--- title: "Anomalies and Their Short-Sale Costs: Muravyev, Pearson & Pollet (2025)" description: >- Distilled: across 162 asset pricing anomalies, average long-short abnormal returns of 0.14%/month vanish once stock borrow fees are accounted for, either by fee adjustment or by dropping high-fee stocks; the result holds for subsets including microcaps, high-fee anomalies, and factor-mimicking portfolios. J. Finance 2025, CC BY 4.0. Nine core results with source locators, datasets used, the identification strategy, and the estimating specifications with exact panel-regression equations. sidebar: label: Muravyev-Pearson-Pollet 2025 order: 1 tags: [paper-summary, anomalies, short-selling, asset-pricing, limits-to-arbitrage, portfolio-sort, panel-regression, open-access, cc-by, peer-reviewed, unreplicated, data:wrds, data:open-source-asset-pricing, data:markit-securities-finance] paper: authors: Dmitriy Muravyev, Neil D. Pearson, Joshua M. Pollet authorList: - { family: Muravyev, given: "Dmitriy", affiliation: "Gies College of Business, University of Illinois at Urbana-Champaign; Canadian Derivatives Institute" } - { family: Pearson, given: "Neil D.", affiliation: "Gies College of Business, University of Illinois at Urbana-Champaign; Canadian Derivatives Institute" } - { family: Pollet, given: "Joshua M.", affiliation: "Gies College of Business, University of Illinois at Urbana-Champaign" } year: 2025 venue: The Journal of Finance 80(6), December 2025, 3639-3694 venueShort: J. Finance 2025 licenseShort: CC BY 4.0 resultsCount: 9 citedByCount: 5 jel: codes: [G12, G14] assignedBy: claude-opus-4-8 date: 2026-06-05 topics: ['Financial Markets and Investment Strategies', 'Insurance and Financial Risk Management'] dataAccess: licensed-commercial outcome: - cross-sectional anomaly long-short returns - net-of-fee long-short abnormal returns across 162 anomalies outcomeClass: [security-returns] doi: 10.1111/jofi.13501 license: 'CC BY 4.0 (confirmed via Crossref DOI metadata: content-version vor, URL creativecommons.org/licenses/by/4.0/, delay-in-days 0, start 2025-09-30; corroborated by artifact p.3639 Creative Commons Attribution License statement)' access: open machineAccess: 'blocked-paywall (Wiley site wrapper; not tested directly 2026-05-31; CC-BY VOR licence confirmed in Crossref DOI metadata)' redistribution: 'extract-only (CC BY 4.0 permits mirroring; PDF not hosted in this batch)' methods: role: applies-method family: descriptive buildsFrom: [portfolio-sort, panel-regression] identification: descriptive contributionType: [new-fact, measurement] mechanisms: [limits-to-arbitrage] scope: region: US assetClass: US equities (CRSP common stocks) period: 2006-07..2020-12 frequency: monthly dataType: [market, accounting] granularity: [security] n: "554,253 stock-months (162 anomaly signals, Jul 2006-Dec 2020)" findings: - { ref: R1, outcome: cross-sectional anomaly long-short returns, metric: alpha, value: "0.14%/mo, t=2.87", direction: positive } - { ref: R2, outcome: net-of-fee long-short abnormal returns across 162 anomalies, metric: alpha, value: "0.04%/mo, t=0.84", direction: none, vsBenchmark: "below unadjusted full-sample mean of 0.14%/mo" } - { ref: R3, outcome: net-of-fee long-short abnormal returns across 162 anomalies, metric: alpha, value: "-0.01%/mo, t=-0.24", direction: none } - { ref: R4, outcome: cross-sectional anomaly long-short returns, metric: coefficient, value: "-0.0883, t=-1.96", direction: negative } - { ref: R5, outcome: cross-sectional anomaly long-short returns, metric: alpha, value: "before-fee L/S +0.36% (t=5.06); excl. high-fee +0.11% (t=1.39); net-of-fee -0.05% (t=-0.62)", direction: mixed, vsBenchmark: "net-of-fee vs. before-fee microcap L/S" } - { ref: R6, outcome: net-of-fee long-short abnormal returns across 162 anomalies, metric: alpha, value: "excl. high-fee -0.04% (t=-0.21); net-of-fee 0.02% (t=0.10)", direction: none } - { ref: R7, outcome: net-of-fee long-short abnormal returns across 162 anomalies, metric: alpha, value: "momentum -0.01% (t=-0.11); profitability 0.21% (t=0.59)", direction: none } - { ref: R8, outcome: cross-sectional anomaly long-short returns, metric: alpha, value: "CAPM L/S 0.45% (t=0.81); tail-risk L/S 0.43% (t=0.97)", direction: none } - { ref: R9, outcome: net-of-fee long-short abnormal returns across 162 anomalies, metric: alpha, value: "0.03%, t=0.47", direction: none, vsBenchmark: "vs. -0.24% (t=-2.92) in unadjusted Panel A" } resultType: overturns relatesTo: - { cite: 'Chen & Zimmermann (2021)', doi: '10.1561/104.00000112', relation: builds-on, note: 'Uses their 162 anomaly signals from openassetpricing.com as the universe of tested anomalies (p. 3648)' } - { cite: 'Drechsler & Drechsler (2021)', relation: contradicts, note: 'That paper finds positive net-of-fee returns on eight anomalies using lender-side fees; this paper uses buy-side fees and a longer, more recent sample and finds near-zero net-of-fee returns (pp. 3643, 3646)' } - { cite: 'Hou, Xue & Zhang (2020)', relation: tests, note: 'Tests their claim that anomaly returns are concentrated in microcaps; finds that even microcap anomaly returns disappear once borrow fees are accounted for (pp. 3642, 3668)' } - { cite: 'Nagel (2005)', doi: '10.1016/j.jfineco.2004.08.008', relation: builds-on, note: 'Limits-to-arbitrage framework connecting short-sale constraints to anomaly persistence (p. 3643)' } - { cite: 'Stambaugh, Yu & Yuan (2012)', doi: '10.1016/j.jfineco.2011.12.001', relation: builds-on, note: 'Framework connecting short-sale costs to anomaly persistence via sentiment (p. 3643)' } - { cite: 'Daniel, Grinblatt, Titman & Wermers (1997)', doi: '10.1111/j.1540-6261.1997.tb02724.x', relation: builds-on, note: 'Characteristics-matched DGTW benchmark used to compute abnormal returns throughout (p. 3654)' } openQuestions: - 'Why long-side investors continue to hold high-borrow-fee decile 1 stocks despite bearing negative expected returns; candidate explanations include index-fund tracking constraints, capital-gains tax consequences, and inability to identify high-fee stocks (pp. 3679-3680, 3692).' - 'Whether the results hold at daily or weekly strategy frequencies, which the paper leaves outside its scope because execution costs scale with trade frequency differently than borrow fees (p. 3644 fn. 4).' - 'Whether the causality runs primarily from mispricing to borrow fees or from borrow fees to the absence of short arbitrage; the paper notes that both directions likely operate simultaneously (pp. 3642-3643).' replicationCode: status: available licenceVerification: - source: Crossref REST API works/10.1111/jofi.13501 checked: 2026-05-31 by: paper-distiller (claude-sonnet-4-6) found: 'license[].content-version=vor, URL=http://creativecommons.org/licenses/by/4.0/, delay-in-days=0, start=2025-09-30' extraction: - by: paper-distiller (claude-sonnet-4-6) date: 2026-05-31 role: extracted note: Full text read (pp. 3639-3694, 12 tables, 12 figures); nine results extracted from the CC-BY PDF. Not human-verified. Not reproduced. Replication code is published as Supporting Information but has not been run here. - by: paper-verifier (claude-sonnet-4-6) date: 2026-05-31 role: verified note: Locators and reported magnitudes re-checked against the source PDF; verdict pass. - by: paper-distiller (claude-sonnet-4-6) date: 2026-06-01 role: extracted note: Augment pass. Added methods, scope, relatesTo, openQuestions, replicationCode, proposedVocab frontmatter blocks and three formal body sections (Theory / model, Method, Empirical specifications) with equations and panel-regression specifications transcribed from pp. 3654-3671 of the source PDF read this session. Core results table and Attribution preserved verbatim from the verified version. New sections are extracted, not yet re-verified. - by: paper-verifier (claude-sonnet-4-6) date: 2026-06-01 role: verified note: 'Locators and reported magnitudes re-checked against source PDF for all 9 rows; all confirmed correct. One fix applied: decile 2 fee-adjustment treatment corrected from "long-side" to "short-side" (full fee added), matching p. 3650 of the PDF. No em-dashes found; no colorful adjectives