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class="cdx-message__content">The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.</div></div><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Vulnerability to significant events that affect aggregate outcomes</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Systemic_risk" title="Systemic risk">systemic risk</a>.</div> <p>In <a href="/wiki/Finance" title="Finance">finance</a> and <a href="/wiki/Economics" title="Economics">economics</a>, <b>systematic risk</b> (in economics often called <b>aggregate risk</b> or <b>undiversifiable risk</b>) is vulnerability to events which affect aggregate outcomes such as broad <a href="/wiki/Financial_market" title="Financial market">market</a> returns, total economy-wide resource holdings, or aggregate income. In many contexts, events like earthquakes, epidemics and major weather catastrophes pose aggregate risks that affect not only the distribution but also the total amount of resources. That is why it is also known as contingent risk, unplanned risk or risk events. If every possible outcome of a <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> economic process is characterized by the same aggregate result (but potentially different distributional outcomes), the process then has no aggregate risk. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2></div> <p>Systematic or aggregate risk arises from market structure or dynamics which produce shocks or uncertainty faced by all agents in the market; such shocks could arise from government policy, international economic forces, or acts of nature. In contrast, <a href="/wiki/Modern_portfolio_theory#Systematic_risk_and_specific_risk" title="Modern portfolio theory">specific risk</a> (sometimes called residual risk, <b>unsystematic risk</b>, or <a href="/wiki/Idiosyncrasy#Economics" title="Idiosyncrasy">idiosyncratic risk</a>) is risk to which only specific agents or industries are vulnerable (and is uncorrelated with broad market returns).<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> Due to the idiosyncratic nature of unsystematic risk, it can be reduced or eliminated through <a href="/wiki/Diversification_(finance)" title="Diversification (finance)">diversification</a>; but since all market actors are vulnerable to systematic risk, it cannot be limited through diversification (but it may be insurable). As a result, assets whose returns are negatively correlated with broader market returns command higher prices than assets not possessing this property. </p><p>In some cases, aggregate risk exists due to institutional or other constraints on <a href="/wiki/Complete_market" title="Complete market">market completeness</a>. For countries or regions lacking access to broad <a href="/wiki/Hedge_(finance)" title="Hedge (finance)">hedging markets</a>, events like earthquakes and adverse weather shocks can also act as costly aggregate risks. <a href="/wiki/Robert_Shiller" class="mw-redirect" title="Robert Shiller">Robert Shiller</a> has found that, despite the <a href="/wiki/Globalization" title="Globalization">globalization</a> progress of recent decades, country-level aggregate income risks are still significant and could potentially be reduced through the creation of better global hedging markets (thereby potentially becoming idiosyncratic, rather than aggregate, risks).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Specifically, Shiller advocated for the creation of macro <a href="/wiki/Futures_exchange" title="Futures exchange">futures markets</a>. The benefits of such a mechanism would depend on the degree to which macro conditions are correlated across countries. </p> <div class="mw-heading mw-heading2"><h2 id="In_finance">In finance</h2></div> <p>Systematic risk plays an important role in <a href="/wiki/Asset_allocation" title="Asset allocation">portfolio allocation</a>.<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> Risk which cannot be eliminated through diversification commands returns in excess of the <a href="/wiki/Risk-free_interest_rate" class="mw-redirect" title="Risk-free interest rate">risk-free rate</a> (while idiosyncratic risk does not command such returns since it can be diversified). Over the long run, a well-diversified portfolio provides returns which correspond with its exposure to systematic risk; investors face a trade-off between expected returns and systematic risk. Therefore, an investor's desired returns correspond with their desired exposure to systematic risk and corresponding asset selection. Investors can only reduce a portfolio's exposure to systematic risk by sacrificing expected returns. </p><p>An important concept for evaluating an asset's exposure to systematic risk is <a href="/wiki/Beta_(finance)" title="Beta (finance)">beta</a>. Since beta indicates the degree to which an asset's return is correlated with broader market outcomes, it is simply an indicator of an asset's vulnerability