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vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Risk_premium_application_in_finance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Risk premium application in finance</span> </div> </a> <button aria-controls="toc-Risk_premium_application_in_finance-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 Risk premium application in finance subsection</span> </button> <ul id="toc-Risk_premium_application_in_finance-sublist" class="vector-toc-list"> <li id="toc-Equity_instruments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equity_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Equity instruments</span> </div> </a> <ul id="toc-Equity_instruments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Debt_instruments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Debt_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Debt instruments</span> </div> </a> <ul id="toc-Debt_instruments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Risk_premium_application_in_banking" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Risk_premium_application_in_banking"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Risk premium application in banking</span> </div> </a> <ul id="toc-Risk_premium_application_in_banking-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Using_the_risk_premium_to_produce_valuations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Using_the_risk_premium_to_produce_valuations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Using the risk premium to produce valuations</span> </div> </a> <ul id="toc-Using_the_risk_premium_to_produce_valuations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Risk_premium_application_in_managerial_economics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Risk_premium_application_in_managerial_economics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Risk premium application in managerial economics</span> </div> </a> <ul id="toc-Risk_premium_application_in_managerial_economics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_public_goods" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_public_goods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>In public goods</span> </div> </a> <button aria-controls="toc-In_public_goods-sublist" class="cdx-button cdx-button--weight-quiet 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vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle In agriculture subsection</span> </button> <ul id="toc-In_agriculture-sublist" class="vector-toc-list"> <li id="toc-Of_crop_pathogens" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Of_crop_pathogens"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Of crop pathogens</span> </div> </a> <ul id="toc-Of_crop_pathogens-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Of_investment_in_genetic_research" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Of_investment_in_genetic_research"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Of investment in genetic research</span> </div> </a> <ul id="toc-Of_investment_in_genetic_research-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Example_of_observed_risk_premium" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Example_of_observed_risk_premium"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Example of observed risk premium</span> </div> </a> <ul id="toc-Example_of_observed_risk_premium-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Empirical_estimates_of_risk_premium_from_securities_markets" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Empirical_estimates_of_risk_premium_from_securities_markets"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Empirical estimates of risk premium from securities markets</span> </div> </a> <ul id="toc-Empirical_estimates_of_risk_premium_from_securities_markets-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header 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</div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Risk premium</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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mw-list-item"><a href="https://ca.wikipedia.org/wiki/Prima_de_risc" title="Prima de risc – Catalan" lang="ca" hreflang="ca" data-title="Prima de risc" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Risikopr%C3%A4mie" title="Risikoprämie – German" lang="de" hreflang="de" data-title="Risikoprämie" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BC%CE%BF%CE%B9%CE%B2%CE%AE_%CE%BA%CE%B9%CE%BD%CE%B4%CF%8D%CE%BD%CE%BF%CF%85" title="Αμοιβή κινδύνου – Greek" lang="el" hreflang="el" data-title="Αμοιβή κινδύνου" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Prima_de_riesgo" title="Prima de riesgo – Spanish" lang="es" hreflang="es" data-title="Prima de riesgo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Arrisku-sari" title="Arrisku-sari – Basque" lang="eu" hreflang="eu" data-title="Arrisku-sari" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B5%D8%B1%D9%81_%D8%B1%DB%8C%D8%B3%DA%A9" title="صرف