found.' - by: paper-distiller (claude-sonnet-4-6) date: 2026-06-03 role: extracted note: >- Added classification axes (identification, contributionType, mechanisms, introducesData, data-scope) from a fresh PDF read; existing results and sections unchanged. - by: paper-verifier (claude-sonnet-4-6) date: 2026-06-03 role: verified note: >- Classification axes (identification, contributionType, mechanisms, introducesData, data-scope) re-checked against the source PDF; all axes confirmed correct - no fixes required. - by: paper-distiller (claude-sonnet-4-6) date: 2026-06-04 role: extracted note: >- Added the effectiveness axis (findings[] per Core-results row, resultType) built from the page's already-verified Core-results table and relatesTo edges; existing results and sections unchanged. - by: paper-verifier (claude-sonnet-4-6) date: 2026-06-04 role: verified note: >- Effectiveness axis (findings[] values/direction, resultType) re-checked against the source PDF; all 9 values confirmed exact matches to Tables III, IV, V, VI, IX, XI, XII - no fixes required. rightsSignalConflict: false --- **What this is.** The paper's core results, datasets, identification strategy, and the estimating equations: enough to know what it found and how without reading all 56 pages. To replicate or extend it, read the original at [doi.org/10.1111/jofi.13501](https://doi.org/10.1111/jofi.13501). ## TL;DR Using 162 anomalies from Chen and Zimmermann (2021) and stock borrow fee data from Markit (July 2006 to December 2020), the paper shows that the average long-short abnormal return of 0.14%/month is entirely due to high-fee stocks (borrow fee greater than 1%/year, roughly 12% of stock-month observations). Once high-fee stocks are excluded, or once returns are adjusted for the borrow fee, the average long-short abnormal return collapses to 0.04% or -0.01%/month, respectively, neither significantly different from zero. The result holds across microcap stocks, the 20 anomalies with the highest fees, four factor-mimicking portfolios (momentum, profitability, investment, book-to-market), and five individually named anomalies. Portfolios sorted on theoretically grounded risk measures (CAPM beta, tail-risk beta) are unaffected, serving as a placebo. A short-interest-to-institutional-holdings ratio (from Compustat/13F) works as a publicly available proxy for borrow fees, eliminating the need for Markit data to test exploitability. ## Core results Magnitudes and significance are as reported; `\*`/`\*\*`/`\*\*\*` = 10%/5%/1%. Locators point into the source PDF. | # | Result | Locator | Magnitude | |---|---|---|---| | R1 | Average long-short **abnormal return across 162 anomalies is 0.14%/month before fees**, significantly positive | Table III Panel A, p. 3659 | Mean = 0.14%/mo, t-stat = 2.87\*\*\* | | R2 | **High-fee stocks drive the long-short return**: excluding stocks with borrow fee > 1%/yr, long-short abnormal return drops to 0.04% and is insignificant | Table III Panel B, p. 3659 | Mean = 0.04%/mo, t-stat = 0.84 | | R3 | **Fee-adjusted long-short return is near zero** (borrow fee added back to short-side returns for full sample) | Table III Panel C, p. 3659 | Mean = -0.01%/mo, t-stat = -0.24 | | R4 | **Unadjusted decile 1 abnormal returns are approximately linear in the borrow fee**, slope -0.088 (approx. -1/12 per 1 ppt fee) | Table V col. 1, p. 3671 | Slope = -0.0883, t-stat = -1.96\* | | R5 | **Microcap anomaly returns are also entirely due to high-fee stocks**: before fees decile 1 = -0.48%/mo (t = -2.92); excluding high-fee stocks decile 1 = +0.09% (t = 0.76); fee-adjusted = +0.08% (t = 0.50) | Table IV, p. 3669 | Before-fee L/S = +0.36% (t = 5.06); after drop = +0.11% (t = 1.39); net-of-fee = -0.05% (t = -0.62) | | R6 | **High-fee anomaly subset (20 anomalies, avg fee > 4%/yr)**: before-fee long-short = 0.41%/mo (t = 2.08); excluding high-fee stocks = -0.04%/mo; fee-adjusted long-short = 0.02%/mo (near zero, insignificant) | Table VI, p. 3673 | Exclud. high-fee L/S = -0.04% (t = -0.21); net-of-fee = 0.02% (t = 0.10) | | R7 | **Momentum and