to systematic risk. Hence, the <a href="/wiki/Capital_asset_pricing_model" title="Capital asset pricing model">capital asset pricing model (CAPM)</a> directly ties an asset's equilibrium price to its exposure to systematic risk. </p> <div class="mw-heading mw-heading3"><h3 id="A_simple_example">A simple example</h3></div> <p>Consider an investor who purchases stock in many firms from most global industries. This investor is vulnerable to systematic risk but has diversified away the effects of idiosyncratic risks on his portfolio value; further reduction in risk would require him to acquire risk-free assets with lower returns (such as <a href="/wiki/United_States_Treasury_security" title="United States Treasury security">U.S. Treasury securities</a>). On the other hand, an investor who invests all of his money in one industry whose returns are typically uncorrelated with broad market outcomes (<a href="/wiki/Beta_(finance)" title="Beta (finance)">beta</a> close to zero) has limited his exposure to systematic risk but, due to lack of diversification, is highly vulnerable to idiosyncratic risk. </p> <div class="mw-heading mw-heading2"><h2 id="In_economics">In economics</h2></div> <p>Aggregate risk can be generated by a variety of sources. <a href="/wiki/Fiscal_policy" title="Fiscal policy">Fiscal</a>, <a href="/wiki/Monetary_policy" title="Monetary policy">monetary</a>, and <a href="/wiki/Regulation" title="Regulation">regulatory</a> policy can all be sources of aggregate risk. In some cases, shocks from phenomena like weather and natural disaster can pose aggregate risks. Small economies can also be subject to aggregate risks generated by international conditions such as <a href="/wiki/Terms_of_trade" title="Terms of trade">terms of trade</a> shocks. </p><p>Aggregate risk has potentially large implications for economic growth. For example, in the presence of credit rationing, aggregate risk can cause bank failures and hinder <a href="/wiki/Capital_accumulation" title="Capital accumulation">capital accumulation</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Banks may respond to increases in profitability-threatening aggregate risk by raising standards for quality and quantity <a href="/wiki/Credit_rationing" title="Credit rationing">credit rationing</a> to reduce monitoring costs; but the practice of lending to small numbers of borrowers reduces the diversification of bank portfolios (<a href="/wiki/Concentration_risk" title="Concentration risk">concentration risk</a>) while also denying credit to some potentially productive firms or industries. As a result, capital accumulation and the overall productivity level of the economy can decline. </p><p>In economic modeling, model outcomes depend heavily on the nature of risk. Modelers often incorporate aggregate risk through shocks to endowments (<a href="/wiki/Budget_constraint" title="Budget constraint">budget constraints</a>), <a href="/wiki/Productivity" title="Productivity">productivity</a>, monetary policy, or external factors like terms of trade. Idiosyncratic risks can be introduced through mechanisms like individual labor productivity shocks; if agents possess the ability to trade assets and lack borrowing constraints, the welfare effects of idiosyncratic risks are minor. The welfare costs of aggregate risk, though, can be significant. </p><p>Under some conditions, aggregate risk can arise from the aggregation of micro shocks to individual agents. This can be the case in models with many agents and <a href="/wiki/Strategic_complements" title="Strategic complements">strategic complementarities</a>;<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> situations with such characteristics include: innovation, search and trading, production in the presence of input complementarities, and information sharing. Such situations can generate aggregate data which are empirically indistinguishable from a data-generating process with aggregate shocks. </p> <div class="mw-heading mw-heading3"><h3 id="Example:_Arrow–Debreu_equilibrium"><span id="Example:_Arrow.E2.80.93Debreu_equilibrium"></span>Example: Arrow–Debreu equilibrium</h3></div> <p>The following example is from <a href="/wiki/Mas-Colell,_Whinston,_and_Green_(1995)" class="mw-redirect" title="Mas-Colell, Whinston, and Green (1995)">Mas-Colell, Whinston, and Green (1995)</a>.