{"id":8533,"date":"2025-01-06T09:39:00","date_gmt":"2025-01-06T09:39:00","guid":{"rendered":"https:\/\/analystprep.com\/blog\/?p=8533"},"modified":"2026-03-02T15:06:43","modified_gmt":"2026-03-02T15:06:43","slug":"portfolio-return-and-variance-calculations-for-cfa-and-frm-exams","status":"publish","type":"post","link":"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/","title":{"rendered":"Portfolio Return and Variance: A Practical Guide for CFA\u00ae and FRM\u00ae Candidates"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What is portfolio return and how is it calculated?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Portfolio return is the weighted average of individual asset returns in a portfolio. It is calculated as the sum of each asset's return multiplied by its portfolio weight.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"How do you calculate portfolio variance?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Portfolio variance measures the total risk of a portfolio. It is calculated using the individual variances of assets and their covariances, weighted by the square of their proportions in the portfolio.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Why is the correlation coefficient important in portfolio theory?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The correlation coefficient determines how two assets move relative to each other. A lower or negative correlation helps reduce overall portfolio risk, making diversification more effective.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What is the minimum variance portfolio (MVP)?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The minimum variance portfolio is the combination of assets that results in the lowest possible portfolio variance, offering the most efficient risk-return trade-off.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"How does diversification reduce risk?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Diversification reduces unsystematic risk by spreading investments across uncorrelated or negatively correlated assets, which smooths out fluctuations from individual asset performance.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Why should CFA and FRM candidates study portfolio return and variance?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Understanding portfolio return and variance is critical for CFA and FRM candidates as it forms the foundation of modern portfolio theory and risk management principles frequently tested in both exams.\"\n      }\n    }\n  ]\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What is the difference between portfolio variance and covariance?\",\n    \"text\": \"What is the difference between portfolio variance and covariance?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Covariance measures how two assets move together. Portfolio variance uses those covariances, along with asset weights and individual risks, to measure the portfolio\\u2019s total risk.\",\n      \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#portfolio-faq-variance-vs-covariance\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What is the difference between portfolio variance and modern portfolio theory?\",\n    \"text\": \"What is the difference between portfolio variance and modern portfolio theory?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Modern Portfolio Theory is the framework for building diversified portfolios. Portfolio variance is the risk metric it relies on to quantify how risky a given portfolio is.\",\n      \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#portfolio-faq-variance-vs-mpt\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"How do you calculate portfolio variance?\",\n    \"text\": \"How do you calculate portfolio variance?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"For a two-asset portfolio, variance is \\u03c3\\u209a\\u00b2 = w\\u2093\\u00b2\\u03c3\\u2093\\u00b2 + w\\u1e8f\\u00b2\\u03c3\\u1e8f\\u00b2 + 2w\\u2093w\\u1e8f\\u03c3\\u2093\\u03c3\\u1e8f\\u03c1\\u2093\\u1e8f, combining weights, individual variances and their correlation. With more assets, you extend the formula to include all pairs.