profitability factor long-short returns are eliminated by borrow fees**: momentum L/S drops from 0.21% to 0.03%/mo after excluding high-fee stocks, profitability from 0.61% to 0.09%/mo; net-of-fee momentum = -0.01%, profitability = 0.21%/mo (annualizes to 2.52%/yr, insignificant) | Table XI, p. 3688 | Momentum net-of-fee L/S: -0.01% (t = -0.11); profitability net-of-fee: 0.21% (t = 0.59) | | R8 | **CAPM-beta and tail-risk-beta sorted portfolios are unaffected** by borrow fee exclusion or adjustment (placebo): CAPM L/S net-of-fee = 0.45%/mo (t = 0.81), tail-risk L/S net-of-fee = 0.43%/mo (t = 0.97) | Table XII, p. 3690 | Net-of-fee CAPM L/S = 0.45%, tail-risk L/S = 0.43%; both insignificant | | R9 | **Short-interest-to-institutional-holdings ratio (Compustat/13F, no Markit needed) replicates the main result**: excluding stocks with SI/IO > 18% reduces decile 1 abnormal return by 0.27%/mo relative to Panel A | Table IX Panel D, p. 3682 | SI/IO exclusion decile 1: 0.03% (t = 0.47) vs. -0.24% (t = -2.92) in Panel A | **Overall (paper's conclusion).** Stock borrow fees function as a common limit to arbitrage that is sufficient to explain the persistence of anomaly returns for marginal investors. The average anomaly cannot be profitably exploited via long-short strategies once shorting costs are incorporated. The residual puzzle is why long-side investors continue to hold high-fee stocks despite bearing negative expected returns relative to low-fee benchmarks. ## Theory / model The paper has no original structural model. It is an applied empirical study operating in the limits-to-arbitrage tradition (Lee, Shleifer, and Thaler (1991); Nagel (2005); Stambaugh, Yu, and Yuan (2012)). The tested hypothesis is: > Stock borrow fees are a common, binding limit to arbitrage that prevents > exploitation of cross-sectional return anomalies and explains their > apparent out-of-sample persistence. **Conceptual identity: borrow fee as shadow dividend.** A short seller pays the daily borrow fee for every day a short position is open. A long-side investor whose shares are lent receives the fee less prime-broker intermediation spreads, but only on the fraction of shares actually borrowed. The fee is therefore a shadow dividend not recorded in CRSP stock returns. The paper's identification logic follows directly (pp. 3640-3641, 3650): $$ \begin{aligned} R^{\text{short,adj}} &= R_{\text{stock}} + f \\ R^{\text{long,adj}} &= R_{\text{stock}} + \text{utilization} \times (1 - \text{spread\_fraction}) \times f \\ &\approx R_{\text{stock}} + \text{utilization} \times 0.7 \times f \end{aligned} $$ - $$f$$ = indicative borrow fee (annualized, converted to monthly) - $$\text{utilization}$$ = shares on loan / lendable shares - D'Avolio (2002) estimates the spread fraction at approximately 0.3 In contrast to Drechsler and Drechsler (2021), who find positive net-of-fee returns on eight anomalies using lender-side fees, this paper uses buy-side fees over a longer and more recent sample and finds near-zero net-of-fee returns. **Identification design.** Two complementary approaches test whether anomaly returns survive after accounting for fees (p. 3640): 1. Exclude high-fee stocks: drop stock-month observations with indicative borrow fee > 1%/year from the sorted portfolios (without resorting). Approximately 12% of stock-months qualify as high-fee; 21% of decile 1 observations do. 2. Fee-adjust returns: add the full fee to returns for short-side portfolios (deciles 1 and 2); add $$\text{utilization} \times 0.7 \times f$$ to returns for long-side portfolios (deciles 3-10). Both approaches use a DGTW characteristics-matched benchmark that excludes high-fee stocks from the benchmark portfolios to avoid contaminating the abnormal-return calculation (p. 3654 fn. 16). **Placebo test.