ریسک – Persian" lang="fa" hreflang="fa" data-title="صرف ریسک" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Prime_de_risque" title="Prime de risque – French" lang="fr" hreflang="fr" data-title="Prime de risque" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Prima_de_risco" title="Prima de risco – Galician" lang="gl" hreflang="gl" data-title="Prima de risco" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A6%AC%EC%8A%A4%ED%81%AC_%ED%94%84%EB%A6%AC%EB%AF%B8%EC%97%84" title="리스크 프리미엄 – Korean" lang="ko" hreflang="ko" data-title="리스크 프리미엄" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Premio_per_il_rischio" title="Premio per il rischio – Italian" lang="it" hreflang="it" data-title="Premio per il rischio" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%A8%D7%9E%D7%99%D7%99%D7%AA_%D7%A1%D7%99%D7%9B%D7%95%D7%9F" title="פרמיית סיכון – Hebrew" lang="he" hreflang="he" data-title="פרמיית סיכון" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Premio_de_risca" title="Premio de risca – Lingua Franca Nova" lang="lfn" hreflang="lfn" 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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">Measure of excess</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid 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href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Risk_premium" title="Special:EditPage/Risk premium">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Risk+premium%22">"Risk premium"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Risk+premium%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Risk+premium%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Risk+premium%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Risk+premium%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Risk+premium%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">March 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Risk_Return_Function_with_Risk_Premium.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Risk_Return_Function_with_Risk_Premium.png/267px-Risk_Return_Function_with_Risk_Premium.png" decoding="async" width="267" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Risk_Return_Function_with_Risk_Premium.png/401px-Risk_Return_Function_with_Risk_Premium.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Risk_Return_Function_with_Risk_Premium.png/534px-Risk_Return_Function_with_Risk_Premium.png 2x" data-file-width="1532" data-file-height="1080" /></a><figcaption>Example of a linear Risk vs Return function and corresponding risk premium</figcaption></figure> <p>A <b>risk premium</b> is a measure of excess return that is required by an individual to compensate being subjected to an increased level of 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> It is used widely in finance and economics, the general definition being the expected risky <a href="/wiki/Rate_of_return" title="Rate of return">return</a> less the <a href="/wiki/Risk-free_interest_rate" class="mw-redirect" title="Risk-free interest rate">risk-free return</a>, as demonstrated by the formula below.<sup id="cite_ref-:3_2-0" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </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 Risk\ premium=E(r)-r_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>i</mi> <mi>s</mi> <mi>k</mi> <mtext> </mtext> <mi>p</mi> <mi>r</mi> <mi>e</mi> <mi>m</mi> <mi>i</mi> <mi>u</mi> <mi>m</mi> <mo>=</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Risk\ premium=E(r)-r_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13df82962f5ee12eb30455bb808bdca57a383992" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.721ex; height:3.009ex;" alt="{\displaystyle Risk\ premium=E(r)-r_{f}}" /></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 E(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ee1487ea5b5cba78e648e2020eed6ac3016bcde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.634ex; height:2.843ex;" alt="{\displaystyle E(r)}" /></span> is the risky expected rate of 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_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c87b228b9a0db910ffa622d7f417de3fa64258a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.185ex; height:2.343ex;" alt="{\displaystyle r_{f}}" /></span> is the risk-free return. </p><p>The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections. Regardless of the application, the market premium can be volatile as both comprising variables can be impacted independent of each other by both cyclical and abrupt changes.<sup id="cite_ref-:3_2-1" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This means that the market premium is dynamic in nature and ever-changing. Additionally, a general observation regardless of application is that the risk premium is larger during economic downturns and during periods of increased uncertainty.