fund pressure: -0.0889 ∗∗∗ (0.0337) - Bank pressure: -0.0615 ∗ (0.0355) - Other pressure: -0.0647 ∗∗ (0.0322) - Observations: 1,864,873 - First-stage strength (Table A2 examples): - Dealer: Coeff (z_{i,t}) = 22.713, t-stat = 3.90, R-squared = 0.2560, F-stat = 6.4 - Hedge fund: Coeff = 6.6, t-stat = 15.10, R-squared = 0.272, F-stat = 2,266.6 - Fund: Coeff = 6.2, t-stat = 14.00, R-squared = 0.297, F-stat = 40.0 ### Theoretical mechanism — model and implications - Core idea: counterparties in OTC markets do not know whether selling is non-fundamental; they demand discounts when trading with counterparties believed to be informed. - Model (variant of Kyle (1985) with imperfect information): - Three traders: liquidity demander (D), liquidity supplier (S), noise trader. - Asset value v ~ Gaussian(mean p0, variance Σ); prior mean p0 observed by all traders but not econometrician. - Signals: v_D = v + ε_D, v_S = v + ε_S with variances σ^2_D and σ^2_S. - Liquidity demander submits market order x; noise trader u has mean 0, variance σ^2_u; supplier observes y = x + u. - Equilibrium price linear form: P(y, v_S) = p0(1−γ) + γ v_s + λ y (Equation 6). - γ and λ expressions (as given in source): - γ = Σ(2σ^2_D + Σ) / [2(σ^2_D + Σ)(σ^2_S + Σ) − Σ^2] (Equation 7) - λ = (1 / 2σ_u) (1−γ) Σ^1/2 / sqrt(σ^2_D + Σ) (Equation 8) [presented in the source as λ = 1 / 2σ_u (1−γ)Σ p σ^2_D + Σ; retain source presentation] - Comparative statics and implications: 1. Price impact λ is decreasing in the variance of noise trading σ^2_u. 2. Price impact λ is increasing in the precision of the liquidity demander’s signal (i.e., as σ^2_D decreases). 3. Price impact λ is decreasing in the precision of the liquidity supplier’s signal (i.e., as σ^2_S decreases). - Implication 1: More informed sellers have greater price impact when selling, even if sales are non-fundamental. - Implication 2: Better informed liquidity suppliers reduce price impact; if well-informed suppliers are constrained or exit, price impacts increase. - Implication 3: OLS regressions of price on trading quantity are inconsistent because public shocks to asset value enter both trading and prices; instrumentation is required to identify Kyle’s lambda. ### Empirical evidence supporting informational mechanism - Evidence consistent with model implications: - Dealers trade with more counterparties in a month than any other trader type, consistent with superior ability to predict future order flow and network connectedness. - Hedge funds trade at the most favourable prices: in any given month they buy at low prices and sell at high prices, consistent with superior information. - Figure summaries (as described in source): - Figure 4 Panel (a): Realised spread (bps) by sector — hedge funds have the most favourable realised spreads. - Figure 4 Panel (b): Counterparties per bond by sector — dealers are the most connected sector. - Key takeaway: Sales of identical assets can have very different price impacts depending on who is selling, driven by perceptions of counterparties’ informativeness (cash-flow information, order-flow awareness, network connectedness). ### Policy and research implications - Research: - The outside selling pressure measure is broadly applicable for identifying exogenous selling across trader types in OTC markets. - Studies should account for who is selling (investor type) not just aggregate sales volumes. - Policy and macroprudential regulation: - Monitoring liquidity risks should employ measures that capture selling pressure across a wide range of financial institutions. - Policy focus should not be limited only to mutual funds; dealers and hedge funds warrant attention given larger price impacts when selling. - Stress testing and fire-sale simulation models should allow price impacts to vary by type of seller. ### Data construction and cleaning (dataset provenance and handling) - Duplicate transactions: - Duplicates: same two firms trading same quantity of same bond at same time with different firms reporting; keep only a single instance. - Winsorisation and filters: - Trading quantities winsorized at the [0.1%, 