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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Explanations_for_anomalies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Explanations_for_anomalies"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Explanations for anomalies</span> </div> </a> <button aria-controls="toc-Explanations_for_anomalies-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Explanations for anomalies subsection</span> </button> <ul id="toc-Explanations_for_anomalies-sublist" class="vector-toc-list"> <li id="toc-Mispricing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mispricing"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Mispricing</span> </div> </a> <ul id="toc-Mispricing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unmeasured_risk" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Unmeasured_risk"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Unmeasured risk</span> </div> </a> <ul id="toc-Unmeasured_risk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limits_to_arbitrage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Limits_to_arbitrage"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Limits to arbitrage</span> </div> </a> <ul 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Financial market is predictability seems to be inconsistent with theories of asset prices</div> <p>A <b>market anomaly</b> in a <a href="/wiki/Financial_market" title="Financial market">financial market</a> is predictability that seems to be inconsistent with (typically risk-based) theories of asset prices.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Standard theories include the <a href="/wiki/Capital_asset_pricing_model" title="Capital asset pricing model">capital asset pricing model</a> and the <a href="/wiki/Fama%E2%80%93French_three-factor_model" title="Fama–French three-factor model">Fama-French Three Factor Model</a>, but a lack of agreement among academics about the proper theory leads many to refer to anomalies without a reference to a benchmark theory (Daniel and Hirschleifer 2015<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and Barberis 2018,<sup id="cite_ref-:1_3-0" class="reference"><a href="#cite_note-:1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> for example). Indeed, many academics simply refer to anomalies as "return predictors", avoiding the problem of defining a benchmark theory.<sup id="cite_ref-:2_4-0" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Academics have documented more than 150 return predictors (see <i><a class="mw-selflink-fragment" href="#List_of_anomalies_documented_in_academic_journals">List of Anomalies Documented in Academic Journals</a>).</i> These "anomalies", however, come with many caveats. Almost all documented anomalies focus on illiquid, small stocks.<sup id="cite_ref-:2_4-1" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Moreover, the studies do not account for trading costs. As a result, many anomalies do not offer profits, despite the presence of predictability.<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Additionally, return predictability declines substantially after the publication of a predictor, and thus may not offer profits in the future.<sup id="cite_ref-:2_4-2" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Finally, return predictability may be due to cross-sectional or time-variation in risk, and thus does not necessarily provide a good investment opportunity. Relatedly, return predictability by itself does not disprove the <a href="/wiki/Efficient_market_hypothesis" class="mw-redirect" title="Efficient market hypothesis">efficient market hypothesis</a>, as one needs to show predictability over and above that implied by a particular model of risk.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The four primary explanations for market anomalies are (1) mispricing, (2) unmeasured <a href="/wiki/Financial_risk" title="Financial risk">risk</a>, (3) <a href="/wiki/Limits_to_arbitrage" title="Limits to arbitrage">limits to arbitrage</a>, and (4) <a href="/wiki/Selection_bias" title="Selection bias">selection bias</a>.<sup id="cite_ref-:2_4-3" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Academics have not reached a consensus on the underlying cause, with prominent academics continuing to advocate for selection bias,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> mispricing,<sup id="cite_ref-:1_3-1" class="reference"><a href="#cite_note-:1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and risk-based theories.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Anomalies can be broadly categorized into time-series and cross-sectional anomalies. Time-series anomalies refer to predictability in the aggregate stock market, such as the often-discussed Cyclically Adjusted Price-Earnings (CAPE) predictor.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> These time-series predictors indicate times in which it is better to be invested in stocks vs a safe asset (such as Treasury bills). Cross-sectional anomalies refer to the predictable out-performance of particular stocks relative to others. For example, the well-known size anomaly<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> refers to the fact that stocks with lower market capitalization tend to out-perform stocks with higher market capitalization in the future. