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<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">Measurement in finance</div> <p>The <b>Sortino ratio</b> measures the <a href="/wiki/Risk_adjusted_return_on_capital" class="mw-redirect" title="Risk adjusted return on capital">risk-adjusted return</a> of an investment <a href="/wiki/Asset" title="Asset">asset</a>, <a href="/wiki/Financial_portfolio" class="mw-redirect" title="Financial portfolio">portfolio</a>, or <a href="/wiki/Trading_strategy" title="Trading strategy">strategy</a>.<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 a modification of the <a href="/wiki/Sharpe_ratio" title="Sharpe ratio">Sharpe ratio</a> but penalizes only those returns falling below a user-specified target or required <a href="/wiki/Rate_of_return" title="Rate of return">rate of return</a>, while the Sharpe ratio penalizes both upside and downside <a href="/wiki/Volatility_(finance)" title="Volatility (finance)">volatility</a> equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. </p><p>The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.<sup id="cite_ref-RedRockCapital_2-0" class="reference"><a href="#cite_note-RedRockCapital-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sortino_ratio&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ratio <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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> is calculated as </p> <dl><dd><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 S={\frac {R-T}{DR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mo>−</mo> <mi>T</mi> </mrow> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\frac {R-T}{DR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6da9e836535cd123acaaa5ba52be2a444717119" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.674ex; height:5.343ex;" alt="{\displaystyle S={\frac {R-T}{DR}}}"></span> ,</dd></dl> <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> is the asset or portfolio average realized return, <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 T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> is the target or required rate of return for the investment strategy under consideration (originally called the minimum acceptable return <i>MAR</i>), 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 DR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle DR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9105ddaced8a65833c4edc21afe410e97136e791" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.688ex; height:2.176ex;" alt="{\displaystyle DR}"></span> is the target semi-deviation (the square root of target semi-variance), termed downside deviation. <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 DR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle DR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9105ddaced8a65833c4edc21afe410e97136e791" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.688ex; height:2.176ex;" alt="{\displaystyle DR}"></span> is expressed in percentages and therefore allows for rankings in the same way as <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>. </p><p>An intuitive way to view downside risk is the annualized standard deviation of returns below the target. Another is the square root of the probability-weighted squared below-target returns. The squaring of the below-target returns has the effect of penalizing failures at a quadratic rate. This is consistent with observations made on the behavior of individual decision making under uncertainty. </p> <dl><dd><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 DR={\sqrt {\int _{-\infty }^{T}(T-r)^{2}f(r)\,dr}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>r</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle DR={\sqrt {\int _{-\infty }^{T}(T-r)^{2}f(r)\,dr}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa327979a022674d4503d1b47c1b021f211d1e6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:28.734ex; height:7.509ex;" alt="{\displaystyle DR={\sqrt {\int _{-\infty }^{T}(T-r)^{2}f(r)\,dr}}}"></span></dd></dl> <p>Here </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 DR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle DR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9105ddaced8a65833c4edc21afe410e97136e791" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.688ex; height:2.176ex;" alt="{\displaystyle DR}"></span> = downside deviation or (commonly known in the financial community) "downside risk" (by extension, <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 DR^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle DR^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19bec6ba427e79126c091b725a36d2b468da1ccc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.743ex; height:2.676ex;" alt="{\displaystyle DR^{2}}"></span> = downside variance), </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 T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> = the annual target return, originally termed the minimum acceptable return <i>MAR</i>, </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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> = the random variable representing the return for the distribution of annual returns <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 f(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1498cdcc03367bb2fefb5da9fe91c89da0577540" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.137ex; height:2.843ex;" alt="{\displaystyle f(r)}"></span>, and </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 f(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1498cdcc03367bb2fefb5da9fe91c89da0577540" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.137ex; height:2.843ex;" alt="{\displaystyle f(r)}"></span> = the <a href="/wiki/Probability_density_function" title="Probability density function">distribution</a> for the annual returns, e.g., the <a href="/wiki/Log-normal_distribution" title="Log-normal distribution">log-normal distribution</a>. </p><p>For the reasons provided below, this <i>continuous</i> formula is preferred over a simpler <i>discrete</i> version that determines the standard deviation of below-target periodic returns taken from the return series. </p> <ol><li>The continuous form permits all subsequent calculations to be made using annual returns, the natural way for investors to specify their investment goals. The discrete form requires monthly returns for there to be sufficient data points to make a meaningful calculation, which in turn requires converting the annual target into a monthly target. This significantly affects the amount of risk that is identified. For example, a goal of earning 1% in every month of one year results in a greater risk than the seemingly equivalent goal of earning 12% in one year.</li> <li>A second reason for strongly preferring the continuous form to the discrete form has been proposed by Sortino & Forsey (1996):</li></ol> <blockquote> <p>"Before we make an investment, we don't know what the outcome will be... After the investment is made, and we want to measure its performance, all we know is what the outcome was, not what it could have been. To cope with this uncertainty, we assume that a reasonable estimate of the range of possible returns, as well as the probabilities associated with estimation of those returns...In statistical terms, the shape of [this] uncertainty is called a probability distribution. In other words, looking at just the discrete monthly or annual values does not tell the whole story." </p> </blockquote> <p>Using the observed points to create a distribution is a staple of conventional performance measurement. For example, monthly returns are used to calculate a fund's mean and standard deviation. Using these values and the properties of the normal distribution, we can make statements such as the likelihood of losing money (even though no negative returns may actually have been observed) or the range within which two-thirds of all returns lies (even though the specific returns identifying this range have not necessarily occurred). Our ability to make these statements comes from the process of assuming the continuous form of the normal distribution and certain of its well-known properties. </p><p>In <a href="/wiki/Post-modern_portfolio_theory" title="Post-modern portfolio theory">post-modern portfolio theory</a> an analogous process is followed. </p> <ol><li>Observe the monthly returns.</li> <li>Fit a distribution that permits asymmetry to the observations.</li> <li>Annualize the monthly returns, making sure the shape characteristics of the distribution are retained.</li> <li>Apply integral calculus to the resultant distribution to calculate the appropriate statistics.