\",\n      \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#portfolio-faq-calc-variance\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Why is portfolio variance important?\",\n    \"text\": \"Why is portfolio variance important?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Portfolio variance captures the overall risk of a portfolio, including diversification effects, so investors can see how the mix of assets affects total volatility.\",\n      \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#portfolio-faq-why-variance-matters\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"How do you calculate portfolio risk?\",\n    \"text\": \"How do you calculate portfolio risk?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Portfolio risk is the standard deviation of portfolio returns. You first compute portfolio variance using the weights, variances and correlations, then take the square root.\",\n      \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#portfolio-faq-calc-risk\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"How do you calculate portfolio return?\",\n    \"text\": \"How do you calculate portfolio return?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Portfolio return is the weighted average of asset returns: E(Rp) = \\u2211 w\\u1d62 r\\u1d62, where each asset\\u2019s expected return is multiplied by its portfolio weight and then summed.\",\n      \"dateCreated\": \"2025-01-06T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#portfolio-faq-calc-return\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n\n\n<p>Picture this\u2014you\u2019re sitting down to tackle the world of portfolio management, trying to make sense of concepts such as risk, return, and variance.<\/p>\n\n\n\n<p>Sound intimidating?<\/p>\n\n\n\n<p>Don\u2019t worry; it doesn\u2019t have to be. <a href=\"https:\/\/analystprep.com\/\">AnalystPrep<\/a>&nbsp;is here to walk you through these critical ideas step by step.<\/p>\n\n\n\n<p>Why does this matter?<\/p>\n\n\n\n<p>If you\u2019re preparing for the CFA\u00ae or FRM\u00ae exams or simply want to sharpen your skills in the real world, grasping these fundamentals is non-negotiable. Concepts like the portfolio return formula, portfolio risk formula, and portfolio variance formula aren\u2019t just exam material\u2014they\u2019re tools that financial professionals use every day to make smarter investment decisions.<\/p>\n\n\n\n<p>This guide is more than just theory; it\u2019s about mastering the formulas, understanding their purpose, and knowing when to apply them. By the time we\u2019re done, you\u2019ll be able to break down portfolio risk and return calculations with confidence.<\/p>\n\n\n\n<p>Let\u2019s get to the bottom of it, shall we?<\/p>\n\n\n\n<div style=\"background:#f3f4f6; padding:16px 14px; border-radius:12px; margin:20px 0; text-align:center;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:inline-flex; align-items:center; justify-content:center; padding:12px 18px; border:2px solid #1d4ed8; border-radius:999px; color:#1d4ed8; text-decoration:none; font-weight:600; font-size:16px; line-height:1; background:#ffffff; white-space:nowrap;\">\n    Test your portfolio return and variance calculations with a free trial\n  <\/a>\n<\/div>\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_80 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Portfolio_Expected_Return\" >Portfolio Expected Return<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Example_1_Portfolio_Expected_Return\" >Example 1: Portfolio Expected Return<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Understanding_the_Markowitz_Portfolio_Theory\" >Understanding the Markowitz Portfolio Theory<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#What_does_it_mean\" >What does it mean?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Why_You_Should_Care\" >Why You Should Care?