<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> </p><p>There are many forms of risk such as <a href="/wiki/Financial_risk" title="Financial risk">financial risk</a>, <a href="/wiki/Physical_hazard" title="Physical hazard">physical risk</a>, and <a href="/wiki/Reputational_risk" class="mw-redirect" title="Reputational risk">reputation risk</a>. The concept of risk premium can be applied to all these risks and the expected payoff from these risks can be determined if the risk premium can be quantified. In the <a href="/wiki/Stock_market" title="Stock market">equity market</a>, the riskiness of a stock can be estimated by the magnitude of the standard deviation from the mean.<sup id="cite_ref-:6_4-0" class="reference"><a href="#cite_note-:6-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> If for example the price of two different stocks were plotted over a year and an average trend line added for each, the stock whose price varies more dramatically about the mean is considered the riskier stock. Investors also analyse many other factors about a company that may influence its risk such as industry <a href="/wiki/Volatility_(finance)" title="Volatility (finance)">volatility</a>, <a href="/wiki/Cash_flow" title="Cash flow">cash flows</a>, <a href="/wiki/Debt" title="Debt">debt</a>, and other market threats.<sup id="cite_ref-:6_4-1" class="reference"><a href="#cite_note-:6-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formal_definition_in_expected_utility_theory">Formal definition in <a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">expected utility theory</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=1" title="Edit section: Formal definition in expected utility theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In expected utility theory, a rational agent has a utility function that maps sure-outcomes to numerical values, and the agent ranks gambles over sure-outcomes by their expected utilities. </p><p>Let the set of possible wealth-levels be <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 \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }" /></span>. A gamble <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 Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}" /></span> is a real-valued random variable. The <b>actuarial value</b> of the gamble is just its expectation: <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 \mathbb {E} [Z]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">E</mi> </mrow> <mo stretchy="false">[</mo> <mi>Z</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {E} [Z]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ae460def73cdd7e3fc18d1a4df03c33ce673331" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.524ex; height:2.843ex;" alt="{\displaystyle \mathbb {E} [Z]}" /></span>. This is independent of any agent. </p><p>Let the agent have a utility function <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 u:\mathbb {R} \to \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u:\mathbb {R} \to \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8564688c74fbbbee8b31ee481936e446bdd092aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.237ex; height:2.176ex;" alt="{\displaystyle u:\mathbb {R} \to \mathbb {R} }" /></span>, with a wealth-level <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 w\in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w\in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa1efeec8ee213ec72013d1a6c413b9a3b6d8f6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.183ex; height:2.176ex;" alt="{\displaystyle w\in \mathbb {R} }" /></span>. The risk-premium of <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 Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}" /></span> for the agent at wealth-level <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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}" /></span> is <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 \pi (w,Z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mo>,</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi (w,Z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd00a2ced303a3c272083ae4d79ad58cae49ad4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.52ex; height:2.843ex;" alt="{\displaystyle \pi (w,Z)}" /></span>, defined as the solution to<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u(w+\mathbb {E} [Z]-\pi )=\mathbb {E} [u(w+Z)].}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">E</mi> </mrow> <mo stretchy="false">[</mo> <mi>Z</mi> <mo stretchy="false">]</mo> <mo>−</mo> <mi>π</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">E</mi> </mrow> <mo stretchy="false">[</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mo>+</mo> <mi>Z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(w+\mathbb {E} [Z]-\pi )=\mathbb {E} [u(w+Z)].}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f252ed6e4893cb980198ddb8220d9230fba9dc4c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.254ex; height:2.843ex;" alt="{\displaystyle u(w+\mathbb {E} [Z]-\pi )=\mathbb {E} [u(w+Z)].