</li></ol> <p>As a caveat, some practitioners have fallen into the habit of using discrete periodic returns to compute downside risk. This method is conceptually and operationally incorrect and negates the foundational statistic of post-modern portfolio theory as developed by Brian M. Rom and Frank A. Sortino. </p> <div class="mw-heading mw-heading2"><h2 id="Usage">Usage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sortino_ratio&action=edit&section=2" title="Edit section: Usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Sortino ratio is used to score a portfolio's risk-adjusted returns relative to an investment target using downside risk. This is analogous to the Sharpe ratio, which scores risk-adjusted returns relative to the risk-free rate using standard deviation. When return distributions are near symmetrical and the target return is close to the distribution median, these two measure will produce similar results. As skewness increases and targets vary from the median, results can be expected to show dramatic differences. </p><p>The Sortino ratio can also be used in trading. For example, whenever you want to get a performance metric for your trading strategy in an asset, you can compute the Sortino ratio to compare your strategy performance with any other strategy. <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>Practitioners who use a lower partial Standard Deviation (LPSD) instead of a standard deviation also tend to use the Sortino ratio instead of the Sharpe ratio. <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> </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=Sortino_ratio&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/Modern_portfolio_theory" title="Modern portfolio theory">Modern portfolio theory</a></li> <li><a href="/wiki/Modigliani_risk-adjusted_performance" title="Modigliani risk-adjusted performance">Modigliani risk-adjusted performance</a></li> <li><a href="/wiki/Omega_ratio" title="Omega ratio">Omega ratio</a></li> <li><a href="/wiki/Post-modern_portfolio_theory" title="Post-modern portfolio theory">Post-modern portfolio theory</a></li> <li><a href="/wiki/Sharpe_ratio" title="Sharpe ratio">Sharpe ratio</a></li> <li><a href="/wiki/Upside_potential_ratio" title="Upside potential ratio">Upside potential ratio</a></li> <li><a href="/wiki/V2_ratio" title="V2 ratio">V2 ratio</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=Sortino_ratio&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 a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .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 id="CITEREFSortinoPrice1994" class="citation journal cs1">Sortino, F.A.; Price, L.N. (1994). "Performance measurement in a downside risk framework". <i><a href="/wiki/Journal_of_Investing" class="mw-redirect" title="Journal of Investing">Journal of Investing</a></i>. <b>3</b> (3): 50–8. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3905%2Fjoi.3.3.59">10.3905/joi.3.3.59</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:155042092">155042092</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Investing&rft.atitle=Performance+measurement+in+a+downside+risk+framework&rft.volume=3&rft.issue=3&rft.pages=50-8&rft.date=1994&rft_id=info%3Adoi%2F10.3905%2Fjoi.3.3.59&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A155042092%23id-name%3DS2CID&rft.aulast=Sortino&rft.aufirst=F.A.&rft.au=Price%2C+L.N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASortino+ratio" class="Z3988"></span></span> </li> <li id="cite_note-RedRockCapital-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-RedRockCapital_2-0">^</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="http://www.redrockcapital.com/Sortino__A__Sharper__Ratio_Red_Rock_Capital.pdf">"Sortino: A 'Sharper' Ratio"</a> <span class="cs1-format">(PDF)</span>. Red Rock Capital<span class="reference-accessdate">. Retrieved <span class="nowrap">February 16,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Sortino%3A+A+%27Sharper%27+Ratio&rft.pub=Red+Rock+Capital&rft_id=http%3A%2F%2Fwww.redrockcapital.com%2FSortino__A__Sharper__Ratio_Red_Rock_Capital.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASortino+ratio" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"> <a rel="nofollow" class="external free" href="https://doi.org/10.1016/j.asoc.2013.09.011">https://doi.org/10.1016/j.asoc.2013.09.011</a>. Chen H.H, Yang C.B. and Peng Y.H., (2014) The trading on the mutual funds by gene expression programming with Sortino ratio, Applied Soft Computing, Volume 15, Pages 219-230, ISSN 1568-4946. </span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Investments (Bodie et al) 11th edition</span> </li> </ol></div></div> <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 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.navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Financial_risk" title="Template:Financial risk"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Financial_risk" title="Template talk:Financial risk"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Financial_risk" title="Special:EditPage/Template:Financial risk"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Financial_risk_and_financial_risk_management" style="font-size:114%;margin:0 4em"><a href="/wiki/Financial_risk" title="Financial risk">Financial risk</a> and <a href="/wiki/Financial_risk_management" title="Financial risk