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#The_Role_of_Standard_Deviation_in_Portfolio_Risk\" >The Role of Standard Deviation in Portfolio Risk<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#The_Big_Picture\" >The Big Picture<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Managing_Portfolio_Risk_with_Minimum_Variance_Portfolios\" >Managing Portfolio Risk with Minimum Variance Portfolios<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Minimum_Variance_Portfolio_MVP_Formula\" >Minimum Variance Portfolio (MVP) Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#The_Practical_Takeaway\" >The Practical Takeaway<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Why_Does_This_Matter\" >Why Does This Matter?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Practical_Application_Why_These_Formulas_Matter\" >Practical Application: Why These Formulas Matter<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Frequently_Asked_Questions_FAQs_About_Portfolio_Variance_Risk_and_Return\" >Frequently Asked Questions (FAQs) About Portfolio Variance, Risk, and Return<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#What_is_the_difference_between_portfolio_variance_and_covariance\" >What is the difference between portfolio variance and covariance?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#What_is_the_difference_between_portfolio_variance_and_modern_portfolio_theory\" >What is the difference between portfolio variance and modern portfolio theory?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#How_do_you_calculate_portfolio_variance\" >How do you calculate portfolio variance?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#Why_is_portfolio_variance_important\" >Why is portfolio variance important?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#How_do_you_calculate_portfolio_risk\" >How do you calculate portfolio risk?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/analystprep.com\/blog\/portfolio-return-and-variance-calculations-for-cfa-and-frm-exams\/#How_do_you_calculate_portfolio_return\" >How do you calculate portfolio return?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Portfolio_Expected_Return\"><\/span><span class=\"primary-color\"><br \/>Portfolio Expected Return<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let\u2019s cut to the chase\u2014calculating the portfolio expected return is all about simplicity and strategy. Think of it as a way to summarize your portfolio&#8217;s performance by weighing the returns of each asset.<\/p>\n<p>If that sounds complex, don\u2019t worry. It\u2019s just math with a purpose.<\/p>\n<p>Here\u2019s the formula that gets the job done:<\/p>\n<p>$${E(R_p)}=\\sum_{i=1}^n{w_ir_i}$$<\/p>\n<p>Where:<\/p>\n<p>\\(i\\) = \\(1, 2, 3, &#8230;, n\\) <em>= <\/em>individual assets in the portfolio.<\/p>\n<p>\\(w_i\\) = the weight attached to asset \\(i\\); and<\/p>\n<p>\\(r_i\\) = expected return of each asset \\(i\\).<\/p>\n<p>Let\u2019s break it down.<\/p>\n<p>The weight of an asset (wiw_iwi\u200b) is simply its market value relative to the total market value of the portfolio. Here\u2019s the formula for that:<\/p>\n<p>$$w_i = \\frac{\\text{Market Value of Asset}}{\\text{Market Value of Portfolio}}$$<\/p>\n<p>So, when you calculate the expected return of a portfolio, you\u2019re really just taking each asset\u2019s return, multiplying it by its weight, and adding it all up. This is the essence of balancing portfolio risk and return, a skill every <a href=\"https:\/\/www.cfainstitute.org\/programs\/cfa-program#overview\">CFA\u00ae<\/a> or <a href=\"https:\/\/www.garp.org\/frm\">FRM\u00ae<\/a> candidate should master.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Example_1_Portfolio_Expected_Return\"><\/span><span class=\"primary-color\">Example 1: Portfolio Expected Return<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Let\u2019s bring this to life with a quick example.<\/p>\n<p>Say your portfolio is split evenly\u201450% in stocks and 50% in bonds. The expected return for stocks is 8%, while bonds sit at 6%. What\u2019s the portfolio&#8217;s expected return?<\/p>\n<p>Here\u2019s the calculation:<\/p>\n<p>$$\\begin{align*}{E(R_p)}&amp;=\\sum_{i=1}^n{w_ir_i}\\\\ &amp; = (0.5 \\times 0.08) + (0.5 \\times 0.06) = 0.07 \\ \\text{or} \\ 7\\%\\end{align*}$$<\/p>\n<p>Simple, right?<\/p>\n<p>By weighing each asset\u2019s contribution, you get a clear picture of your portfolio\u2019s overall performance. And the best part? This approach works no matter how many assets you\u2019re juggling.