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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" 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">Investment portfolio which occupies the "efficient" parts of the risk-return spectrum</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">This article is about a financial mathematical concept. For other frontiers described as efficient, see <a href="/wiki/Production_possibilities_frontier" class="mw-redirect" title="Production possibilities frontier">Production possibilities frontier</a> and <a href="/wiki/Pareto_frontier" class="mw-redirect" title="Pareto frontier">Pareto frontier</a>.</div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:Markowitz_frontier.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e1/Markowitz_frontier.jpg" decoding="async" width="434" height="239" class="mw-file-element" data-file-width="434" data-file-height="239" /></a><figcaption>Efficient Frontier. The <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a> is sometimes referred to as the "Markowitz bullet", and its upward sloped portion is the efficient frontier if no risk-free asset is available. With a risk-free asset, the straight <a href="/wiki/Capital_allocation_line" title="Capital allocation line">capital allocation line</a> is the efficient frontier.</figcaption></figure> <p>In <a href="/wiki/Modern_portfolio_theory" title="Modern portfolio theory">modern portfolio theory</a>, the <b>efficient frontier</b> (or <b>portfolio frontier</b>) is an investment <a href="/wiki/Portfolio_(finance)" title="Portfolio (finance)">portfolio</a> which occupies the "efficient" parts of the <a href="/wiki/Risk%E2%80%93return_spectrum" title="Risk–return spectrum">risk–return spectrum</a>. Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected <a href="/wiki/Return_(finance)" class="mw-redirect" title="Return (finance)">return</a> but with the same <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> of return (i.e., the risk).<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> The efficient frontier was first formulated by <a href="/wiki/Harry_Markowitz" title="Harry Markowitz">Harry Markowitz</a> in 1952;<sup id="cite_ref-markowitz1952_2-0" class="reference"><a href="#cite_note-markowitz1952-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> see <a href="/wiki/Markowitz_model" title="Markowitz model">Markowitz model</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efficient_frontier&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CAPM2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/CAPM2.png/350px-CAPM2.png" decoding="async" width="350" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/CAPM2.png/525px-CAPM2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/9/95/CAPM2.png 2x" data-file-width="641" data-file-height="393" /></a><figcaption><a href="/wiki/Parametric_plot" class="mw-redirect" title="Parametric plot">Parametric plot</a> (as a function of weights <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>) of the expected return and the expected risk for different correlations. The efficient frontier is the upper part of the corresponding curves.</figcaption></figure> <p>A combination of assets, i.e. a portfolio, is referred to as "efficient" if it has the best possible <a href="/wiki/Expected_value" title="Expected value">expected</a> level of return for its level of <a href="/wiki/Financial_risk" title="Financial risk">risk</a> (which is represented by the standard deviation of the portfolio's return).<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Here, every possible combination of risky assets can be plotted in risk–expected return space, and the collection of all such possible portfolios defines a region in this space. In the absence of the opportunity to hold a <a href="/wiki/Risk-free_interest_rate" class="mw-redirect" title="Risk-free interest rate">risk-free asset</a>, this region is the opportunity set (the <a href="/wiki/Feasible_set" class="mw-redirect" title="Feasible set">feasible set</a>). The positively sloped (upward-sloped) top boundary of this region is a portion of a <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a>,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and is called the "efficient frontier". </p><p>If a risk-free asset is also available, the opportunity set is larger, and its upper boundary, the efficient frontier, is a straight line segment emanating from the vertical axis at the value of the risk-free asset's return and tangent to the risky-assets-only opportunity set. All portfolios between the risk-free asset and the tangency portfolio are portfolios composed of risk-free assets and the tangency portfolio, while all portfolios on the linear frontier above and to the right of the tangency portfolio are generated by borrowing at the risk-free rate and investing the proceeds into the tangency portfolio. </p><p>Among certain universes of assets, academics have found that the efficient frontier (the Markowitz model, more broadly) has been susceptible to issues such as model instability where, for example, the reference assets have a high degree of correlation.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Industry_usage">Industry usage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Efficient_frontier&action=edit&section=2" title="Edit section: Industry usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concept, construction and interpretation of the efficient frontier is also used by financial professionals and practitioners. Some documented uses of the efficient frontier are: </p> <ul><li><a href="/wiki/Financial_advisors" class="mw-redirect" title="Financial advisors">Financial advisors</a> when profiling their clients and benchmarking their clients’ investments<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></li> <li><a href="/wiki/Investment_managers" class="mw-redirect" title="Investment managers">Investment managers</a> when building a model portfolio tailored to a given level of risk tolerance<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></li> <li><a href="/wiki/Institutional_investors" class="mw-redirect" title="Institutional investors">Institutional investors</a> when deciding how to allocate capital across international <a href="/wiki/Stock_markets" class="mw-redirect" title="Stock markets">stock markets</a><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></li></ul> <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=Efficient_frontier&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Markowitz_model" title="Markowitz model">Markowitz model</a></li> <li><a href="/wiki/Modern_portfolio_theory" title="Modern portfolio theory">Modern portfolio theory</a></li> <li><a href="/wiki/Critical_line_method" class="mw-redirect" title="Critical line method">Critical line method</a>, an optimization algorithm developed by Markowitz for this problem</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=Efficient_frontier&action=edit&section=4" 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"><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 .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration 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.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.nasdaq.com/investing/glossary/m/markowitz-efficient-frontier">"Markowitz efficient frontier"</a>. <i><a href="/wiki/NASDAQ" class="mw-redirect" title="NASDAQ">NASDAQ</a></i>. nasdaq.com<span class="reference-accessdate">. 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Retrieved <span class="nowrap">2024-07-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=F5+Financial&rft.atitle=Navigating+the+Efficient+Frontier+of+Investing&rft.date=2021-05-28&rft_id=https%3A%2F%2Fwww.f5fp.com%2Fnavigating-the-efficient-frontier-of-investing%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEfficient+frontier" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.stalwart.vg/model-portfolio-service">"Finding the Optimal Model Portfolios"</a>. <i>Stalwart Holdings</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-07-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Stalwart+Holdings&rft.atitle=Finding+the+Optimal+Model+Portfolios&rft_id=https%3A%2F%2Fwww.stalwart.vg%2Fmodel-portfolio-service&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEfficient+frontier" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAbuafAyalaSinclair" class="citation web cs1">Abuaf, Niso; Ayala, Tracyann; Sinclair, Duncan. <a rel="nofollow" class="external text" href="https://activityinsight.pace.edu/nabuaf/intellcont/Global%20equity%20investing%20An%20efficient%20frontier%20approach-1.pdf">"Global equity investing: An efficient frontier approach"</a> <span class="cs1-format">(PDF)</span>. <i>International Finance</i><span class="reference-accessdate">. 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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 class="mw-selflink selflink">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 href="/wiki/Market_anomaly" title="Market anomaly">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 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