management">financial risk management</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Categories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Credit_risk" title="Credit risk">Credit risk</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/Consumer_credit_risk" title="Consumer credit risk">Consumer credit risk</a></li> <li><a href="/wiki/Sovereign_credit_risk" title="Sovereign credit risk">Sovereign credit risk</a></li> <li><a href="/wiki/Settlement_risk" title="Settlement risk">Settlement risk</a></li> <li><a href="/wiki/Default_(finance)" title="Default (finance)">Default risk</a></li> <li><a href="/wiki/Concentration_risk" title="Concentration risk">Concentration risk</a></li> <li><a href="/wiki/Credit_derivative" title="Credit derivative">Credit derivative</a></li> <li><a href="/wiki/Securitization" title="Securitization">Securitization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Market_risk" title="Market risk">Market risk</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/Commodity_risk" title="Commodity risk">Commodity risk</a> (e.g. <a href="/wiki/Volume_risk" title="Volume risk">Volume risk</a>, <a href="/wiki/Basis_risk" title="Basis risk">Basis risk</a>, <a href="/wiki/Shape_risk" title="Shape risk">Shape risk</a>, <a href="/wiki/Holding_period_risk" title="Holding period risk">Holding period risk</a>, <a href="/wiki/Price_area_risk" class="mw-redirect" title="Price area risk">Price area risk</a>)</li> <li><a href="/wiki/Equity_risk" title="Equity risk">Equity risk</a></li> <li><a href="/wiki/Valuation_risk" title="Valuation risk">Valuation risk</a></li> <li><a href="/wiki/Foreign_exchange_risk" title="Foreign exchange risk">FX risk</a></li> <li><a href="/wiki/Margining_risk" title="Margining risk">Margining risk</a></li> <li><a href="/wiki/Interest_rate_risk" title="Interest rate risk">Interest rate risk</a></li> <li><a href="/wiki/Inflation_risk" class="mw-redirect" title="Inflation risk">Inflation risk</a></li> <li><a href="/wiki/Volatility_risk" title="Volatility risk">Volatility risk</a></li> <li><a href="/wiki/Liquidity_risk" title="Liquidity risk">Liquidity risk</a> (e.g. <a href="/wiki/Refinancing_risk" title="Refinancing risk">Refinancing risk</a>, <a href="/wiki/Deposit_risk" title="Deposit risk">Deposit risk</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Operational_risk" title="Operational risk">Operational risk</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/Operational_risk_management" title="Operational risk management">Operational risk management</a></li> <li><a href="/wiki/Business_risk" class="mw-redirect" title="Business risk">Business risk</a></li> <li><a href="/wiki/Model_risk" title="Model risk">Model risk</a></li> <li><a href="/wiki/Reputational_risk" class="mw-redirect" title="Reputational risk">Reputational risk</a></li> <li><a href="/wiki/Country_risk" title="Country risk">Country risk</a></li> <li><a href="/wiki/Political_risk" title="Political risk">Political risk</a></li> <li><a href="/wiki/Legal_risk" title="Legal risk">Legal risk</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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/Execution_risk" class="mw-redirect" title="Execution risk">Execution risk</a></li> <li><a href="/wiki/Profit_risk" title="Profit risk">Profit risk</a></li> <li><a href="/wiki/Systemic_risk" title="Systemic risk">Systemic risk</a></li> <li><a href="/wiki/Non-financial_risk" title="Non-financial risk">Non-financial risk</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Financial_risk_modeling" title="Financial risk modeling">Modeling</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/Arbitrage_pricing_theory" title="Arbitrage pricing theory">Arbitrage pricing theory</a></li> <li><a href="/wiki/Black%E2%80%93Scholes_model" title="Black–Scholes model">Black–Scholes model</a></li> <li><a href="/wiki/Replicating_portfolio" title="Replicating portfolio">Replicating portfolio</a></li> <li><a href="/wiki/Cashflow_matching" title="Cashflow matching">Cash flow matching</a></li> <li><a href="/wiki/Expected_shortfall" title="Expected shortfall">Conditional Value-at-Risk (CVaR)</a></li> <li><a href="/wiki/Copula_(probability_theory)" class="mw-redirect" title="Copula (probability theory)">Copula</a></li> <li><a href="/wiki/Drawdown_(economics)" title="Drawdown (economics)">Drawdown</a></li> <li><a href="/wiki/First-hitting-time_model" title="First-hitting-time model">First-hitting-time model</a></li> <li><a href="/wiki/Immunization_(finance)" title="Immunization (finance)">Interest rate immunization</a></li> <li><a href="/wiki/Market_portfolio" title="Market portfolio">Market portfolio</a></li> <li><a href="/wiki/Modern_portfolio_theory" title="Modern