<\/p>\n<p>The expected return of a portfolio formula is your first step in understanding the intricate dance between risk and return. But don\u2019t stop here\u2014mastering this calculation opens the door to managing portfolio risk and optimizing returns.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Understanding_the_Markowitz_Portfolio_Theory\"><\/span><strong>Understanding the Markowitz Portfolio Theory<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Imagine sitting across from <a href=\"https:\/\/www.google.com\/url?client=internal-element-cse&amp;cx=d3e808ce541fcebf5&amp;q=https:\/\/corporatefinanceinstitute.com\/resources\/career-map\/sell-side\/capital-markets\/harry-markowitz\/&amp;sa=U&amp;ved=2ahUKEwjJ3NGDr8uKAxWTK_sDHQoPIqMQFnoECAYQAQ&amp;usg=AOvVaw3hnqAVc05Y0sYw6iXH1A1k&amp;fexp=72801196,72801194,72801195\">Harry Markowitz<\/a> himself, the brain behind one of the most influential theories in finance.<\/p>\n<p>His big idea?<\/p>\n<p>Diversification isn\u2019t just a buzzword\u2014it\u2019s the secret sauce to managing portfolio risk and optimizing returns. He showed the world how to minimize risk without compromising the potential for great returns.<\/p>\n<p>Now, that\u2019s revolutionary.<\/p>\n<p>At the heart of the <a href=\"https:\/\/www.google.com\/url?client=internal-element-cse&amp;cx=d3e808ce541fcebf5&amp;q=https:\/\/www.investopedia.com\/terms\/h\/harrymarkowitz.asp&amp;sa=U&amp;ved=2ahUKEwjJ3NGDr8uKAxWTK_sDHQoPIqMQFnoECAwQAQ&amp;usg=AOvVaw2wBCuVgAc2gkNUjP37JaBU&amp;fexp=72801196,72801194,72801195\">Markowitz Portfolio Theory<\/a> lies a formula that evaluates portfolio variance, the measure of how risky your investments are when considered together.<\/p>\n<p>Let\u2019s unpack it:<\/p>\n<p>$$\\begin{align*}\\text{Portfolio variance}&amp;=\\sigma_p^2 \\\\&amp;={w_X^2\\sigma_X^2}+{w_Y^2\\sigma_Y^2}+2w_Xw_Y{\\sigma_X}{\\sigma_Y}{\\rho_{XY}}\\end{align*}$$<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_does_it_mean\"><\/span><strong>What does it mean?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\\(w_X, w_Y\\)\u200b: These are the weights of assets \\(X\\) and \\(Y\\) in the portfolio. Think of them as the slices of a pie chart that represent how much of each asset you\u2019re holding.<\/li>\n<li>\\(\\sigma_X, \\sigma_Y\\): These represent the standard deviations of assets \\(X\\)and \\(Y\\), which is just a fancy way of saying their individual risks.<\/li>\n<li>\\(\\rho_{XY}\\): This is the correlation coefficient between \\(X\\)and \\(Y\\)\u2014a measure of how these two assets move together.<\/li>\n<\/ul>\n<p>Why is this formula such a big deal?<\/p>\n<p>It\u2019s the foundation for calculating the risk and return of a portfolio. It doesn\u2019t just look at individual asset risks. Instead, it takes into account how these assets interact with each other, whether they\u2019re positively correlated, negatively correlated, or somewhere in between.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Why_You_Should_Care\"><\/span><strong>Why You Should Care?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here\u2019s the beauty of it: the Markowitz Portfolio Theory formula makes portfolio risk management a science rather than a guessing game. It helps you balance your portfolio to achieve maximum returns for a given level of risk or minimize risk for a specific return target.<\/p>\n<p>Think of it as your personal portfolio risk calculator, giving you the power to see how tweaking asset weights impacts total risk.<\/p>\n<p>The bottom line?<\/p>\n<p>Understanding this theory is essential for <a href=\"https:\/\/analystprep.com\/cfa\/\">CFA\u00ae<\/a> and <a href=\"https:\/\/analystprep.com\/frm\/\">FRM\u00ae<\/a> candidates. It\u2019s not just an exam concept; it\u2019s a real-world tool for building smarter portfolios and managing portfolio total risk.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Role_of_Standard_Deviation_in_Portfolio_Risk\"><\/span><strong>The Role of Standard Deviation in Portfolio Risk<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let\u2019s get one thing straight: portfolio risk is not just the sum of all individual asset risks. That would be too easy, wouldn\u2019t it? Instead, we use the standard deviation of a portfolio to measure its total risk, capturing both systematic and unsystematic components. What makes this fascinating is how the correlation between assets comes into play, reducing overall risk compared to simply adding up individual volatilities.