99.9%] levels. - Trade reports removed where transaction price (as a % of par) is listed as under 20 or over 250. - Agency trading: - Dealer-as-agent trades (dealer buys on behalf of client or matches two client trades) imply the dealer is neither net seller nor buyer; such trades drop out of net-selling analyses and numerator of Equation 1. - Weekly aggregation causes offsetting dealer trades within short windows to drop out. - Mutual fund holdings coverage (Table A4): - 2019 Q3: Percentage of instruments held by mutual funds = 50.1 ; Percentage of issuance held by mutual funds = 1.3 - 2019 Q4: Percentage of instruments held by mutual funds = 52.1 ; Percentage of issuance held by mutual funds = 1.3 - 2020 Q1: Percentage of instruments held by mutual funds = 37.8 ; Percentage of issuance held by mutual funds = 0.5 - 2020 Q2: Percentage of instruments held by mutual funds = 48.0 ; Percentage of issuance held by mutual funds = 0.6 *Source: wpiea2024168-print-pdf — extracted content from the provided PDF.* ### 1. Introduction ### 1. Introduction ### Research question and contribution - Central question: When an asset is sold, what happens to its price? Answers are critical for understanding asset fire sales, real effects of financial market fluctuations, and determinants of market liquidity. - Main methodological contribution: a new, general measure of selling pressure—outside selling pressure—unrelated to an asset’s fundamental value, applicable to any transactions data with identifiable counterparties. - Applicability: the measure can be used across investor types and markets where trade repositories identify counterparties and assets. ### Data and empirical setting - Dataset: regulatory transaction-level data on trading in corporate and government bonds by financial firms in the United Kingdom from 1st January 2019 to 1st July 2020. - Coverage: trades by dealers, non-dealer banks, hedge funds, asset managers (including mutual funds) and other types of firm; bonds of British and foreign issuers; bonds denominated in sterling and other currencies. - Key data features: - Around 85% of the bonds in the sample are corporate bonds, with the remainder being government bonds. - Government bonds are traded more frequently and account for slightly over half the trades in the sample. - 80% of the instruments and over 90% of the trades are in sterling, euro or dollar instruments. - 3% of traders are dealers but they account for half of total trading. - Each trader on average trades 78 bonds a week. - Each bond is traded by 10 traders each week conditional on being traded at all that week. - Observation frequency: weekly aggregation of trade data (finer than the common monthly or quarterly frequencies). - Complementary data: bond-level characteristics from Eikon Fixed Income; mutual fund data (total net assets, net flows, portfolio holdings) from Morningstar for 2019 Q3 to 2020 Q2 (funds selected hold between 38-52% of bonds traded in the transaction dataset). ### Identification strategy: outside selling pressure - Problem addressed: endogeneity of observed sales (sales may reflect signals about fundamentals or extrinsic motivations). - Core insight: if an investor sells many unrelated assets at the same time, the sales are more likely driven by the investor (non-fundamental) rather than asset-specific fundamentals. - Measure defined: outside selling pressure — net sales of bonds other than bond i by the same market participants. - Controls to account for correlated shocks: issuer-time fixed effects, bond fixed effects, and time since the bond was issued (following Choi et al. (2020)). - Instrumental variable use: outside selling pressure is used as an instrument for investors’ sales of bond i; e.g., comparing Dell A and Dell B when sellers of Dell A are net sellers of other bonds to a greater extent than sellers of Dell B. ### Empirical findings on price impact - Aggregate price impact: - Moving from the 5th to the 95th percentile of outside selling pressure is associated with a 25 basis point fall in prices. - These effects persist but halve after a couple of weeks and disappear within five