<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> Consider a simple exchange economy with two identical agents, one (divisible) good, and two potential states of the world (which occur with some probability). Each agent has expected utility in the form <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 _{1}*u_{i}(x_{1i})+\pi _{2}*u_{i}(x_{2i})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>∗</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>∗</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi _{1}*u_{i}(x_{1i})+\pi _{2}*u_{i}(x_{2i})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0943d46e3a38f9555d1ce22c8e9e024fa6e39bb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.768ex; height:2.843ex;" alt="{\displaystyle \pi _{1}*u_{i}(x_{1i})+\pi _{2}*u_{i}(x_{2i})}"></span> 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 \pi _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/542cbd3dacd0a061d666ed7fc4ed7ad15b47444b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.379ex; height:2.009ex;" alt="{\displaystyle \pi _{1}}"></span> 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 \pi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b4d39c450ad33d7c407aec6fff9f225463ac1f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.379ex; height:2.009ex;" alt="{\displaystyle \pi _{2}}"></span> are the probabilities of states 1 and 2 occurring, respectively. In state 1, agent 1 is endowed with one unit of the good while agent 2 is endowed with nothing. In state 2, agent 2 is endowed with one unit of the good while agent 1 is endowed with nothing. That is, denoting the vector of endowments in state <i>i</i> 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 \omega _{i},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{i},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b76a1ded4b2b64d769506140c69d5209deb81a5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.892ex; height:2.009ex;" alt="{\displaystyle \omega _{i},}"></span> we have <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 \omega _{1}=(1,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1}=(1,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d43203d61521054c8318e3d83fd4b501856985f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.767ex; height:2.843ex;" alt="{\displaystyle \omega _{1}=(1,0)}"></span>, <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 \omega _{2}=(0,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{2}=(0,1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/072f18649ada476ddfe5d9b50a9ac7cb4eea1ec2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.767ex; height:2.843ex;" alt="{\displaystyle \omega _{2}=(0,1)}"></span>. Then the aggregate endowment of this economy is one good regardless of which state is realized; that is, the economy has no aggregate risk. It can be shown that, if agents are allowed to make trades, the ratio of the price of a claim on the good in state 1 to the price of a claim on the good in state 2 is equal to the ratios of their respective probabilities of occurrence (and, hence, the marginal rates of substitution of each agent are also equal to this ratio). That 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 p_{1}/p_{2}=\pi _{1}/\pi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}/p_{2}=\pi _{1}/\pi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8b7822d16a4d9939d7ec7e7ca03869e8eaf91f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:14.719ex; height:2.843ex;" alt="{\displaystyle p_{1}/p_{2}=\pi _{1}/\pi _{2}}"></span>. If allowed to do so, agents make trades such that their consumption is equal in either state of the world. </p><p>Now consider an example with aggregate risk. The economy is the same as that described above except for endowments: in state 1, agent 1 is endowed two units of the good while agent 2 still receives zero units; and in state 2, agent 2 still receives one unit of the good while agent 1 receives nothing. That 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 \omega _{1}=(2,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{1}=(2,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81091a85419aac61bd0c939434924497e4830433" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.767ex; height:2.843ex;" alt="{\displaystyle \omega _{1}=(2,0)}"></span>, <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 \omega _{2}=(0,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{2}=(0,1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/072f18649ada476ddfe5d9b50a9ac7cb4eea1ec2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.767ex; height:2.843ex;" alt="{\displaystyle \omega _{2}=(0,1)}"></span>. Now, if state 1 is realized, the aggregate endowment is 2 units; but if state 2 is realized, the aggregate endowment is only 1 unit; this economy is subject to aggregate risk. Agents cannot fully insure and guarantee the same consumption in either state. It can be shown that, in this case, the price ratio will be less than the ratio of probabilities of the two states: <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 p_{1}/p_{2}<\pi _{1}/\pi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo><</mo> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}/p_{2}<\pi _{1}/\pi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25303b56ace268da1ecc60a24c46f7a9eb5daab4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:14.719ex; height:2.843ex;" alt="{\displaystyle p_{1}/p_{2}<\pi _{1}/\pi _{2}}"></span>, so <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 p_{1}/\pi _{1}<p_{2}/\pi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo><</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}/\pi _{1}<p_{2}/\pi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b0fc3667ea0c0452f31bd9a1756f319d565e005" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:14.719ex; height:2.843ex;" alt="{\displaystyle p_{1}/\pi _{1}<p_{2}/\pi _{2}}"></span>. Thus, for example, if the two states occur with equal probabilities, then <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 p_{1}<p_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo><</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}<p_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bef2ca59922b6b1b78efb42528c41d6ef474f5ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:7.635ex; height:2.176ex;" alt="{\displaystyle p_{1}<p_{2}}"></span>. This is the well-known finance result that the contingent claim that delivers more resources in the state of low market returns has a higher price. </p> <div class="mw-heading mw-heading3"><h3 id="In_heterogeneous_agent_models">In heterogeneous agent models</h3></div> <p>While the inclusion of aggregate risk is common in <a href="/wiki/Macroeconomic_model" title="Macroeconomic model">macroeconomic models</a>, considerable challenges arise when researchers attempt to incorporate aggregate uncertainty into models with <a href="/wiki/Heterogeneous_agents" class="mw-redirect" title="Heterogeneous agents">heterogeneous agents</a>. In this case, the entire distribution of allocational outcomes is a <a href="/wiki/State_variable" title="State variable">state variable</a> which must be carried across periods. This gives rise to the well-known <a href="/wiki/Curse_of_dimensionality" title="Curse of dimensionality">curse of dimensionality</a>. One approach to the dilemma is to let agents ignore attributes of the aggregate distribution, justifying this assumption by referring to <a href="/wiki/Bounded_rationality" title="Bounded rationality">bounded rationality</a>. Den Haan (2010) evaluates several algorithms which have been applied to solving the Krusell and Smith (1998) model, showing that solution accuracy can depend heavily on solution method.<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><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> Researchers should carefully consider the results of accuracy tests while choosing solution methods and pay particular attention to grid selection.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (May 2014)">according to whom?</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_projects">In projects</h2></div> <p>Systematic risk exists in projects and is called the overall project risk bred by the combined effect of uncertainty in external environmental factors such as <a href="/wiki/PESTLE" class="mw-redirect" title="PESTLE">PESTLE</a>, <a href="/wiki/Volatility,_uncertainty,_complexity_and_ambiguity" class="mw-redirect" title="Volatility, uncertainty, complexity and ambiguity">VUCA</a>, etc. It is also called contingent or unplanned risk or simply uncertainty because it is of unknown likelihood and unknown impact. In contrast, systemic risk is known as the individual project risk, caused by internal factors or attributes of the project system or culture. This is also known as inherent, planned, event or condition risk caused by known unknowns such as variability or ambiguity of impact but 100% probability of occurrence. Both systemic and systematic risks are residual risk. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <ul><li><a href="/wiki/Modern_portfolio_theory" title="Modern portfolio theory">Modern portfolio theory</a></li> <li><a href="/wiki/Capital_asset_pricing_model" title="Capital asset pricing model">Capital asset pricing model</a></li> <li><a href="/wiki/Risk_modeling" class="mw-redirect" title="Risk modeling">Risk modeling</a></li> <li><a href="/wiki/Taleb_distribution" title="Taleb distribution">Taleb distribution</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.researchgate.net/figure/Systemic-risk-cube-with-three-forms-of-risks_fig2_269722642">"Figure 1: Systemic risk cube with three forms of risks"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Figure+1%3A+Systemic+risk+cube+with+three+forms+of+risks&rft_id=https%3A%2F%2Fwww.researchgate.net%2Ffigure%2FSystemic-risk-cube-with-three-forms-of-risks_fig2_269722642&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASystematic+risk" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShiller1995" class="citation journal cs1"><a href="/wiki/Robert_Shiller" class="mw-redirect" title="Robert Shiller">Shiller, R.</a> (1995). 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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 href="/wiki/Sortino_ratio" title="Sortino ratio">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 class="mw-selflink selflink">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" 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