}" /></span><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><p>Note that the risk-premium depends both on the gamble itself, the agent's utility function, and the wealth-level of the agent. This can be understood intuitively by considering a real gamble. Some people may be quite willing to take the gamble and thus have a low risk-premium, while others are more averse. Further, as one's wealth increases, one is usually less perturbed by the gamble, whose stakes diminshes relative to one's wealth, consequently the risk-premium <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 \pi (w,Z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mo>,</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi (w,Z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd00a2ced303a3c272083ae4d79ad58cae49ad4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.52ex; height:2.843ex;" alt="{\displaystyle \pi (w,Z)}" /></span> often decreases as <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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}" /></span> increases, holding <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 Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}" /></span> constant. </p> <div class="mw-heading mw-heading2"><h2 id="Risk_premium_application_in_finance">Risk premium application in finance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=2" title="Edit section: Risk premium application in finance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The risk premium is used extensively in finance in areas such as asset pricing, portfolio allocation and risk management.<sup id="cite_ref-:3_2-2" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Two fundamental aspects of finance, being equity and debt instruments, require the use and interpretation of associated risk premiums with the inputs for each explained below: </p> <div class="mw-heading mw-heading3"><h3 id="Equity_instruments">Equity instruments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=3" title="Edit section: Equity instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Stock_market" title="Stock market">stock market</a> the risk premium is the expected return of a company stock, a group of company stocks, or a portfolio of all stock market company stocks, minus the risk-free rate.<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> The return from equity is the sum of the <a href="/wiki/Dividend_yield" title="Dividend yield">dividend yield</a> and <a href="/wiki/Capital_gains" class="mw-redirect" title="Capital gains">capital gains</a> and the risk free rate can be a treasury bond yield.<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> </p><p>For example, if an investor has a choice between a risk-free treasury bond with a bond yield of 3% and a risky company equity asset, the investor may require a greater return of 8% from the risky company. This would result in a risk premium of 5%. Individual investors set their own risk premium depending on their level of risk aversion.<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> The formula can be rearranged to find the expected return on an investment given a stated risk premium and risk-free rate. For example, if the investor in the example above required a risk premium of 9% then the expected return on the equity asset would have to be 12%. </p> <div class="mw-heading mw-heading3"><h3 id="Debt_instruments">Debt instruments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=4" title="Edit section: Debt instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The risk premium associated with <a href="/wiki/Bond_(finance)" title="Bond (finance)">bonds</a>, known as the <a href="/wiki/Credit_spread_(bond)" class="mw-redirect" title="Credit spread (bond)">credit spread</a>, is the difference between a risky bond and the risk free treasury bond with greater risk demanding a greater risk premium as compensation.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Risk_premium_application_in_banking">Risk premium application in banking</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=5" title="Edit section: Risk premium application in banking"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Risk premiums are essential to the banking sector and can provide a large amount of information to investors and customers alike. For instance, the risk premium for a savings account is determined by the bank through the interest that they set on their savings accounts for customers.<sup id="cite_ref-:0_10-0" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This less the interest rate set by the central bank provides the risk premium. Stakeholders can interpret a large premium as an indication of increased default risk which has flow on effects such as negatively impacting the public's confidence in the financial system which can ultimately lead to bank runs which is dangerous for an economy.