<\/p>\n<p>Here\u2019s the formula that brings it all together:<\/p>\n<p>$$\\begin{align*}\\text{Portfolio standard deviation}&amp;=\\sqrt{\\text{Portfolio Variance}}\\\\ &amp;=\\sqrt{\\sigma_p^2}\\\\ &amp;=\\sqrt{{w_X^2\\sigma_X^2}+{w_Y^2\\sigma_Y^2}+2w_Xw_Y\\sigma_X\\sigma_Y\\rho_{XY}}\\end{align*}$$<\/p>\n<p>Now, let\u2019s break it down:<\/p>\n<ul>\n<li>\\(w_X, w_Y\\)\u200b: These are the weights of assets \\(X\\) and \\(Y\\). They tell us how much each asset contributes to the overall portfolio.<\/li>\n<li>\\(\\sigma_X, \\sigma_Y\\): These are the standard deviations\u2014or individual risks\u2014of assets \\(X\\)and \\(Y\\).<\/li>\n<li>\\(\\rho_{XY}\\): This is the correlation coefficient between \\(X\\) and \\(Y\\), showing how these assets move relative to each other.<\/li>\n<\/ul>\n<p>The formula is like a finely tuned machine that balances all these factors to calculate portfolio total risk.<\/p>\n<p><strong>Example 2: Let\u2019s Crunch the Numbers<\/strong><\/p>\n<p>Picture this: you have a portfolio with two assets, Asset A and Asset B. Here\u2019s the setup:<\/p>\n<ul>\n<li>Asset A: w = 80%, \\(\\sigma\\) = 16%.<\/li>\n<li>Asset B: w=20%, \\(\\sigma\\) =25%.<\/li>\n<li>Correlation:\\(\\rho = 0.6\\).<\/li>\n<\/ul>\n<p>First, calculate the portfolio variance:<\/p>\n<p>$$\\begin{align*}\\text{Portfolio variance}=&amp;{w_X^2\\sigma_X^2}+{w_Y^2\\sigma_Y^2}+2w_Xw_Y{\\sigma_X}{\\sigma_Y}{\\rho_{XY}}\\\\=&amp;{(0.8)^2}\\times{(0.16)^2}+{(0.2)^2}\\times{(0.25)^2}+\\\\&amp;2(0.8)(0.2)(0.16)(0.25)(0.6)\\\\=&amp;2.66\\%\\end{align*}$$<\/p>\n<p>Next, take the square root to get the portfolio standard deviation:<\/p>\n<p>$$\\begin{align*}\\text{Portfolio standard deviation}=&amp;\\sqrt{{w_X^2\\sigma_X^2}+{w_Y^2\\sigma_Y^2}+2w_Xw_Y\\sigma_X\\sigma_Y\\rho_{XY}}\\\\=&amp;\\sqrt{2.66\\%}\\\\=&amp;16.3\\%\\end{align*}$$<\/p>\n<p>What does this tell us?<\/p>\n<p>Despite one asset having a high volatility, the interaction between the two assets\u2014thanks to their weights and correlation\u2014keeps the overall portfolio risk in check. This is why portfolio risk management is all about balancing these dynamics.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Big_Picture\"><\/span><strong>The Big Picture<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Understanding the portfolio risk formula is more than just a math exercise. It\u2019s a practical tool for managing portfolio total risk in both exams and real life. Whether you&#8217;re handling portfolio risk and return questions and answers on exam day or making real-world investment decisions, this knowledge is your competitive edge.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Managing_Portfolio_Risk_with_Minimum_Variance_Portfolios\"><\/span><strong>Managing Portfolio Risk with Minimum Variance Portfolios<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Have you ever wondered if there\u2019s a way to balance risk and return without sweating over every market fluctuation? That\u2019s exactly where the minimum variance portfolio (MVP) comes into play. It\u2019s like the holy grail for risk-conscious investors. The MVP focuses on achieving the lowest possible portfolio risk for a given level of expected return. Think of it as a strategy that optimizes the weights of your assets to minimize overall portfolio variance.<\/p>\n<p>So, how does it work?<\/p>\n<p>Let\u2019s break down the formula that makes it all happen.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Minimum_Variance_Portfolio_MVP_Formula\"><\/span><strong>Minimum Variance Portfolio (MVP) Formula<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For a two-asset portfolio, the optimal weights \\(w_X\\) and \\(w_Y\\) are calculated using:<\/p>\n<p>$$\\begin{align}w_X &amp;= \\frac{\\sigma_Y^2 &#8211; \\rho_{XY} \\sigma_X \\sigma_Y}{\\sigma_X^2 + \\sigma_Y^2 &#8211; 2 \\rho_{XY} \\sigma_X \\sigma_Y}\\\\w_Y &amp;= 1 &#8211; w_X\\end{align}$$\u200b<\/p>\n<p>Here\u2019s what these components mean:<\/p>\n<ul>\n<li>\\(w_X, w_Y\\): These are the asset weights that minimize your portfolio variance. They\u2019re the magic numbers you need for your portfolio risk management strategy.