weeks. - Price impacts are greater in corporate than government bonds. - Price impacts are greater during the dash-for-cash (March 2020) than in the rest of the sample period. - Heterogeneity by seller type (instrumenting with type-specific outside selling pressure): - Dealers’ selling has much larger price impact than any other sector. - Hedge funds are the second most impactful sector. - Asset management companies that house mutual funds have relatively minor effects, all else equal. - Robustness: results hold across different ways of measuring prices and selling pressure, and across different regression specifications. ### Theoretical mechanism - Proposed explanation: counterparties in OTC markets do not observe whether selling is non-fundamental; they may demand price discounts when trading with counterparties they believe might have private information. - Informational roles: - Dealers’ business models give them access to private information about trading flows and issuer conditions. - Hedge funds’ business models are based around gaining and benefiting from informational advantage. - Formal model: a variant of Kyle (1985) with imperfect information, noise traders, and correlated signals received by liquidity demanders (informed sellers) and liquidity suppliers (counterparties). - In equilibrium, price impact of a sale is increasing in how well informed the liquidity demander is. - Price impact is decreasing in how well informed the liquidity supplier is. - OLS estimation of price impact is inconsistent when public signals that drive both price and trading are unobserved by the econometrician; identification (e.g., via the outside selling pressure instrument) is required to estimate Kyle’s lambda. ### Empirical evidence supporting the mechanism - Dealers trade with more counterparties in a month than any other trader type, consistent with superior ability to predict future order flow. - Hedge funds trade at the most favorable prices in the data: in any given month they buy at low prices and sell at high prices, consistent with superior information. ### Implications for research and policy - For research: - The outside selling pressure measure is a broadly applicable tool for identifying exogenous selling across trader types in OTC markets. - Results highlight the importance of studying who is selling, not just aggregate sales volumes. - For policymakers and macroprudential regulation: - Monitoring liquidity risks should employ measures that capture selling pressure across a wide range of financial institutions. - Policy focus should not be limited only to mutual funds; attention should also be given to dealers and hedge funds given their larger price impacts when selling. - Stress testing and fire-sale simulation models should allow price impacts to vary by type of seller. *Source: wpiea2024168-print-pdf - 1. Introduction (https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024168-print-pdf.pdf).* ### 4. Research design ### 4. Research design ### Intuition and identification - If an investor trading bond i at time t is simultaneously net selling many other assets that are unrelated (price-relevant fundamentals uncorrelated with bond i), then those trades are likely driven by the investor’s condition rather than idiosyncratic properties of bond i. - Conversely, if an investor is trading bond i for purely idiosyncratic reasons, then, on average, her sales of other assets should be zero. - The paper formalises this by constructing measures of net sales and transactions of other bonds (issued by entities other than iss_i) for each trader j and bond i at time t and using these to form an outside selling pressure instrument. ### Definitions and construction of the selling-pressure measure - Let s_{i,j,t} be the net sales of bond i by trader j at time t, where s_{i,j,t} > 0 indicates net selling. - Let iss_i be the issuer of bond i. - Define net sales of other-issuer bonds: - z^{NS}_{i,j,t} = Σ_k 1(iss_i ≠ iss_k) s_{k,j,t} - Define transactions in other-issuer bonds: - z^{T}_{i,j,t} = Σ_k 1(iss_i ≠ iss_k) |s_{k,j,t}| - Outside selling pressure for bond i at time