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Explanations_for_anomalies">Explanations for anomalies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=1" title="Edit section: Explanations for anomalies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Mispricing">Mispricing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=2" title="Edit section: Mispricing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many, if not most, of the papers which document anomalies attribute them to mispricing (Lakonishok, Shelifer, and Visny 1994,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> for example). The mispricing explanation is natural, as anomalies are by definition deviations from a benchmark theory of asset prices. "Mispricing" is then defined as the deviation relative to the benchmark. </p><p>The most common benchmark is the <a href="/wiki/Capital_asset_pricing_model" title="Capital asset pricing model">CAPM</a> (Capital-Asset-Pricing Model). The deviation from this theory is measured by a non-zero intercept in an estimated <a href="/wiki/Security_market_line" title="Security market line">security market line</a>. This intercept is commonly denoted by the Greek letter alpha: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(R_{t}-R_{f,t})=\alpha +\beta [E(R_{M,t}-R_{f,t})]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">[</mo> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(R_{t}-R_{f,t})=\alpha +\beta [E(R_{M,t}-R_{f,t})]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a5d48dd045358b359b74e6d0e1a92a7af8974e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:38.557ex; height:3.009ex;" alt="{\displaystyle E(R_{t}-R_{f,t})=\alpha +\beta [E(R_{M,t}-R_{f,t})]\,}"></span> </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d65b678ee539ac36de96b554af181ac03b7f16a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.59ex; height:2.509ex;" alt="{\displaystyle R_{t}}"></span> is the return on the anomaly, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{f,t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{f,t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdc95985fcc3486d1190972a3557acd5f32f2504" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.951ex; height:2.843ex;" alt="{\displaystyle R_{f,t}}"></span> is the return on the risk-free rate, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> is the slope from regressing the anomaly's return on the market's return, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{M,t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{M,t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b088b44c5ae3d94eacfc3762878d1e4fafe618ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.774ex; height:2.843ex;" alt="{\displaystyle R_{M,t}}"></span> is the return on the "market", often proxied by the return on the <a href="/wiki/Center_for_Research_in_Security_Prices" title="Center for Research in Security Prices">CRSP</a> index (an index of all publicly traded U.S. stocks). </p><p>The mispricing explanations are often contentious within academic finance, as academics do not agree on the proper benchmark theory (see Unmeasured Risk, below). This disagreement is closely related to the "joint-hypothesis problem" of the <a href="/wiki/Efficient_market_hypothesis" class="mw-redirect" title="Efficient market hypothesis">efficient market hypothesis</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Unmeasured_risk">Unmeasured risk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=3" title="Edit section: Unmeasured risk"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Risk_factor_(finance)" title="Risk factor (finance)">Risk factor (finance)</a></div> <p>Among academics, a common response to claims of mispricing was the idea that the anomaly captures a dimension of risk that is missing from the benchmark theory. For example, the anomaly may generate expected returns beyond those measured using the CAPM regression because the time-series of its returns are correlated with labor income, which is not captured by standard proxies for the market return.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Perhaps the most well-known example of this unmeasured risk explanation is found in Fama and French's seminar paper on their 3-factor model: "if assets are priced rationally, variables that are related to average returns ... ..., must proxy for sensitivity to common (shared and thus undiversifiable) risk factors in returns. The [3-factor model] time-series regressions give direct evidence on this issue."