<\/li>\n<li>\\(\\sigma_X, \\sigma_Y\\)\u200b: The standard deviations of assets \\(X\\) and \\(Y\\), representing their individual risks.<\/li>\n<li>\\(\\rho_{XY}\\): The correlation coefficient between the two assets, which determines how their returns move relative to each other.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"The_Practical_Takeaway\"><\/span><strong>The Practical Takeaway<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>At its core, the MVP isn\u2019t just about minimizing risk\u2014it\u2019s about doing so intelligently. By leveraging tools like the portfolio risk calculator or mastering the portfolio variance formula, you can navigate risk and return decisions with confidence. And that\u2019s exactly what separates good investors from great ones.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Why_Does_This_Matter\"><\/span><strong>Why Does This Matter?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Think about it.<\/p>\n<p>You\u2019re sitting down to build a portfolio, whether for an investor or yourself. Now, wouldn\u2019t it be incredible to know exactly how much of each asset to allocate to achieve the lowest possible risk? That\u2019s the beauty of the minimum variance portfolio formula. It doesn\u2019t leave you guessing. Instead, it gives you a precise way to calculate asset weights, helping you strike the perfect balance between risk and return.<\/p>\n<p>But let\u2019s not stop at theory.<\/p>\n<p>This formula isn\u2019t just for crunching numbers in a textbook or acing <a href=\"https:\/\/www.garp.org\/_hcms\/analytics\/search\/conversion?redirect=aHR0cHM6Ly93d3cuZ2FycC5vcmcvdmlkZW8vYWdncmVnYXRpb24tb2YtcG9ydGZvbGlvLXJpc2s%3D&amp;ct=SEARCH&amp;pid=20013225&amp;cid=58959704973&amp;t=cG9ydGZvbGlvIHJpc2s%3D&amp;d=www.garp.org&amp;c=2&amp;c=3&amp;c=6&amp;rp=1&amp;ab=false&amp;opcid=&amp;rs=UNKNOWN&amp;hs-expires=1766956554&amp;hs-version=1&amp;hs-signature=APUk-v6_aou1VoNnH25kfH2wi8L3-v_6Uw\">portfolio risk<\/a> and return questions and answers on your CFA\u00ae or FRM\u00ae exam. It\u2019s a practical tool you\u2019ll turn to time and again in real-world portfolio risk management. From choosing the right asset mix to minimizing volatility, the MVP formula is a cornerstone of informed decision-making.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Practical_Application_Why_These_Formulas_Matter\"><\/span><strong>Practical Application: Why These Formulas Matter<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here\u2019s the thing\u2014understanding these formulas isn\u2019t just about passing your exams (although that\u2019s a big plus). They\u2019re the foundation of financial decision-making. Imagine sitting in a meeting, confidently discussing the portfolio risk formula or explaining how you optimized weights using the minimum variance portfolio formula. You\u2019re not just showcasing your expertise; you\u2019re demonstrating what it means to be a true finance professional.<\/p>\n<p>Whether you\u2019re wading into portfolio variance calculations, figuring out the standard deviation of a portfolio formula, or applying these tools in a portfolio risk calculator, these formulas empower you to make smarter, data-driven decisions. They give you an edge\u2014both in the classroom and the boardroom.<\/p>\n<p>So, the next time you see a complex formula like this, don\u2019t shy away. Instead, see it as a gateway to mastering portfolio total risk, fine-tuning asset allocation, and excelling in risk and return of portfolio strategies. That\u2019s the kind of expertise that sets you apart.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_FAQs_About_Portfolio_Variance_Risk_and_Return\"><\/span><strong>Frequently Asked Questions (FAQs) About Portfolio Variance, Risk, and Return<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h4><span class=\"ez-toc-section\" id=\"What_is_the_difference_between_portfolio_variance_and_covariance\"><\/span><strong>What is the difference between portfolio variance and covariance?