t for a set of investors J: - z_{i,t,J} = (Σ_{j∈J} 1(s_{i,j,t} > 0) z^{NS}_{i,j,t}) / (Σ_{j∈J} 1(s_{i,j,t} > 0) z^{T}_{i,j,t}) - In initial regressions J is all traders; sector-level analysis splits J into dealers, banks, funds, hedge funds, and others. ### Econometric strategy - Two types of regressions are run. 1) Two-stage least squares (structural specification): - p_{i,t} = Σ_J β_J s^{V}_{i,t,J} + X_{i,t} γ + ε_{i,t} (equation (2)) - s^{V}_{i,t,J} denotes net sales of i at time t by investor type J as a percentage of the average weekly trading volume in that bond (average taken over all weeks in which that bond trades). - p_{i,t} denotes the bond’s price. - X_{i,t} is a set of control variables. - Use z_{i,t,J} as an instrumental variable for s^{V}_{i,t,J}. - β_J is interpreted as the marginal causal effect of sales by sector J on prices. 2) Reduced-form specification: - p_{i,t} = Σ_J δ_J z_{i,t,J} + X_{i,t} η + ν_{i,t} (equation (3)) - δ_J is the marginal effect of outside selling pressure from sector J on prices. - For aggregate selling pressure (all traders), the reduced-form is used because total net sales sum to zero by construction, so the structural regressor has no variation. ### Addressing simultaneity and endogeneity - Outside selling pressure z_{i,t,J} serves as an exogenous shifter of traders’ demand (instrument) to address: - Simultaneity: price and quantity are jointly determined; an exogenous shifter is needed to identify structural parameters. - Endogeneity/reverse causality: sales might be driven by signals about the bond’s value—instrumental variable approach mitigates this. - Minimal use of bond i information: pressure measure uses only the sign of trades in bond i while computing pressure from other bonds, reducing direct linkage to i’s fundamentals. - Use notional net sales rather than value-based measures to avoid mechanical correlations identified in Wardlaw (2020). ### Fixed effects and remaining identification concerns - Include demanding fixed effects and controls to eliminate endogeneity concerns: - Issuer-time fixed effects are included in each regression, exploiting within issuer-time variation (e.g., contrasting Dell Bond A vs Dell Bond B in the same period). - Instrument fixed effects and control for time since issuance of the bond are also included. - Identification assumption after controls and fixed effects: - cov(z_{i,t}, ε_{i,t} | X_{i,t}) = 0 - Acknowledged concern: possibility of remaining fundamental variation that survives both the instrumental variable and fixed effects; addressed by instrument fixed effects and additional controls. - Trade-off noted: issuer-time fixed effects will absorb some non-fundamental variation, potentially reducing variation available for estimation, but results retain ample non-fundamental variation for precise estimation. ### Properties of the outside selling-pressure measure - Distributional summaries: - Table 3 summarises distributions of p_{i,t}, z_{i,t} and s^{V}_{i,t}. - Figure 1 plots distribution of z_{i,t} through time for all traders; a spike is observed during the ‘dash for cash’ in March 2020. - Correlations with other fire-sale proxies: - Measure is positively but weakly correlated with mutual-fund-flow-based fire-selling measures (Coval and Stafford (2007); Wardlaw (2020), including F2S and F2V). - Table 4 shows correlations between outside selling pressure (calculated only for funds) and these flow-induced pressure measures. - Authors note no requirement for strong correlation with these proxies and question their appropriateness as measures of non-fundamental sales. - Measure captures non-fundamental trading broadly; drivers may include mechanical rebalancing, mandate shifts, changes in demand for liquidity, or distress-driven fire sales. The paper remains agnostic about the drivers and focuses on measuring impacts conditional on non-fundamental sales being triggered. - Temporal patterns: - Spike in March 2020 (‘dash for cash’). - Dispersion of selling pressure increases at end of calendar year (possible artifact of fewer trades or window-dressing behavior). ### Implications for