<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>The unmeasured risk explanation is closely related to the shortcomings of the CAPM as a theory of risk as well as shortcomings of empirical tests of the CAPM and related models. Perhaps the most common critique of the CAPM is that it is derived in a single period setting, and thus is missing dynamic features like periods of high uncertainty. In a more general setting, the CAPM typically implies multiple risk factors, as shown in <a href="/wiki/Intertemporal_CAPM" title="Intertemporal CAPM">Merton's Intertemporal CAPM</a> theory. Moreover, the ICAPM generally implies the expected returns vary over time, and thus time-series predictability is not clear evidence of mispricing. Indeed, since the CAPM cannot at all capture dynamic expected returns, evidence of time-series predictability is less often regarded as mispricing as compared to cross-sectional predictability. </p><p>Empirical shortcomings primarily regard the difficulty in measuring wealth or <a href="/wiki/Marginal_utility" title="Marginal utility">marginal utility</a>. Theoretically, wealth includes not only stock market wealth, but also non-tradable wealth like private assets and future labor income. In the <a href="/wiki/Consumption-based_capital_asset_pricing_model" title="Consumption-based capital asset pricing model">consumption CAPM</a>, (which is theoretically equivalent to Merton's ICAPM), the proper proxy for wealth is consumption, which is difficult to measure (Savov 2011,<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> for example). </p><p>Despite the theoretical soundness of the unmeasured risk explanation, there is little consensus among academics about the proper risk model over and above the CAPM. Propositions include the well-known Fama-French 3-Factor Model, Fama-French-Carhart 4-factor model, Fama-French 5-factor model, and Stambaugh and Yuan's 4-factor model.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> These models are all empirically-oriented, rather than derived from a formal theory of equilibrium like Merton's ICAPM. </p> <div class="mw-heading mw-heading3"><h3 id="Limits_to_arbitrage">Limits to arbitrage</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=4" title="Edit section: Limits to arbitrage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Limits_to_arbitrage" title="Limits to arbitrage">Limits to arbitrage</a></div> <p>Anomalies are almost always documented using closing prices from the CRSP dataset. These prices do not reflect trading costs, which can prevent arbitrage and thus the elimination predictability. Moreover, almost all anomalies are documented using equally-weighted portfolios,<sup id="cite_ref-:2_4-4" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and thus require trading of illiquid (costly-to-trade) stocks. </p><p>The limits to arbitrage explanation can be thought of as a refinement of the mispricing framework. A return pattern only offers profits if the returns it offers survives trading costs, and thus should not be considered mispricing unless trading costs are accounted for. </p><p>A large literature documents that trading costs greatly reduce anomaly returns. This literature goes back to Stoll and Whaley (1983) and Ball, Kothari, and Shanken (1995).<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> A recent paper that studies dozens of anomalies finds that trading costs have a massive effect on the average anomaly (Novy-Marx and Velikov 2015).<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Selection_bias">Selection bias</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=5" title="Edit section: Selection bias"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Selection_bias" title="Selection bias">Selection bias</a></div> <p>The documented anomalies are likely the best performers from a much larger set of potential return predictors. This selection creates a bias and implies that estimates of the profitability of anomalies is overstated. This explanation for anomalies is also known as data snooping, p-hacking, data mining, and <a href="/wiki/Data_dredging" title="Data dredging">data dredging</a>, and is closely related to the <a href="/wiki/Multiple_comparisons_problem" title="Multiple comparisons problem">multiple comparisons problem</a>. Concerns about selection bias in anomalies goes back at least to Jensen and Bennington (1970).<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Most research on selection bias in market anomalies focuses on particular subsets of predictors. For example, Sullivan, Timmermann, and White (2001) show that calendar-based anomalies are no longer significant after adjusting for selection bias.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> A recent meta-analysis of the size premium shows that the reported estimates of the size premium are exaggerated twofold because of selection bias.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Research on selection bias for anomalies more generally is relatively limited and inconclusive. McLean and Pontiff (2016) use an out-of-sample test to show that selection bias accounts for at most 26% of the typical anomaly's mean return during the sample period of the original publication. To show this, they replicate almost 100 anomalies, and show that the average anomaly's return is only 26% smaller in the few years immediately after the end of the original samples. As some of this decline may be due to investor learning effects, the 26% is an upper bound.