<sup id="cite_ref-:0_10-1" class="reference"><a href="#cite_note-:0-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>The risk premium is equally important for a bank's assets with the risk premium on loans, defined as the loan interest charged to customers less the risk free government bond, needing to be sufficiently large to compensate the institution for the increased default risk associated with providing a loan.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Using_the_risk_premium_to_produce_valuations">Using the risk premium to produce valuations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=6" title="Edit section: Using the risk premium to produce valuations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One of the most important applications of risk premiums is to estimate the value of financial assets. There are a number of models used in finance to determine this with the most widely used being the <a href="/wiki/Capital_asset_pricing_model" title="Capital asset pricing model">Capital Asset Pricing Model</a> or CAPM.<sup id="cite_ref-:1_12-0" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> CAPM uses investment risk and expected return to estimate a value for the investment. In Finance, CAPM is generally used to estimate the required rate of return for an equity. This required rate of return can then be used to estimate a price for the stock which can be done via a number of methods.<sup id="cite_ref-:1_12-1" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The formula for CAPM is: </p> <dl><dd>CAPM = (The Risk Free Rate) + <dl><dd>(The Beta of the Security) * (The Market Risk Premium)<sup id="cite_ref-:2_13-0" class="reference"><a href="#cite_note-:2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></dd></dl></dd></dl> <p>In this model, we use the implied risk premium (market return less risk-free rate) and multiply this with the <a href="/wiki/Beta_(finance)" title="Beta (finance)">beta</a> of the security. The beta of a security is the measure of a security's volatility relative to the broader market to understand its historical share price movement compared to the market.<sup id="cite_ref-:1_12-2" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> If the beta of a stock is 1.0 then a 10% increase in the market will translate to a 10% increase in stock price. If the Beta of a stock is 1.5 then a 10% increase in the market will translate to a 15% increase in the stock price and if the beta of a stock is 0.5 a 10% market increase will translate to a 5% stock price increase and likewise with decreases in the market. This beta is generally found via statistical analysis of the share price history of a stock. Therefore CAPM aims to provide a simple model in order to estimate the required return of an investment which uses the theory of risk premiums. This helps to provide investors with a simple means of determining what return an investment should be relative to its risk.<sup id="cite_ref-:2_13-1" class="reference"><a href="#cite_note-:2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Risk_premium_application_in_managerial_economics">Risk premium application in managerial economics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=7" title="Edit section: Risk premium application in managerial economics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The risk premium concept is equally applicable in managerial economics. The risk premium is largely correlated with <a href="/wiki/Risk_aversion" title="Risk aversion">risk aversion</a> with the larger the risk aversion of an individual or business the larger the risk premium the party will be willing to pay to avoid the risk.<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> </p><p>Regarding workers, the risk premium increases as the risk of injury increases and manifests in practice with average wages in dangerous jobs being higher for this reason.<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> Another way in which the risk premium can be interpreted from the workers perspective is that risk is valued by the market, in the form of wage discrepancies between risky and less risky jobs, with a worker able to determine what amount they are willing to forgo to engage in a less risky job.<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> In this instance the risk premium provides insight into the strength of correlation between risk and the average job type earnings with a larger premium potentially suggesting that there is a greater risk and/ or a lack of workers willing to take the risk.<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> </p><p>The level of risk associated with the risk premium concept does not need to be physical risk but it can also incorporate risk surrounding the job, such as <a href="/wiki/Job_security" title="Job security">job security</a>.<sup id="cite_ref-:4_18-0" class="reference"><a href="#cite_note-:4-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Higher risk of unemployment  is compensated with a higher wage with this being a reason as to why fixed-term contracts generally include a higher wage.