estimation and interpretation - The instrument and fixed effects together aim to ensure that identified variation reflects non-fundamental selling rather than issuer-level fundamentals. - Reduced-form estimates (equation (3)) provide δ_J, marginal effects of outside selling pressure on prices. - Two-stage least squares estimates (equation (2)) at sector level use sector-specific z_{i,t,J} as instruments to recover β_J, the marginal causal effect of sector J’s sales (scaled by average weekly trading volume). *Source: wpiea2024168-print-pdf — 4. Research design* ### 6. Why does it matter who is selling? ### 6. Why does it matter who is selling? ### 6.1. Intuition - The instrumental variables approach identifies selling that the econometrician knows to be unrelated to the asset’s fundamentals, but market counterparties do not know this at the time of the trade. - Counterparties face a signal-extraction problem: they must infer whether an observed sale reveals private information about the asset. - Two types of ‘fundamental’ properties (Amihud et al., 2005): - Cash-flow fundamentals: information about asset cash flows (natural fundamentals even without trading frictions). - Liquidity/convenience fundamentals: information related to order flow or likely changes in future trading conditions that influence asset price (relevant in markets with frictions and liquidity premia). - Dealers possess multiple informational advantages: - Direct lending relationships with issuers and involvement in underwriting (Goldstein et al., 2021). - Observation of a large portion of order flow in OTC bond markets, conferring informational advantages (Bessembinder et al., 2006; Kondor and Pinter, 2022; Pagano and Roell, 1996). - In opaque OTC bond markets where transactions are not publicly reported, dealer sales plausibly encode fundamental information prompting counterparties to demand larger discounts. - Hedge funds are typically considered informed traders: - Often research intensive, suggesting advantages on cash-flow fundamentals. - Evidence suggests hedge funds also hold informational advantages regarding future trading flows and bond fundamentals (Czech et al., 2021c). ### 6.2. Model - Purpose: Formalize intuition in a Kyle (1985) style model capturing both fundamental and non-fundamental selling to derive heterogeneous price impacts of selling. #### 6.2.1. Setting - Three traders: liquidity demander (subscript D), liquidity supplier (subscript S), and a noise trader. - Single asset with end-of-period value v. Prior distribution of v is Gaussian with mean p0 and variance Σ. The prior mean, p0, is observed by all traders but not by the econometrician. - Signals: - v_D = v + ε_D - v_S = v + ε_S - ε_D and ε_S are uncorrelated error terms with mean zero and variances σ^2_D and σ^2_S respectively. - Liquidity demander submits market order x. Noise traders submit market order u with mean 0 and variance σ^2_u. Liquidity supplier observes y = x + u but not the parts. - Model extensions relative to Kyle (1985): - Noise added to the informed agent’s signal. - Supplier has its own (noisy) signal, allowing parameterization of relative informativeness. - Alternative interpretation: liquidity demander and noise trader can be components of a single agent whose trades mix fundamental and non-fundamental motives (funding shocks, distress, regulatory needs). From the counterparty’s view, sales for fundamental and non-fundamental reasons are indistinguishable. - Liquidity supplier sets price p and takes the other side; liquidity supply is perfectly competitive (zero profits on average); liquidity demanders make profits on average (informational advantage), noise traders incur offsetting losses. - Price impact (Kyle’s lambda) is the amount price falls as a function of market order y = u + x. #### 6.2.2. Equilibrium - Equilibrium price is linear in prior, supplier’s signal, and trading quantity: - P(y, v_S) = p0(1−γ) + γ v_s + λ y (Equation 6) - Parameters: - γ = Σ(2σ^2_D + Σ) / [2(σ^2_D + Σ)(σ^2_S + Σ) − Σ^2] (Equation 7) - λ = (1 / 2σ_u) (1−γ) Σ^1/2 / sqrt(σ^2_D + Σ) (Equation 8) [presented in the source as