** Portfolios sorted by CAPM beta and tail-risk beta (Kelly and Jiang (2014)) are theoretically grounded risk measures, not behavioral anomalies. If borrow fees reflect arbitrage frictions specific to mispriced stocks, these sorted portfolios should be insensitive to borrow-fee adjustments. The insensitivity result (Table XII, p. 3690) provides placebo support. ## Method The paper applies `portfolio-sort` and `panel-regression` methods. There is no newly proposed estimator; the methodological contribution is the systematic application of buy-side borrow fees to a comprehensive, out-of-sample anomaly universe. **DGTW abnormal return construction (pp. 3654-3655).** For each stock $$i$$ and month $$t$$, the abnormal return is: $$ \text{DGTW\_ETB}_{i,t} = R_{i,t} - R_{\text{benchmark},i,t} $$ - $$R_{\text{benchmark},i,t}$$ is the equal-weighted return of the DGTW characteristics-matched portfolio, constructed excluding stocks with borrow fee > 1%/year (to prevent high-fee benchmark contamination). The benchmark portfolios match on market capitalization, book-to-market, and prior six-month momentum, following Daniel et al. (1997). **Portfolio-level aggregation.** The abnormal return on a sorted decile portfolio in month $$t$$ is the cross-sectional average of stock-level abnormal returns within that decile. For each anomaly, the time-series average is computed over the performance evaluation period (July 2006 to December 2020, 14.5 years). The cross-sectional mean across the 162 anomalies is the headline statistic (p. 3654). **Fee adjustment procedure (pp. 3650, 3666-3667).** The monthly fee is the simple average of daily indicative fees over the 21-trading-day return evaluation window. For decile 1 stocks (short side), the full fee is added to the stock return. For decile 3-10 stocks (long side, held or lent), the expected fee received is: $$ \text{fee\_received}_{i,t} = \text{utilization}_{i,t} \times 0.7 \times f_{i,t} $$ This is added to the stock return. Decile 2 uses the same adjustment as decile 1 in both the fee-exclusion analysis and the fee-adjustment analysis (i.e., the full fee is added to decile 2 stock returns, treating it as short-side). **Standard-error treatment.** All t-statistics on cross-sectional averages are computed using a panel regression in which the monthly portfolio return for each anomaly is regressed onto decile fixed effects; standard errors are double-clustered by anomaly and month. The estimate for each decile fixed effect is the average return on the corresponding decile with the appropriate t-statistic (pp. 3655-3656). ## Empirical specifications The paper's results come from three types of portfolio-performance constructions rather than a single OLS regression. Each is described below with the estimating equation. **Specification 1: Cross-sectional mean of decile abnormal returns (R1-R3, R5-R6, Table III p. 3659).** For each anomaly $$a$$, the time-series average abnormal return on decile $$d$$ is: $$ \mu_{a,d} = \frac{1}{T} \sum_{t=1}^{T} \text{DGTW\_ETB}_{a,d,t} $$ The cross-sectional mean across anomalies (the headline statistic) and the corresponding t-statistic are extracted from the panel regression: $$ \text{DGTW\_ETB}_{a,d,t} = \alpha_d + \epsilon_{a,d,t} $$ - LHS: monthly decile portfolio abnormal return for anomaly $$a$$, decile $$d$$, month $$t$$ - RHS: decile fixed effects $$\alpha_d$$ (one per decile 1-10) - SE: double-clustered by anomaly $$a$$ and month $$t$$ - Sample: 162 anomalies, July 2006 to December 2020, varying N per anomaly The long-short result is $$\alpha_1 - \alpha_{10}$$ (decile 1 minus decile 10, since anomaly signals are signed so decile 1 is the short side). The procedure is applied in three versions: (A) all stocks, no fee adjustment; (B) excluding high-fee stocks (fee > 1%/yr); (C) fee-adjusted returns. **Specification 2: Relation between anomaly returns and borrow fees (R4, Table V p. 3671).** For each anomaly, the average decile 1 borrow fee $$f_a$$ is regressed on the average abnormal return to show the approximately linear relationship: $$ \mu_{a,1} = \beta_0 + \beta_1 f_a + u_a $$ - LHS: time-series average abnormal return on decile 1 portfolio, anomaly $$a$$ - RHS: average indicative borrow fee for decile 1 stocks of anomaly $$a$$ at portfolio formation date - SE: double-clustered by anomaly and month (panel version with month controls) - Key result: $$\beta_1 = -0.0883$$ (t = -1.96*), approximately $$-1/12$$ The slope of approximately $$-1/12$$ means a 1 percentage-point increase in the annual fee corresponds to roughly $$-1/12$$ percentage points per month in abnormal return, consistent with complete fee absorption of the anomaly signal (p. 3671). **Specification 3: SI/IO exclusion as Markit substitute (R9, Table IX Panel D p. 3682).