portfolio theory">Modern portfolio theory</a></li> <li><a href="/wiki/Omega_ratio" title="Omega ratio">Omega ratio</a></li> <li><a href="/wiki/Risk-adjusted_return_on_capital" title="Risk-adjusted return on capital">RAROC</a></li> <li><a href="/wiki/Risk-free_interest_rate" class="mw-redirect" title="Risk-free interest rate">Risk-free rate</a></li> <li><a href="/wiki/Risk_parity" title="Risk parity">Risk parity</a></li> <li><a href="/wiki/Sharpe_ratio" title="Sharpe ratio">Sharpe ratio</a></li> <li><a class="mw-selflink selflink">Sortino ratio</a></li> <li><a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a> (<a href="/wiki/Proportional_hazards_model" title="Proportional hazards model">Proportional hazards model</a>)</li> <li><a href="/wiki/Tracking_error" title="Tracking error">Tracking error</a></li> <li><a href="/wiki/Value_at_risk" title="Value at risk">Value-at-Risk (VaR)</a> and extensions (<a href="/wiki/Profit_at_risk" title="Profit at risk">Profit at risk</a>, <a href="/wiki/Margin_at_risk" title="Margin at risk">Margin at risk</a>, <a href="/wiki/Liquidity_at_risk" title="Liquidity at risk">Liquidity at risk</a>, <a href="/wiki/Cash_flow_at_risk" class="mw-redirect" title="Cash flow at risk">Cash flow at risk</a>, <a href="/wiki/Earnings_at_risk" title="Earnings at risk">Earnings at risk</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basic concepts</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/Asset_allocation" title="Asset allocation">Asset allocation</a></li> <li><a href="/wiki/Asset_and_liability_management" title="Asset and liability management">Asset and liability management</a></li> <li><a href="/wiki/Asset_pricing" title="Asset pricing">Asset pricing</a></li> <li><a href="/wiki/Bad_debt" title="Bad debt">Bad debt</a></li> <li><a href="/wiki/Capital_asset" title="Capital asset">Capital asset</a></li> <li><a href="/wiki/Capital_structure" title="Capital structure">Capital structure</a></li> <li><a href="/wiki/Corporate_finance" title="Corporate finance">Corporate finance</a></li> <li><a href="/wiki/Cost_of_capital" title="Cost of capital">Cost of capital</a></li> <li><a href="/wiki/Diversification_(finance)" title="Diversification (finance)">Diversification</a></li> <li><a href="/wiki/Economic_bubble" title="Economic bubble">Economic bubble</a></li> <li><a href="/wiki/Enterprise_value" title="Enterprise value">Enterprise value</a></li> <li><a href="/wiki/Environmental,_social,_and_governance" title="Environmental, social, and governance">ESG</a></li> <li><a href="/wiki/Exchange_traded_fund" class="mw-redirect" title="Exchange traded fund">Exchange traded fund</a></li> <li><a href="/wiki/Expected_return" title="Expected return">Expected return</a></li> <li><a href="/wiki/Finance" title="Finance">Financial</a> <ul><li><a href="/wiki/Financial_adviser" title="Financial adviser">adviser</a></li> <li><a href="/wiki/Financial_analysis" title="Financial analysis">analysis</a></li> <li><a href="/wiki/Financial_analyst" title="Financial analyst">analyst</a></li> <li><a href="/wiki/Financial_asset" title="Financial asset">asset</a></li> <li><a href="/wiki/Financial_betting" title="Financial betting">betting</a></li> <li><a href="/wiki/Financial_crime" title="Financial crime">crime</a></li> <li><a href="/wiki/Financial_engineering" title="Financial engineering">engineering</a></li> <li><a href="/wiki/Financial_law" title="Financial law">law</a></li> <li><a href="/wiki/Financial_risk" title="Financial risk">risk</a></li> <li><a href="/wiki/Financial_social_work" title="Financial social work">social work</a></li></ul></li> <li><a href="/wiki/Fundamental_analysis" title="Fundamental analysis">Fundamental analysis</a></li> <li><a href="/wiki/Growth_investing" title="Growth investing">Growth investing</a></li> <li><a href="/wiki/Hazard" title="Hazard">Hazard</a></li> <li><a href="/wiki/Hedge_(finance)" title="Hedge (finance)">Hedge</a></li> <li><a href="/wiki/Investment_management" title="Investment management">Investment management</a></li> <li><a href="/wiki/Risk" title="Risk">Risk</a></li> <li><a href="/wiki/Risk_pool" title="Risk pool">Risk pool</a></li> <li><a href="/wiki/Risk_of_ruin" title="Risk of ruin">Risk of ruin</a></li> <li><a href="/wiki/Systematic_risk" title="Systematic risk">Systematic risk</a></li> <li><a href="/wiki/Mathematical_finance" title="Mathematical finance">Mathematical finance</a></li> <li><a href="/wiki/Moral_hazard" title="Moral hazard">Moral hazard</a></li> <li><a href="/wiki/Risk-return_spectrum" class="mw-redirect" title="Risk-return spectrum">Risk-return spectrum</a></li> <li><a href="/wiki/Speculation" title="Speculation">Speculation</a></li> <li><a href="/wiki/Speculative_attack" title="Speculative