<sup id="cite_ref-:4_18-1" class="reference"><a href="#cite_note-:4-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> CEO's in industries with high volatility are subject to increased risk of dismissal.<sup id="cite_ref-:5_19-0" class="reference"><a href="#cite_note-:5-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Dismissed CEO's often undergo a period of unemployment after dismissal and frequently settle for jobs in smaller firms with lower remuneration.<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> Due to this, and assuming there is demand competition within the labor market, they often require a higher remuneration than CEO's in non-volatile industries as a risk premium.<sup id="cite_ref-:5_19-1" class="reference"><a href="#cite_note-:5-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_public_goods">In public goods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=8" title="Edit section: In public goods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="In_invasive_species_management">In invasive species management</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=9" title="Edit section: In invasive species management"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Option_value_(cost%E2%80%93benefit_analysis)" title="Option value (cost–benefit analysis)">option value</a> of whether to invest in <a href="/wiki/Invasive_species" title="Invasive species">invasive species</a> quarantine and/or management is a risk premium in some models.<sup id="cite_ref-Finnoff-et-al-2010_21-0" class="reference"><a href="#cite_note-Finnoff-et-al-2010-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_agriculture">In agriculture</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=10" title="Edit section: In agriculture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Of_crop_pathogens">Of crop pathogens</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=11" title="Edit section: Of crop pathogens"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Farmers cope with <a href="/wiki/Crop_pathogen" class="mw-redirect" title="Crop pathogen">crop pathogen</a> risks and losses in various ways, mostly by trading off between management methods and pricing that includes risk premiums. For example in the northern <a href="/wiki/United_States" title="United States">United States</a>, <a href="/wiki/Fusarium_head_blight" class="mw-redirect" title="Fusarium head blight">Fusarium head blight</a> is a constant problem. Then in 2000 the release of a <a href="/wiki/Crop_disease_resistance" class="mw-redirect" title="Crop disease resistance">multiply-resistant</a> cultivar of wheat dramatically reduced the necessary risk premium. The total planted area of MR wheats was dramatically expanded, due to this essentially costless tradeoff to the new cultivar.<sup id="cite_ref-Zhu-et-al-2019_22-0" class="reference"><a href="#cite_note-Zhu-et-al-2019-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Of_investment_in_genetic_research">Of investment in genetic research</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=12" title="Edit section: Of investment in genetic research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Estimates of costs of research and development - including <a href="/wiki/Patent" title="Patent">patent</a> costs - of new crop genes and other agricultural biotechnologies must include the risk premium of those which do not ultimately obtain patent approval.<sup id="cite_ref-Arnold-Ogielska-Zei-2002_23-0" class="reference"><a href="#cite_note-Arnold-Ogielska-Zei-2002-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Example_of_observed_risk_premium">Example of observed risk premium</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=13" title="Edit section: Example of observed risk premium"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Suppose a <a href="/wiki/Game_show" title="Game show">game show</a> participant may choose one of two doors, one that hides $1,000 and one that hides $0. Further, suppose that the host also allows the contestant to take $500 instead of choosing a door. The two options (choosing between door 1 and door 2, or taking $500) have the same expected value of $500, so no risk premium is being offered for choosing the doors rather than the guaranteed $500. </p><p>A contestant <a href="/wiki/Risk_neutral" class="mw-redirect" title="Risk neutral">unconcerned about risk</a> is indifferent between these choices. A <a href="/wiki/Risk_aversion" title="Risk aversion">risk-averse</a> contestant will choose no door and accept the guaranteed $500, while a <a href="/wiki/Risk_aversion#Example" title="Risk aversion">risk-loving</a> contestant will derive utility from the uncertainty and will therefore choose a door. </p><p>If too many contestants are risk averse, the game show may encourage selection of the riskier choice (gambling on one of the doors) by offering a positive risk premium. If the game show offers $1,600 behind the good door, increasing to $800 the expected value of choosing between doors 1 and 2, the risk