<sup id="cite_ref-:2_4-5" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In contrast, Harvey, Liu, and Zhu (2016) adapt multiple testing adjustments from statistics such as the <a href="/wiki/False_discovery_rate" title="False discovery rate">False Discovery Rate</a> to asset pricing "factors". They refer to a factor as any variable that helps explain the cross-section of expected returns, and thus include many anomalies in their study. They find that multiple-testing statistics imply that factors with t-stats < 3.0 should not be considered statistically significant, and conclude that most published findings are likely false.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="List_of_anomalies_documented_in_academic_journals">List of anomalies documented in academic journals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=6" title="Edit section: List of anomalies documented in academic journals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <b>small firm effect</b> proposes that small companies outperform larger ones. It has been debated in academic journals as to whether the effect is real or arises due to certain systemic errors.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>It is related to the <a href="/wiki/Neglected_firm_effect" title="Neglected firm effect">neglected firm effect</a>. </p> <table class="wikitable sortable"> <tbody><tr> <th>Description</th> <th>Author(s)</th> <th>Year</th> <th>Journal</th> <th>Broad Category </th></tr> <tr> <td>Change in capital investment, industry adjusted</td> <td>Abarbanell and Bushee</td> <td>1998</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Gross Margin growth over sales growth</td> <td>Abarbanell and Bushee</td> <td>1998</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Proxy Fights</td> <td>Ikenberry and Lakonishok</td> <td>1993</td> <td>Journal of Business</td> <td>Cross-Sectional </td></tr> <tr> <td>Sales growth over inventory growth</td> <td>Abarbanell and Bushee</td> <td>1998</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Sales growth over overhead growth</td> <td>Abarbanell and Bushee</td> <td>1998</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Operating Cash flows to price</td> <td>Desai, Rajgopal, and Benkatachalam</td> <td>2004</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Earnings Forecast</td> <td>Elgers, Lo, and Pfeiffer</td> <td>2001</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Growth in Long term net operating assets</td> <td>Fairfield, Whisenant and Yohn</td> <td>2003</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Earnings Surprise</td> <td>Foster, Olsen and Shevliln</td> <td>1984</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Percent Operating Accruals</td> <td>Hafzalla, Lundholm, and Van Winkle</td> <td>2011</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Percent Total Accruals</td> <td>Hafzalla, Lundholm, and Van Winkle</td> <td>2011</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Real dirty surplus</td> <td>Landsman et al.</td> <td>2011</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Taxable income to income</td> <td>Lev and Nissim</td> <td>2004</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Piotroski F-score</td> <td>Piotroski</td> <td>2000</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Accruals</td> <td>Sloan</td> <td>1996</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Asset Turnover</td> <td>Soliman</td> <td>2008</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in Asset Turnover</td> <td>Soliman</td> <td>2008</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in Noncurrent Operating Assets</td> <td>Soliman</td> <td>2008</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in Net Working Capital</td> <td>Soliman</td> <td>2008</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in Profit Margin</td> <td>Soliman</td> <td>2008</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Profit Margin</td> <td>Soliman</td> <td>2008</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Abnormal Accruals</td> <td>Xie</td> <td>2001</td> <td>The Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Earnings Consistency</td> <td>Alwathainani</td> <td>2009</td> <td>British Accounting Review</td> <td>Cross-Sectional </td></tr> <tr> <td>Deferred Revenue</td> <td>Prakash and Sinha</td> <td>2012</td> <td>Contemporary Accounting Research</td> <td>Cross-Sectional </td></tr> <tr> <td>Sales-to-price</td> <td>Barbee, Mukherji, and Raines</td> <td>1996</td> <td>Financial Analysts' Journal</td> <td>Cross-Sectional </td></tr> <tr> <td>earnings / assets</td> <td>Balakrishnan, Bartov, and Faurel</td> <td>2010</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Net debt financing</td> <td>Bradshaw, Richardson, and Sloan</td> <td>2006</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Net equity financing</td> <td>Bradshaw, Richardson, and Sloan</td> <td>2006</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Net external financing</td> <td>Bradshaw, Richardson, and Sloan</td> <td>2006</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Net Operating Assets</td> <td>Hirschleifer, Hou Teoh, and