λ = 1 / 2σ_u (1−γ)Σ p σ^2_D + Σ; interpreted here as the expression given in the text—retain exact source presentation] - Comparative statics for price impact: 1. Price impact is decreasing in the variance of noise trading σ^2_u. 2. Price impact is increasing in the precision of the liquidity demander’s signal v_D. 3. Price impact is decreasing in the precision of the liquidity supplier’s signal v_S. - Special case: if the liquidity supplier receives no signal and the liquidity demander’s information is perfect, the model simplifies to Kyle’s original setup, yielding the classical Kyle’s lambda (price impact equal to half the ratio of standard deviations of asset value to noise trading). In the general version, price impact depends additionally on the precision of traders’ signals. #### 6.2.3. Implications - Implication 1. Traders that are more informed will have greater price impact when selling. - Price impact increases with the precision of the liquidity demander’s signal. - Sales by traders typically seen as more informed generate larger price impacts, even if the sale is non-fundamental (noise) — informed traders cannot credibly claim to be uninformed. - Implication 2. Better informed liquidity suppliers will lead to lower price impact. - Price impact decreases with the precision of the liquidity supplier’s signal. - Less informed suppliers face greater adverse selection and supply liquidity only at worse prices. When specialist (well-informed) suppliers are constrained or exit, price impacts increase. - Implication 3. Regressing price on trading quantity gives inconsistent estimates of price impact. - In the model, observed trading y_t is the sum of informed trading and noise trading; price p_t is the equilibrium price: - p_t = p0 + λ y_t + e_t (Equation 9) - e_t = p0(1−γ) + γ v_s,t (Equation 10) - Let v_t = p0 + ε_v,t with ε_v,t mean 0 and variance Σ. Informed trading x_t = σ_u p σ^2_D + Σ (ε_v,t + ε_D,t) and e_t = γ(ε_v,t + ε_S,t). - Presence of ε_v,t in both regressor (via informed trading) and error term shows OLS is inconsistent because shocks to asset value drive both price and trading. Identification of Kyle’s lambda requires an instrument capturing noise trading uncorrelated with information-based trading; this motivates the empirical instrumental-variable approach used. ### 6.3. Empirical evidence on the mechanism - Aim: Provide evidence that perceptions of who is informed drive heterogeneous price impacts. - Two forms of informational advantage in bond markets: 1. Better information on future cash flows of a bond. 2. Better information on future trading in a bond. - Evidence summarized (described with reference to Figure 4 in the source): - Panel 1: For each firm trading a bond in a month, compute (average sell price − average buy price) and regress on sector dummies. - Estimates suggest hedge funds trade at the most favourable prices, consistent with their arbitrage role and evidence they are informed traders (Czech et al., 2021c). This supports that hedge fund sales have relatively large price impacts due to informational advantage. - Panel 2: For each firm trading a bond in a month, compute the number of counterparties that firm trades that bond with and regress on sector dummies. - Dealers are the most connected sector, consistent with intermediary role and ability to extract information via connections (Kacperczyk and Pagnotta, 2019; Brancaccio et al., 2017). Superior connectedness supports the argument that dealer sales have large price impacts due to informational advantages. ### Key takeaway points - Sales of identical assets can have very different price impacts depending on who is selling, driven by perceptions of counterparties’ informativeness. - Dealers and hedge funds generate significantly larger price impacts than other investor types, consistent with informational advantages (cash-flow information, order-flow awareness, and network connectedness). - Identification of true price impact requires instrumentation for exogenous (noise) selling because OLS regressions of price on trade quantity are biased by endogenous informed trading. *Source: IMF Working Paper — section “6. Why does it matter who is selling?” from the provided PDF content.