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Think of portfolio variance as the bigger picture and covariance as a piece of the puzzle.<\/p>\n<ul>\n<li><strong>Portfolio Variance<\/strong>: This calculates the total risk of a portfolio, considering how all the assets interact with one another. It uses the weights of assets, their individual risks, and their correlations to give you a comprehensive measure of risk.<\/li>\n<li><strong>Covariance<\/strong>: This shows how two assets move in relation to each other\u2014whether they rise and fall together or move in opposite directions.<\/li>\n<\/ul>\n<p>In short, covariance measures the relationship between assets, while portfolio variance uses that relationship to calculate the portfolio&#8217;s total risk. Without covariance, there\u2019s no portfolio variance.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"What_is_the_difference_between_portfolio_variance_and_modern_portfolio_theory\"><\/span><strong>What is the difference between portfolio variance and modern portfolio theory?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Modern Portfolio Theory (MPT) is the strategy; portfolio variance is the tool.<\/p>\n<p>MPT, developed by Harry Markowitz, is all about diversification\u2014mixing assets to balance risk and return. Portfolio variance, on the other hand, is the mathematical calculation that tells you how risky your portfolio is.<\/p>\n<p>While MPT helps you design an efficient portfolio, portfolio variance is how you measure the success of that design. The two go hand in hand, but one provides the philosophy, and the other does the math.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"How_do_you_calculate_portfolio_variance\"><\/span><strong>How do you calculate portfolio variance?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>It might sound complex, but once you get the hang of it, it\u2019s straightforward.<\/p>\n<p>Here\u2019s the formula for a two-asset portfolio:<\/p>\n<p>$$\\sigma_p^2=w_X^2\\sigma_X^2 + w_Y^2 \\sigma_Y^2 + 2w_Xw_Y \\sigma_X \\sigma_Y \\rho_{XY}$$<\/p>\n<ul>\n<li><strong>Weights<\/strong> <strong>(<\/strong>\\(\\mathbf{w_X, w_Y}\\)<strong> )<\/strong>: How much of each asset is in your portfolio.<\/li>\n<li><strong>Variances (<\/strong>\\(\\mathbf{\\sigma_X^2,\\sigma_X^2}\\)<strong>)<\/strong>: The individual risk of each asset.<\/li>\n<li><strong>Correlation (<\/strong>\\(\\mathbf{\\rho_{XY}}\\)<strong>)<\/strong>: How assets move together.<\/li>\n<\/ul>\n<p>You\u2019ll plug these values into the formula, calculate the components, and sum them up. If your portfolio has many assets, you\u2019ll use the expanded version of the formula to include all their relationships.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Why_is_portfolio_variance_important\"><\/span><strong>Why is portfolio variance important?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Because risk isn\u2019t just about individual assets\u2014it\u2019s about how they work together.<\/p>\n<p>Portfolio variance helps you see the total risk of your portfolio, not just the sum of its parts. It factors in diversification, showing you how combining assets with different behaviors can lower risk.<\/p>\n<p>This insight is crucial. Whether you\u2019re fine-tuning investments or answering exam questions, understanding portfolio variance is the key to managing risk like a pro.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"How_do_you_calculate_portfolio_risk\"><\/span><strong>How do you calculate portfolio risk?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Portfolio risk is the standard deviation of your portfolio, and here\u2019s the formula you need for a two-asset portfolio:<\/p>\n<p>$$\\sigma_p = \\sqrt{w_X^2 \\sigma_X^2 + w_Y^2 \\sigma_Y^2 + 2w_Xw_Y \\sigma_X \\sigma_Y \\rho_{XY}}$$<\/p>\n<p>Start with the portfolio variance formula, calculate the variance, and then take the square root to find the standard deviation.<\/p>\n<p>This isn\u2019t just about math. It\u2019s about understanding how volatile your portfolio is. The lower the portfolio risk, the more stable your returns.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"How_do_you_calculate_portfolio_return\"><\/span><strong>How do you calculate portfolio return?