Zhang</td> <td>2004</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in depreciation to gross PPE</td> <td>Holthausen Larcker</td> <td>1992</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in equity to assets</td> <td>Richardson, Sloan Soliman and Tuna</td> <td>2005</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in current operating assets</td> <td>Richardson, Sloan Soliman and Tuna</td> <td>2005</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in current operating liabilities</td> <td>Richardson, Sloan Soliman and Tuna</td> <td>2005</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in financial liabilities</td> <td>Richardson, Sloan Soliman and Tuna</td> <td>2005</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in long-term investment</td> <td>Richardson, Sloan Soliman and Tuna</td> <td>2005</td> <td>Journal of Accounting and Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Enterprise component of BM</td> <td>Penman, Richardson, and Tuna</td> <td>2007</td> <td>Journal of Accounting Research</td> <td>Cross-Sectional </td></tr> <tr> <td>Leverage component of BM</td> <td>Penman, Richardson, and Tuna</td> <td>2007</td> <td>Journal of Accounting Research</td> <td>Cross-Sectional </td></tr> <tr> <td>Net debt to price</td> <td>Penman, Richardson, and Tuna</td> <td>2007</td> <td>Journal of Accounting Research</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in Taxes</td> <td>Thomas and Zhang</td> <td>2011</td> <td>Journal of Accounting Research</td> <td>Cross-Sectional </td></tr> <tr> <td>IPO and no R&D spending</td> <td>Gou, Lev, and Shi</td> <td>2006</td> <td>Journal of Business, Finance and Accounting</td> <td>Cross-Sectional </td></tr> <tr> <td>Change in capex (two years)</td> <td>Anderson and Garcia-Feijoo</td> <td>2006</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Idiosyncratic risk</td> <td>Ang, Hodrick, Xing, and Zhang</td> <td>2006</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Junk Stock Momentum</td> <td>Avramov, Chordia, Jostova, and Philipov</td> <td>2007</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Maximum return over month</td> <td>Bali, Cakici, and Whitelaw</td> <td>2010</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Consensus Recommendation</td> <td>Barber, Lehavy, McNichols, and Trueman</td> <td>2001</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Down forecast EPS</td> <td>Barber, Lehavy, McNichols, and Trueman</td> <td>2001</td> <td>Journal of Finance</td> 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Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Long-run reversal</td> <td>De Bondt and Thaler</td> <td>1985</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Exchange Switch</td> <td>Dharan Ikenberry</td> <td>1995</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Credit Rating Downgrade</td> <td>Dichev Piotroski</td> <td>2001</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>EPS Forecast Dispersion</td> <td>Diether et al.</td> <td>2002</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Unexpected R&D increase</td> <td>Eberhart et al.</td> <td>2004</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Organizational Capital</td> <td>Eisfeldt and Papanikolaou</td> <td>2013</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Pension Funding Status</td> <td>Franzoni and Martin</td> <td>2006</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> 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<td>2005</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Dividend Yield</td> <td>Naranjo et al.</td> <td>1998</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Share issuance (1 year)</td> <td>Pontiff and Woodgate</td> <td>2008</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Initial Public Offerings</td> <td>Ritter</td> <td>1991</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Firm Age - Momentum</td> <td>Zhang</td> <td>2004</td> <td>Journal of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Book to market</td> <td>Stattman</td> <td>1980</td> <td>The Chicago MBA</td> <td>Cross-Sectional </td></tr> <tr> <td>Bid-ask spread</td> <td>Amihud and Mendelsohn</td> <td>1986</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Institutional Ownership for stocks with high short interest</td> <td>Asquith, Pathak, and Ritter</td> <td>2005</td> <td>Journal of 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Momentum</td> <td>Grinblatt Moskowitz</td> <td>1999</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Dividends</td> <td>Hartzmark Salomon</td> <td>2013</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>net income / book equity</td> <td>Haugen and Baker</td> <td>1996</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Cash-flow variance</td> <td>Haugen and Baker</td> <td>1996</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Volume to market equity</td> <td>Haugen and Baker</td> <td>1996</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Volume Trend</td> <td>Haugen and Baker</td> <td>1996</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> <td>Return Seasonality</td> <td>Heston and Sadka</td> <td>2008</td> <td>Journal of