** The same Specification 1 panel regression is applied after excluding stock-months where short interest divided by institutional holdings (SI/IO, from Compustat monthly short interest and 13F filings) exceeds 18%: $$ \text{DGTW\_ETB}_{a,d,t} = \alpha_d + \epsilon_{a,d,t} \quad \text{[restricted sample]} $$ - Restriction: drop stock-months with $$(\text{short\_interest}_{i,t-1} / \text{inst\_holdings}_{i,t-1}) > 0.18$$ - Cutoff 18% chosen to match approximately 12% of stock-months excluded by fee > 1% cutoff - SE: double-clustered by anomaly and month - Key result: decile 1 $$\alpha$$ changes by +0.27%/mo relative to unadjusted baseline, decile 1 $$\alpha$$ = +0.03% (t = 0.47) vs. -0.24% (t = -2.92) with all stocks Robustness: microcap extension (all stocks, market cap below 20th percentile NYSE, Table IV p. 3669), which tests the claim of Hou, Xue, and Zhang (2020) that anomaly returns are concentrated in microcaps and finds that even microcap anomaly returns disappear once borrow fees are accounted for; 20 highest-fee anomalies (Table VI p. 3673); subsets by t-statistic, pre-sample Sharpe ratio, and publication venue (Table VII p. 3674); long-side investor perspective with varying intermediation fractions (Table VIII p. 3678); five specific anomalies (Table X p. 3685); four factor-based long-short portfolios (Table XI p. 3688). ## Datasets used | Dataset | Role in paper | Wiki page | |---|---|---| | Chen and Zimmermann (2021) anomaly signals (openassetpricing.com), Jan 2000 to Dec 2020; 202 anomalies, 162 retained | Anomaly signal construction; decile portfolio assignment | [Open Source Asset Pricing](/wiki/datasets/open-source-asset-pricing/) | | Markit Securities Finance Buy Side Analytics Data Feed, daily from Jun 28 2006 | Stock borrow fees (indicative fee = buy-side expected borrow cost); utilization | no page yet | | CRSP (via WRDS) common stocks, returns, delisting returns | Stock returns, market cap filters, sample construction | [WRDS / CRSP / Compustat](/wiki/commercial/wrds/) (licensed) | | Compustat (via WRDS) short interest + 13F institutional holdings | Proxy for borrow fee (SI/IO ratio) for researchers without Markit access | [WRDS / CRSP / Compustat](/wiki/commercial/wrds/) (licensed) | Sample: 554,253 stock-months (162 anomaly signals, Jul 2006 to Dec 2020), after dropping stocks below $1 price or $50 mn market cap and requiring at least 4 days of borrow fee observations per month. ## When to read the full paper Use the [original](https://doi.org/10.1111/jofi.13501) if you are: replicating (code in the journal's Supporting Information); extending the borrow fee adjustment methodology; examining the specific anomaly-by-anomaly results in the Internet Appendix; or auditing factor return attrition (Section VI). The locators above point to the exact tables. For "what did this paper find," the table above is the intended default. ## Attribution and rights Source: peer-reviewed, *The Journal of Finance* 80(6). This distillation was extracted by an LLM on 2026-05-31 and augmented on 2026-06-01; it is **not human-verified or independently reproduced**. CC BY 4.0 permits this adaptation; the verbatim PDF is not hosted in this batch but CC permits mirroring. > **Attribution (CC BY 4.0).** Muravyev, Dmitriy, Neil D. Pearson, and Joshua > M. Pollet. "Anomalies and Their Short-Sale Costs." *The Journal of Finance* > 80, no. 6 (December 2025): 3639-3694. DOI: 10.1111/jofi.13501. > Copyright 2025 The Author(s). Licensed under > [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). > This page is an **adaptation** by the Institute for Automated Research: > core results extracted and re-expressed; **changes were made**.