premium becomes $300 (i.e. $800 expected value minus $500 guaranteed amount). Contestants requiring a minimum risk compensation of less than $300 will choose a door instead of accepting the guaranteed $500. </p> <div class="mw-heading mw-heading2"><h2 id="Empirical_estimates_of_risk_premium_from_securities_markets">Empirical estimates of risk premium from securities markets</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=14" title="Edit section: Empirical estimates of risk premium from securities markets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schroeder estimated risk premiums ranging from 4.83 to 7.75 percent in securities markets in the United Kingdom and the European Union under multiple models, with most estimates ranging between 6.3 and 7.2 percent.<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> </p> <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=Risk_premium&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Equity_risk" title="Equity risk">Equity risk</a></li> <li><a href="/wiki/Interest" title="Interest">Interest</a></li> <li><a href="/wiki/Risk" title="Risk">Risk</a></li> <li><a href="/wiki/Risk_aversion" title="Risk aversion">Risk aversion</a></li> <li><a href="/wiki/Risk_neutral" class="mw-redirect" title="Risk neutral">Risk neutral</a></li> <li><a href="/wiki/Risk-loving" class="mw-redirect" title="Risk-loving">Risk-loving</a></li> <li><a href="/wiki/Minimum_acceptable_rate_of_return" title="Minimum acceptable rate of return">Minimum acceptable rate of return</a></li> <li><a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">Expected utility hypothesis</a></li> <li><a href="/wiki/LIBOR%E2%80%93OIS_spread" class="mw-redirect" title="LIBOR–OIS spread">LIBOR–OIS spread</a></li> <li><a href="/wiki/Risk_parity" title="Risk parity">Risk premia parity</a></li> <li><a href="/wiki/Kelly_criterion" title="Kelly criterion">Kelly criterion</a></li></ul> </div> <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=Risk_premium&action=edit&section=16" 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 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Edward; Hadlock, Charles J. (2002). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.2139/ssrn.313381">"Management Turnover Across the Corporate Hierarchy"</a>. <i>SSRN Electronic Journal</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2139%2Fssrn.313381">10.2139/ssrn.313381</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1556-5068">1556-5068</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:219722544">219722544</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SSRN+Electronic+Journal&rft.atitle=Management+Turnover+Across+the+Corporate+Hierarchy&rft.date=2002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A219722544%23id-name%3DS2CID&rft.issn=1556-5068&rft_id=info%3Adoi%2F10.2139%2Fssrn.313381&rft.aulast=Fee&rft.aufirst=C.+Edward&rft.au=Hadlock%2C+Charles+J.&rft_id=http%3A%2F%2Fdx.doi.org%2F10.2139%2Fssrn.313381&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARisk+premium" class="Z3988"></span></span> </li> <li id="cite_note-Finnoff-et-al-2010-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Finnoff-et-al-2010_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFinnoffMcIntoshShogrenSims2010" class="citation journal cs1">Finnoff, David; McIntosh, Chris; Shogren, Jason F.; Sims, Charles; Warziniack, Travis (2010). "Invasive Species and Endogenous Risk". <i><a href="/wiki/Annual_Review_of_Resource_Economics" title="Annual Review of Resource Economics">Annual Review of Resource Economics</a></i>. <b>2</b> (1). <a href="/wiki/Annual_Reviews_(publisher)" title="Annual Reviews (publisher)">Annual Reviews</a>: <span class="nowrap">77–</span>100. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.resource.050708.144212">10.1146/annurev.resource.050708.144212</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1941-1340">1941-1340</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Resource+Economics&rft.atitle=Invasive+Species+and+Endogenous+Risk&rft.volume=2&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E77-%3C%2Fspan%3E100&rft.date=2010&rft_id=info%3Adoi%2F10.1146%2Fannurev.resource.050708.144212&rft.issn=1941-1340&rft.aulast=Finnoff&rft.aufirst=David&rft.au=McIntosh%2C+Chris&rft.au=Shogren%2C+Jason+F.&rft.au=Sims%2C+Charles&rft.au=Warziniack%2C+Travis&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARisk+premium" class="Z3988"></span></span> </li> <li id="cite_note-Zhu-et-al-2019-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Zhu-et-al-2019_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFZhuHaoMergoumBai2019" class="citation journal cs1">Zhu, Zhanwang; Hao, Yuanfeng; Mergoum, Mohamed; Bai, Guihua; Humphreys, Gavin; Cloutier, Sylvie; Xia, Xianchun; He, Zhonghu (2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.cj.2019.06.003">"Breeding wheat for resistance to Fusarium head blight in the Global North: China, USA, and Canada"</a>. <i>The Crop Journal</i>. <b>7</b> (6). <a href="/w/index.php?title=Crop_Science_Society_of_China&action=edit&redlink=1" class="new" title="Crop Science Society of China (page does not exist)">Crop Science Society of China</a> (<a href="/wiki/Elsevier" title="Elsevier">Elsevier</a>): <span class="nowrap">730–</span>738. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.cj.2019.06.003">10.1016/j.cj.2019.06.003</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2214-5141">2214-5141</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:199629483">199629483</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Crop+Journal&rft.atitle=Breeding+wheat+for+resistance+to+Fusarium+head+blight+in+the+Global+North%3A+China%2C+USA%2C+and+Canada&rft.volume=7&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E730-%3C%2Fspan%3E738&rft.date=2019&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A199629483%23id-name%3DS2CID&rft.issn=2214-5141&rft_id=info%3Adoi%2F10.1016%2Fj.cj.2019.06.003&rft.aulast=Zhu&rft.aufirst=Zhanwang&rft.au=Hao%2C+Yuanfeng&rft.au=Mergoum%2C+Mohamed&rft.au=Bai%2C+Guihua&rft.au=Humphreys%2C+Gavin&rft.au=Cloutier%2C+Sylvie&rft.au=Xia%2C+Xianchun&rft.au=He%2C+Zhonghu&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252Fj.cj.2019.06.003&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARisk+premium" class="Z3988"></span></span> </li> <li id="cite_note-Arnold-Ogielska-Zei-2002-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Arnold-Ogielska-Zei-2002_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFArnoldOgielska-Zei2002" class="citation journal cs1">Arnold, Beth E.; Ogielska-Zei, Eva (2002). "Patenting Genes and Genetic Research Tools: Good or Bad for Innovation?". <i><a href="/wiki/Annual_Review_of_Genomics_and_Human_Genetics" title="Annual Review of Genomics and Human Genetics">Annual Review of Genomics and Human Genetics</a></i>. <b>3</b> (1). <a href="/wiki/Annual_Reviews_(publisher)" title="Annual Reviews (publisher)">Annual Reviews</a>: <span class="nowrap">415–</span>432. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.genom.3.032102.170635">10.1146/annurev.genom.3.032102.170635</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1527-8204">1527-8204</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/12142363">12142363</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Genomics+and+Human+Genetics&rft.atitle=Patenting+Genes+and+Genetic+Research+Tools%3A+Good+or+Bad+for+Innovation%3F&rft.volume=3&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E415-%3C%2Fspan%3E432&rft.date=2002&rft.issn=1527-8204&rft_id=info%3Apmid%2F12142363&rft_id=info%3Adoi%2F10.1146%2Fannurev.genom.3.032102.170635&rft.aulast=Arnold&rft.aufirst=Beth+E.&rft.au=Ogielska-Zei%2C+Eva&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARisk+premium" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDavid_Schroeder2007" class="citation journal cs1">David Schroeder (16 October 2007). <a rel="nofollow" class="external text" href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=493042">"The Implied Equity Risk Premium - An Evaluation of Empirical Methods"</a>. <i>KREDIT und KAPITAL</i>. <b>40</b> (4): <span class="nowrap">583–</span>613. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0023-4591">0023-4591</a>. <a href="/wiki/WDQ_(identifier)" class="mw-redirect" title="WDQ (identifier)">Wikidata</a> <a href="https://www.wikidata.org/wiki/Q106644168" class="extiw" title="d:Q106644168">Q106644168</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=KREDIT+und+KAPITAL&rft.atitle=The+Implied+Equity+Risk+Premium+-+An+Evaluation+of+Empirical+Methods&rft.volume=40&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E583-%3C%2Fspan%3E613&rft.date=2007-10-16&rft.issn=0023-4591&rft.au=David+Schroeder&rft_id=https%3A%2F%2Fpapers.ssrn.com%2Fsol3%2Fpapers.cfm%3Fabstract_id%3D493042&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARisk+premium" class="Z3988"></span>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Risk_premium&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.einsurance.cf/2015/02/fundamental-risk-versus-systematic-risk.html">Fundamental Risk versus Systematic Risk</a></li> <li><a rel="nofollow" class="external text" href="http://www.hussman.net/html/longterm.htm">Hussman Funds – Estimating the Long-Term Return on Stocks – June 1998</a></li> <li><a rel="nofollow" class="external text" href="https://ssrn.com/abstract=846546">Earnings Quality and the Equity Risk Premium: A Benchmark Model</a></li> <li>Ruben D. Cohen (2002) "The Relationship Between the Equity Risk Premium, Duration and Dividend Yield <a rel="nofollow" class="external text" href="http://rdcohen.50megs.com/ERPabstract.htm">(download)</a>," <i>Wilmott Magazine</i>, pp 84–97, November issue.</li> <li>Ruben D. Cohen "The Long-run Behaviour of the S&P Composite Price Index and its Risk Premium <a rel="nofollow" class="external text" href="http://rdcohen.50megs.com/LTRPabstract.htm">(download)</a>."</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output 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