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Portfolio return is simpler than it sounds. It\u2019s just a weighted average of the returns of your assets.<\/p>\n<p>$${E(R_p)}=\\sum_{i=1}^n{w_ir_i}$$<\/p>\n<p>Here\u2019s how it works:<\/p>\n<ol>\n<li>Multiply each asset&#8217;s weight by its expected return.<\/li>\n<li>Add those numbers together.<\/li>\n<\/ol>\n<p>For example, if 70% of your portfolio is in stocks with an 8% return and 30% in bonds with a 5% return, your portfolio return would be:<\/p>\n<p>$$E(R_p) = (0.7 \\times 0.08) + (0.3 \\times 0.05) = 0.071 \\ \\text{ or }\\\u00a0 7.1\\%$$<\/p>\n<p><strong>Related Articles<\/strong><\/p>\n<p>If you found this guide insightful, you\u2019ll love exploring these related topics. Each article is designed to expand your understanding and equip you with valuable tools for your journey in finance:<\/p>\n<ul>\n<li><a href=\"https:\/\/analystprep.com\/blog\/top-formulas-to-help-you-pass-cfa-exams\/\">Top Formulas to Help You Pass CFA Exams<\/a><\/li>\n<li><a href=\"https:\/\/analystprep.com\/blog\/reasons-why-investment-management-is-a-great-career-for-you\/\">Reasons Why Investment Management Is a Great Career for You<\/a><\/li>\n<li><a href=\"https:\/\/analystprep.com\/blog\/frm-syllabus\/\">FRM Syllabus<\/a><\/li>\n<li><a href=\"https:\/\/analystprep.com\/blog\/which-books-are-good-for-frm-part-i\/\">Which Books Are Good for FRM Part I?<\/a><\/li>\n<\/ul>\n<p>Each link opens a new door to deeper knowledge and preparation strategies. Best wishes!<\/p>\n<p><blockquote class=\"wp-embedded-content\" data-secret=\"pUIP0xSZj1\"><a href=\"https:\/\/analystprep.com\/shop\/frm-part-1-and-part-2-complete-course-by-analystprep\/\">FRM Part 1 and Part 2 Complete Online Course<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;FRM Part 1 and Part 2 Complete Online Course&#8221; &#8212; AnalystPrep\" src=\"https:\/\/analystprep.com\/shop\/frm-part-1-and-part-2-complete-course-by-analystprep\/embed\/#?secret=kMS7sz0JkI#?secret=pUIP0xSZj1\" data-secret=\"pUIP0xSZj1\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n\n\n<div style=\"margin: 40px 0; padding: 30px; text-align: center; background-color: #f5f8fc; border-radius: 10px;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     class=\"ap-cta\"\n     data-cta-text=\"Start Free Trial\"\n     data-cta-type=\"button\"\n     data-cta-location=\"bottom_content\"\n     data-page-type=\"blog\"\n     style=\"\n       display: inline-block;\n       padding: 14px 26px;\n       font-size: 18px;\n       font-weight: 700;\n       color: #ffffff;\n       background-color: #0b5ed7;\n       border-radius: 8px;\n       text-decoration: none;\n     \">\n    Start Free Trial \u2192\n  <\/a>\n  <p style=\"margin-top: 12px; font-size: 15px; color: #333;\">\n    Practice portfolio\u2011return &#038; risk problems with full worked solutions and CFA\u00ae\u2011style question sets.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Picture this\u2014you\u2019re sitting down to tackle the world of portfolio management, trying to make sense of concepts such as risk, return, and variance. Sound intimidating? Don\u2019t worry; it doesn\u2019t have to be. AnalystPrep&nbsp;is here to walk you through these critical&#8230;<\/p>\n","protected":false},"author":11,"featured_media":12141,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[70,71],"tags":[78,83,89],"class_list":["post-8533","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cfa","category-frm","tag-cfa","tag-frm","tag-standard-deviation-of-portfolio","blog-post","animate"],"acf":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/comments?post=8533"}],"version-history":[{"count":48,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8533\/revisions"}],"predecessor-version":[{"id":14187,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8533\/revisions\/14187"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media\/12141"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media?parent=8533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/categories?post=8533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/tags?post=8533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}