attack">Speculative attack</a></li> <li><a href="/wiki/Statistical_finance" title="Statistical finance">Statistical finance</a></li> <li><a href="/wiki/Strategic_financial_management" title="Strategic financial management">Strategic financial management</a></li> <li><a href="/wiki/Stress_test_(financial)" title="Stress test (financial)">Stress test (financial)</a></li> <li><a href="/wiki/Structured_finance" title="Structured finance">Structured finance</a></li> <li><a href="/wiki/Structured_product" title="Structured product">Structured product</a></li> <li><a href="/wiki/Systemic_risk" title="Systemic risk">Systemic risk</a></li> <li><a href="/wiki/Toxic_asset" title="Toxic asset">Toxic asset</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Financial_economics" title="Financial economics">Financial economics</a></li> <li><a href="/wiki/Investment_management" title="Investment management">Investment management</a></li> <li><a href="/wiki/Mathematical_finance" title="Mathematical finance">Mathematical finance</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Financial_ratios" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a 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(CAPE)</li> <li><a href="/wiki/Capitalization_rate" title="Capitalization rate">Capitalization rate</a> (Cap Rate)</li> <li><a href="/wiki/CROCI" class="mw-redirect" title="CROCI">Cash return on cash invested</a> (CROCI)НТЦв</li> <li><a href="/wiki/Debt-to-equity_ratio" title="Debt-to-equity ratio">Debt-to-equity</a> (D/E)</li> <li><a href="/wiki/Dividend_cover" title="Dividend cover">Dividend cover</a></li> <li><a href="/wiki/Dividend_payout_ratio" title="Dividend payout ratio">Dividend payout</a></li> <li><a href="/wiki/Earnings_yield" title="Earnings yield">Earnings yield</a> (E/P)</li> <li><a href="/wiki/EV/EBITDA" class="mw-redirect" title="EV/EBITDA">Enterprise value/EBITDA</a> (EV/EBITDA)</li> <li><a href="/wiki/EV/GCI" title="EV/GCI">Enterprise value/gross cash invested</a> (EV/GCI)</li> <li><a href="/wiki/EV/Sales" class="mw-redirect" title="EV/Sales">Enterprise value/sales</a> (EV/Sales)</li> <li><a href="/wiki/Loan-to-value_ratio" title="Loan-to-value ratio">Loan-to-value</a> (LTV)</li> <li><a href="/wiki/Omega_ratio" title="Omega ratio">Omega</a></li> <li><a href="/wiki/Operating_margin" title="Operating margin">Operating margin</a></li> <li><a href="/wiki/P/B_ratio" title="P/B ratio">Price-to-book</a> (P/B)</li> <li><a href="/wiki/Present_value_of_growth_opportunities" title="Present value of growth opportunities">Present value of growth opportunities</a> (PVGO)</li> <li><a href="/wiki/Price/cash_flow_ratio" class="mw-redirect" title="Price/cash flow ratio">Price/cash flow</a> (P/CF)</li> <li><a href="/wiki/Price%E2%80%93earnings_ratio" title="Price–earnings ratio">Price-earnings</a> (P/E)</li> <li><a href="/wiki/PEG_ratio" title="PEG ratio">Price-earnings to growth</a> (PEG)</li> <li><a href="/wiki/Price%E2%80%93sales_ratio" title="Price–sales ratio">Price-sales</a> (P/S)</li> <li><a href="/wiki/Profit_margin" title="Profit margin">Profit margin</a></li> <li><a href="/wiki/Return_on_assets" title="Return on assets">Return on assets</a> (ROA)</li> <li><a href="/wiki/Return_on_net_assets" title="Return on net assets">Return on net assets</a> (RONA)</li> <li><a href="/wiki/Return_on_capital" title="Return on capital">Return on capital</a> (ROC)</li> <li><a href="/wiki/Return_on_capital_employed" title="Return on capital employed">Return on capital employed</a> (ROCE)</li> <li><a href="/wiki/Return_on_equity" title="Return on equity">Return on equity</a> (ROE)</li> <li><a href="/wiki/Return_on_tangible_equity" title="Return on tangible equity">Return on tangible equity</a> (ROTE)</li> <li><a href="/wiki/Risk-adjusted_return_on_capital" title="Risk-adjusted return on capital">Risk-adjusted return on capital</a> (RAROC)</li> <li><a href="/wiki/Risk_return_ratio" class="mw-redirect" title="Risk return ratio">Risk return</a> (RRR)</li> <li><a href="/wiki/Sharpe_ratio" title="Sharpe ratio">Sharpe</a></li> <li><a href="/wiki/Short_interest_ratio" title="Short interest ratio">Short interest</a> (SIR)</li> <li><a class="mw-selflink selflink">Sortino</a></li> <li><a href="/wiki/Sustainable_growth_rate" title="Sustainable growth rate">Sustainable growth</a> (SGR)</li> <li><a href="/wiki/Treynor_ratio" title="Treynor ratio">Treynor</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Sortino_ratio&oldid=1222900265">https://en.wikipedia.org/w/index.php?title=Sortino_ratio&oldid=1222900265</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Financial_ratios" title="Category:Financial ratios">Financial ratios</a></li><li><a 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