* ### References ### wpiea2024168-print-pdf - References ### References cited - Acharya, V. V. and Pedersen, L. H. (2005). Asset pricing with liquidity risk. 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The Journal of Finance, 75(6):3221–3243. ### Key empirical table summaries and exact statistics - Table 1: Summary Statistics (Panel A: Bonds; Panel B: Traders) - Panel A: Bonds - Type: Corporate 8544, Government 1556 - Currency: GBP 711, EUR 2644, USD 4739, Other 206 - Maturity: 0-5 years 4521, 6-10 years 3744, 11-20 years 712, 21+ years 1124 - Panel B: Traders - Sector: Fund 4315, Bank 914, Dealer 351, Hedge Fund 62, Other 3918 - Note: first numeric column shows raw shares; second numeric column shows percentage of total trades accounted for by each bond and trader type. ‘Other’ traders include pensions funds, liability-driven investment funds, central counterparties, principal trading firms, brokerage firms, and sovereign wealth funds, among other firm types. - Table 2: Instruments & Traders per week - Number - Instruments 23,588 - Traders 2,922 - Instruments per Trader 78 - Traders per Instrument 10 - Note: averages across weeks; only instruments and traders that traded at least once each week; excludes traders with missing trader IDs. - Table 3: Prices, Sales & Pressure (Mean, Std. dev., 95th-5th pctile) - Prices p_{i,t}: Mean 99.82, Std. dev. 4.86, 95th-5th pctile 5.65 - Sales s^V_{i,t}: Mean 0.366, Std. dev. 7.73, 95th-5th pctile 144.06 - Pressure z_{i,t}: Mean 0.02, Std. dev. 0.22, 95th-5th pctile 0.68 - Notes: Prices expressed as a percentage of par. Saless^V_{i,t} are net sales as a percentage of average trading volume. Pressurez_{i,t} defined in Equation 1 and takes values between -1 and 1. - Table 4: Outside selling pressure and fund-flow-based measures (regression of fund outside selling pressure z^F_{i,t}) - Coval-Stafford coefficient: 0.049 ∗∗∗ (standard errors (0.001) and (0.002) shown across columns) - Wardlaw F2V coefficient: 0.018 ∗∗∗ (standard errors (0.0005) and (0.0007)) - Wardlaw F2S coefficient: 0.019 ∗∗∗ and 0.003 ∗∗∗ (standard errors (0.0005) and (0.0008)) - R^2 reported: 0.005, 0.002, 0.002, 0.38, 0.30, 0.30 (across columns) - Observations: 335,335; 830,292; 830,292; 335,335; 830,292; 830,292 - Fixed effects: Issuer-Week, Instrument fixed effects included in columns with higher R^2 - Note: measures multiplied by −1 and percentile-ranked between 0 and 1; Coval and Stafford (2007); Wardlaw (2020). - Table 5: Price changes and selling pressure (reduced-form regressions of Price (%) on Pressurez_{i,t}) - Pressurez_{i,t} coefficients across columns: -0.3208 ∗∗, -0.2486 ∗∗∗, -0.2991 ∗∗∗, -0.3727 ∗∗∗ - Standard errors: (0.1366), (0.0961), (0.0552), (0.0521) - R^2: 0.8054, 10.8231, 00.84703, 0.89582 (as printed across columns) - Observations: 1,514,387 in each column - Fixed effects vary by column: Instrument fixed effects always Yes; Week fixed effects, Country-Week, Country-Sector-Week, Issuer-Week included in different specifications. - Note: Time since issuance included as a control. Standard errors two-way clustered. ∗∗∗, ∗∗, ∗ denote significance at the 0.1%, 1% and 5% levels. - Table 6: Heterogeneity: bond type and stressed periods (Price (%)) - Columns: Corporate, Government, March 2020, Rest of sample - Pressurez_{i,t} coefficients: - Corporate: -0.468 ∗∗∗ (standard error (0.055)) - Government: -0.102 (standard error (0.114)) - March 2020: -0.593 ∗∗∗ (standard error (0.176)) - Rest of sample: -0.402 ∗∗∗ (standard error (0.052)) - R^2: 0.89, 0.90, 0.97, 0.90 - Observations: 1,193,684; 320,703; 80,541; 1,433,846 - Fixed effects: Issuer-Week and Instrument fixed effects Yes in all columns. - Note: Time since issuance included as an additional control. - Table 7: Sector sales & pressure (Sector means, Std dev, 95th-5th pctile) - Saless^V_{i,t} (mean; std dev; 95th-5th pctile) - Bank: -0.64; 6.06; 6.5 - Dealer: -0.56; 8.71; 49.8 - Fund: 0.54; 8.37; 8.4 - Hedge fund: 0.11; 4.4; 3.5 - Other: 0.34; 2.65; 2.4 - Pressurez_{i,t} (mean; std dev; 