Financial Economics</td> <td>Cross-Sectional </td></tr> <tr> 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<td>Cross-Sectional </td></tr> <tr> <td>Mohanram G-score</td> <td>Mohanram</td> <td>2005</td> <td>Review of Accounting Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Order backlog</td> <td>Rajgopal, Shevlin and Venkatachalam</td> <td>2003</td> <td>Review of Accounting Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Inventory Growth</td> <td>Thomas and Zhang</td> <td>2002</td> <td>Review of Accounting Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Operating Leverage</td> <td>Novy-Marx</td> <td>2010</td> <td>Review of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Decline in Analyst Coverage</td> <td>Scherbina</td> <td>2008</td> <td>Review of Finance</td> <td>Cross-Sectional </td></tr> <tr> <td>Earnings surprise of big firms</td> <td>Hou</td> <td>2007</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Industry return of big firms</td> <td>Hou</td> <td>2007</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Price delay</td> <td>Hou and Moskowitz</td> <td>2005</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Tail risk beta</td> <td>Kelly and Jiang</td> <td>2014</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Kaplan Zingales index</td> <td>Lamont, Polk, and Saa-Requejo</td> <td>2001</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Growth in advertising expenses</td> <td>Lou</td> <td>2014</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Composite debt issuance</td> <td>Lyandres, Sun and Zhang</td> <td>2008</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Real estate holdings</td> <td>Tuzel</td> <td>2010</td> <td>Review of Financial Studies</td> <td>Cross-Sectional </td></tr> <tr> <td>Book-to-market and accruals</td> <td>Bartov and Kim</td> <td>2004</td> <td>Review of Quantitative Finance and Accounting</td> <td>Cross-Sectional </td></tr> <tr> <td>Weekend Effect</td> <td>Smirlock and Starks</td> <td>1986</td> <td>Journal of Financial Economics</td> <td>Time-Series </td></tr> <tr> <td>January Effect</td> <td>Keims</td> <td>1985</td> <td>Journal of Financial Economics</td> <td>Time-Series </td></tr> <tr> <td>Turn of the Month Effect</td> <td>Agrawal and Tandon</td> <td>1994</td> <td>Journal of International Money and Finance</td> <td>Time-Series </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Neglected_firm_effect" title="Neglected firm effect">Neglected firm effect</a></li> <li><a href="/wiki/Low-volatility_anomaly" title="Low-volatility anomaly">Low-volatility anomaly</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Market_anomaly&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output 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title="Template talk:Financial markets navigation"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Financial_markets_navigation" title="Special:EditPage/Template:Financial markets navigation"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Financial_markets" style="font-size:114%;margin:0 4em"><a href="/wiki/Financial_market" title="Financial market">Financial markets</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <a href="/wiki/Capital_market" title="Capital market">markets</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Primary_market" title="Primary market">Primary market</a></li> <li><a href="/wiki/Secondary_market" title="Secondary market">Secondary market</a></li> <li><a href="/wiki/Third_market" title="Third market">Third market</a></li> <li><a href="/wiki/Fourth_market" title="Fourth market">Fourth market</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <a href="/wiki/Stock" title="Stock">stocks</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Common_stock" title="Common stock">Common stock</a></li> <li><a href="/wiki/Golden_share" title="Golden share">Golden share</a></li> <li><a href="/wiki/Preferred_stock" title="Preferred stock">Preferred stock</a></li> <li><a href="/wiki/Restricted_stock" title="Restricted stock">Restricted stock</a></li> <li><a href="/wiki/Tracking_stock" title="Tracking stock">Tracking stock</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Share_capital" title="Share capital">Share capital</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Authorised_capital" title="Authorised capital">Authorised capital</a></li> <li><a href="/wiki/Issued_shares" title="Issued shares">Issued shares</a></li> <li><a href="/wiki/Shares_outstanding" title="Shares outstanding">Shares outstanding</a></li> <li><a href="/wiki/Treasury_stock" title="Treasury stock">Treasury stock</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Participants</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Broker" title="Broker">Broker</a> <ul><li><a href="/wiki/Floor_broker" title="Floor broker">Floor broker</a></li> <li><a href="/wiki/Inter-dealer_broker" title="Inter-dealer broker">Inter-dealer broker</a></li></ul></li> <li><a href="/wiki/Broker-dealer" title="Broker-dealer">Broker-dealer</a></li> <li><a href="/wiki/Market_maker" title="Market maker">Market maker</a></li> <li><a href="/wiki/Trader_(finance)" title="Trader (finance)">Trader</a> <ul><li><a href="/wiki/Floor_trader" title="Floor trader">Floor trader</a></li> <li><a href="/wiki/Proprietary_trading" title="Proprietary trading">Proprietary trader</a></li></ul></li> <li><a href="/wiki/Quantitative_analyst" class="mw-redirect" title="Quantitative analyst">Quantitative analyst</a></li> <li><a href="/wiki/Investor" title="Investor">Investor</a></li> <li><a href="/wiki/Hedge_(finance)" title="Hedge (finance)">Hedger</a></li> <li><a href="/wiki/Speculator" class="mw-redirect" title="Speculator">Speculator</a></li> <li><a href="/wiki/Arbitrage" title="Arbitrage">Arbitrager</a> <ul><li><a href="/wiki/Scalping_(trading)" title="Scalping (trading)">Scalper</a></li></ul></li> <li><a href="/wiki/Financial_regulation" title="Financial regulation">Regulator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Trading venues</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Exchange_(organized_market)" title="Exchange (organized market)">Exchange</a> <ul><li><a href="/wiki/List_of_stock_exchanges" class="mw-redirect" title="List of stock exchanges">List of stock exchanges</a></li> <li><a href="/wiki/List_of_stock_exchange_trading_hours" class="mw-redirect" title="List of stock exchange trading hours">Trading hours</a></li></ul></li> <li><a href="/wiki/Over-the-counter_(finance)" title="Over-the-counter (finance)">Over-the-counter</a> (off-exchange)</li> <li><a href="/wiki/Alternative_trading_system" title="Alternative trading system">Alternative trading system</a> (ATS)</li> <li><a href="/wiki/Multilateral_trading_facility" title="Multilateral trading facility">Multilateral trading facility</a> (MTF)</li> <li><a href="/wiki/Electronic_communication_network" title="Electronic communication network">Electronic communication network</a> (ECN)</li> <li><a href="/wiki/Direct_market_access" title="Direct market access">Direct market access</a> (DMA)</li> <li><a href="/wiki/Straight-through_processing" title="Straight-through processing">Straight-through processing</a> (STP)</li> <li><a href="/wiki/Dark_pool" title="Dark pool">Dark pool</a> (private exchange)</li> <li><a href="/wiki/Crossing_network" title="Crossing network">Crossing network</a></li> <li><a href="/wiki/Foreign_exchange_aggregator" title="Foreign exchange aggregator">Liquidity aggregator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Stock_valuation" title="Stock valuation">Stock valuation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alpha_(finance)" title="Alpha (finance)">Alpha</a></li> <li><a href="/wiki/Arbitrage_pricing_theory" title="Arbitrage pricing theory">Arbitrage pricing theory</a> (APT)</li> <li><a href="/wiki/Beta_(finance)" title="Beta (finance)">Beta</a></li> <li><a href="/wiki/Buffett_indicator" title="Buffett indicator">Buffett indicator</a> (Cap-to-GDP)</li> <li><a href="/wiki/Book_value" title="Book value">Book value</a> (BV)</li> <li><a href="/wiki/Capital_asset_pricing_model" title="Capital asset pricing model">Capital asset pricing model</a> (CAPM)</li> <li><a href="/wiki/Capital_market_line" title="Capital market line">Capital market line</a> (CML)</li> <li><a href="/wiki/Dividend_discount_model" title="Dividend discount model">Dividend discount model</a> (DDM)</li> <li><a href="/wiki/Dividend_yield" title="Dividend yield">Dividend yield</a></li> <li><a href="/wiki/Earnings_yield" title="Earnings yield">Earnings yield</a></li> <li><a href="/wiki/EV/EBITDA" class="mw-redirect" title="EV/EBITDA">EV/EBITDA</a></li> <li><a href="/wiki/Fed_model" title="Fed model">Fed model</a></li> <li><a href="/wiki/Net_asset_value" title="Net asset value">Net asset value</a> (NAV)</li> <li><a href="/wiki/Security_characteristic_line" title="Security characteristic line">Security characteristic line</a></li> <li><a href="/wiki/Security_market_line" title="Security market line">Security market line</a> (SML)</li> <li><a href="/wiki/T-model" title="T-model">T-model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Trading theories<br /> and <a href="/wiki/Trading_strategy" title="Trading strategy">strategies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithmic_trading" title="Algorithmic trading">Algorithmic trading</a></li> <li><a href="/wiki/Buy_and_hold" title="Buy and hold">Buy and hold</a></li> <li><a href="/wiki/Contrarian_investing" title="Contrarian investing">Contrarian investing</a></li> <li><a href="/wiki/Dollar_cost_averaging" title="Dollar cost averaging">Dollar cost averaging</a></li> <li><a href="/wiki/Efficient-market_hypothesis" title="Efficient-market hypothesis">Efficient-market hypothesis</a> (EMH)</li> <li><a href="/wiki/Fundamental_analysis" title="Fundamental analysis">Fundamental analysis</a></li> <li><a href="/wiki/Growth_stock" title="Growth stock">Growth stock</a></li> <li><a href="/wiki/Market_timing" title="Market timing">Market timing</a></li> <li><a href="/wiki/Modern_portfolio_theory" title="Modern portfolio theory">Modern portfolio theory</a> (MPT)</li> <li><a href="/wiki/Momentum_investing" title="Momentum investing">Momentum investing</a></li> <li><a href="/wiki/Mosaic_theory_(investments)" title="Mosaic theory (investments)">Mosaic theory</a></li> <li><a href="/wiki/Pairs_trade" title="Pairs trade">Pairs trade</a></li> <li><a href="/wiki/Post-modern_portfolio_theory" title="Post-modern portfolio theory">Post-modern portfolio theory</a> (PMPT)</li> <li><a href="/wiki/Random_walk_hypothesis" title="Random walk hypothesis">Random walk hypothesis</a> (RMH)</li> <li><a href="/wiki/Sector_rotation" title="Sector rotation">Sector rotation</a></li> <li><a href="/wiki/Style_investing" title="Style investing">Style investing</a></li> <li><a href="/wiki/Swing_trading" title="Swing trading">Swing trading</a></li> <li><a href="/wiki/Technical_analysis" title="Technical analysis">Technical analysis</a></li> <li><a href="/wiki/Trend_following" title="Trend following">Trend following</a></li> <li><a href="/wiki/Value_averaging" title="Value averaging">Value averaging</a></li> <li><a href="/wiki/Value_investing" title="Value investing">Value investing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related terms</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bid%E2%80%93ask_spread" title="Bid–ask spread">Bid–ask spread</a></li> <li><a href="/wiki/Block_trade" title="Block trade">Block trade</a></li> <li><a href="/wiki/Cross_listing" title="Cross listing">Cross listing</a></li> <li><a href="/wiki/Dividend" title="Dividend">Dividend</a></li> <li><a href="/wiki/Dual-listed_company" title="Dual-listed company">Dual-listed company</a></li> <li><a href="/wiki/DuPont_analysis" title="DuPont analysis">DuPont analysis</a></li> <li><a href="/wiki/Efficient_frontier" title="Efficient frontier">Efficient frontier</a></li> <li><a href="/wiki/Financial_law" title="Financial law">Financial law</a></li> <li><a href="/wiki/Flight-to-quality" title="Flight-to-quality">Flight-to-quality</a></li> <li><a href="/wiki/Government_bond" title="Government bond">Government bond</a></li> <li><a href="/wiki/Greenspan_put" title="Greenspan put">Greenspan put</a></li> <li><a href="/wiki/Haircut_(finance)" title="Haircut (finance)">Haircut</a></li> <li><a href="/wiki/Initial_public_offering" title="Initial public offering">Initial public offering</a> (IPO)</li> <li><a href="/wiki/Long_(finance)" title="Long (finance)">Long</a></li> <li><a href="/wiki/Mandatory_offer" title="Mandatory offer">Mandatory offer</a></li> <li><a href="/wiki/Margin_(finance)" title="Margin (finance)">Margin</a></li> <li><a class="mw-selflink selflink">Market anomaly</a></li> <li><a href="/wiki/Market_capitalization" title="Market capitalization">Market capitalization</a></li> <li><a href="/wiki/Market_depth" title="Market depth">Market depth</a></li> <li><a href="/wiki/Market_manipulation" title="Market manipulation">Market manipulation</a></li> <li><a href="/wiki/Market_trend" title="Market trend">Market trend</a></li> <li><a href="/wiki/Mean_reversion_(finance)" title="Mean reversion (finance)">Mean reversion</a></li> <li><a href="/wiki/Momentum_(finance)" title="Momentum (finance)">Momentum</a></li> <li><a href="/wiki/Open_outcry" title="Open outcry">Open outcry</a></li> <li><a href="/wiki/Order_book" title="Order book">Order book</a></li> <li><a href="/wiki/Position_(finance)" title="Position (finance)">Position</a></li> <li><a href="/wiki/Public_float" title="Public float">Public float</a></li> <li><a href="/wiki/Public_offering" title="Public offering">Public offering</a></li> <li><a href="/wiki/Rally_(stock_market)" title="Rally (stock market)">Rally</a></li> <li><a href="/wiki/Returns-based_style_analysis" title="Returns-based style analysis">Returns-based style analysis</a></li> <li><a href="/wiki/Reverse_stock_split" title="Reverse stock split">Reverse stock split</a></li> <li><a href="/wiki/Share_repurchase" title="Share repurchase">Share repurchase</a></li> <li><a href="/wiki/Short_(finance)" title="Short (finance)">Short selling</a></li> <li><a href="/wiki/Short_squeeze" title="Short squeeze">Short squeeze</a></li> <li><a href="/wiki/Slippage_(finance)" title="Slippage (finance)">Slippage</a></li> <li><a href="/wiki/Speculation" title="Speculation">Speculation</a></li> <li><a href="/wiki/Squeeze-out" title="Squeeze-out">Squeeze-out</a></li> <li><a href="/wiki/Stock_dilution" title="Stock dilution">Stock dilution</a></li> <li><a href="/wiki/Stock_exchange" title="Stock exchange">Stock exchange</a></li> <li><a href="/wiki/Stock_market_index" title="Stock market index">Stock market index</a></li> <li><a href="/wiki/Stock_split" title="Stock split">Stock split</a></li> <li><a href="/wiki/Stock_swap" title="Stock swap">Stock swap</a></li> <li><a href="/wiki/Trade_(financial_instrument)" class="mw-redirect" title="Trade (financial instrument)">Trade</a></li> <li><a href="/wiki/Tender_offer" title="Tender offer">Tender offer</a></li> <li><a href="/wiki/Uptick_rule" title="Uptick rule">Uptick rule</a></li> <li><a href="/wiki/Volatility_(finance)" title="Volatility (finance)">Volatility</a></li> <li><a href="/wiki/Voting_interest" title="Voting interest">Voting interest</a></li> <li><a href="/wiki/Yield_(finance)" title="Yield (finance)">Yield</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img 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