95th-5th pctile) - Bank: 0.01; 0.14; 0.40 - Dealer: 0.00; 0.07; 0.12 - Fund: 0.01; 0.16; 0.40 - Hedge fund: 0.00; 0.07; 0.00 - Other: 0.01; 0.16; 0.32 - Note: Saless^V_{i,t} are net sales by investor type as a percentage of average trading volume. Pressurez_{i,t} defined in Equation 1 as net selling of bonds other than i by investors of a given type; values between -1 and 1. ### Figures — empirical patterns (annotated notes and exact labels) - Figure 1: Outside selling pressure through time - Plots mean, 10th pctile, 90th pctile of z_{i,t} across bonds for each week over 2019–01 to 2020–07. - Caption: For each week compute mean, 10th and 90th percentiles of z_{i,t} across bonds, where z_{i,t} computed across all traders. - Figure 2: Price impacts through time - Y-axis: Coefficient on outside selling pressure; X-axis: Weeks after shock (0,2,4,6) - Caption: Runs regressions as in Equation 4 relating price at t+τ to pressure and controls at t. Includes bonds traded on at least 7 consecutive weeks. Coefficient for τ = 0 need not match Table 5 column. - Figure 3: Price impact by sector - Shows estimated β coefficient in Equation 2 for sectors: Other, Fund, Bank, Hedge Fund, Dealer. - X-axis values include estimates roughly between -0.12 and 0.00 (visual scale printed as −0.12 −0.08 −0.04 0.00). - Caption: β is marginal effect of increasing sales by a sector on asset price. Prices as percentage of par. Sales as net sales by investor type as percentage of average trading volume. Controls include issuer-time and instrument fixed effects and time since issuance. Standard errors clustered at issuer-time and instrument levels. Error bars show 95% confidence intervals. - Figure 4: Trading performance & network connections by sector - Panel (a) Realised spread (bps) — horizontal bar values plotted from 0.00 to 0.15 (visual ticks 0.00 0.05 0.10 0.15) - Panel (b) Counterparties per bond — horizontal bar values plotted from 2.0 to 4.0 (visual ticks 2.0 2.5 3.0 3.5 4.0) - Sectors: Other, Fund, Bank, Hedge Fund, Dealer - Caption: Left panel computes for each firm the difference between average sell price and average buy price per bond-month, averaged over months and bonds; right panel counts unique counterparties per bond per firm-month then averages. Horizontal bars show 95% confidence intervals. ### Appendix A — Model proof and comparative statics (Section 6.2) - Equilibrium: pricing rule conjectured P(y,v_S) = μ + γ v_S + λ y (Equation A.2). - Liquidity demander optimality yields x = α + β v_D (Equation A.4) with - α = (w_D p_0 (1−γ) − μ) / (2λ) (Equation A.5) - β = (1−w_D)(1−γ) / (2λ) (Equation A.6) - First-order conditions and matching coefficients give - μ / 2 = [1 − (1−w_D)(1−γ) / 2] w_S p_0 − w_D p_0 (1−γ)^2 / 2 + [1 − (1−w_D)(1−γ) / 2] (1−w_S) v_S (Equation A.9) - γ = [1 − (1−w_D)(1−γ) / 2] (1−w_S) (Equation A.10) - Rearranged closed-form: γ = (1−w_S)(1 + w_D) / [2 − (1−w_S)(1−w_D)] (Equation A.11) - 1 − γ = 2 w_S / [2 − (1−w_S)(1−w_D)] (Equation A.12) - Expression for λ obtained by FOC on λ and rearrangement; final λ expression referenced as given in Section 6.2 after algebra (square-root step noted). - μ simplifies to μ = p_0 (1−γ). - Liquidity demander strategy final form: x = (σ_u / p) * (σ^2_D + Σ)^{-1} (v_D − p_0) (final displayed expression with variables as given). - Comparative statics (exact expressions preserved) - 1 − γ = 2 σ^2_S (σ^2_D + Σ) / [2(σ^2_D + Σ)(σ^2_S + Σ) − Σ^2] - λ = [1 / (2 σ_u)] (1 − γ) Σ / sqrt(σ^2_D + Σ) - Observations: - As the variance of noise trading σ^2_u increases, price impact λ decreases. - As the precision of the demander’s signal increases (σ^2_D decreases), price impact λ increases. - As the precision of the supplier’s signal increases (σ^2_S decreases), price impact λ decreases. - Alternative rewrites shown for 1 − γ: - 1 − γ = 2 σ^2_S (σ^2_D + Σ) / [2 σ^2_S (σ^2_D + Σ) + 2 Σ σ^2_D + Σ^2] - 1 − γ = 2 σ^2_S (σ^2_D + Σ) / [2(σ^2_D + Σ)(σ^2_S + Σ) − Σ^2] *Content based on wpiea2024168-print-pdf - References* ### Appendix B. Details on construction of dataset --- _Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024168-print-pdf.pdf_