{"id":589,"date":"2019-10-10T13:27:00","date_gmt":"2019-10-10T13:27:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=589"},"modified":"2026-01-26T06:30:56","modified_gmt":"2026-01-26T06:30:56","slug":"covariance-joint-probability","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/","title":{"rendered":"Calculating Covariance Given a Joint Probability Function"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Probability Concepts (2021 Level I CFA\u00ae Exam \u2013 Reading 8)\",\n  \"description\": \"This lecture on probability concepts for CFA Level 1 covers definitions, types of probabilities, odds, conditional and unconditional probabilities, rules like multiplication and total probability, Bayes' theorem, portfolio analysis, covariance, and counting methods such as permutations and combinations. It emphasizes practical applications for finance and investment decision-making.\",\n  \"uploadDate\": \"2021-11-01T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/hu47ZbsskEw\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/hu47ZbsskEw\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw\",\n  \"duration\": \"PT48M33S\"\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\": \"The following table represents the estimated returns for two motor vehicle production brands \u2013 TY and Ford, in 3 industrial environments: strong (50% probability), average (30% probability) and weak (20% probability).\",\n    \"text\": \"Given the above joint probability function, the covariance between TY and Ford returns is closest to:\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C.\\n\\nFirst, we must start by calculating the expected return for each brand:\\n\\nExpected return for TY = (0.5 * 6%) + (0.3 * 3%) + (0.2 * (-1%)) = 3.7%\\n\\nExpected return for Ford = (0.5 * 10%) + (0.3 * 4%) + (0.2 * (-4%)) = 5.29%\\n\\nNext, we can now compute the covariance:\\n\\nCovariance = 0.5(6%-3.7%)(10%-5.4%) + 0.3(3%-3.7%)(4%-5.4%) + 0.2(-1%-3.7%)(-4%-5.4%) = 5.29% + 0.294% + 8.836% = 0.1442\"\n    }\n  }\n}\n<\/script>\n\n\n\n<p><iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n<\/p>\n<p>Covariance between variables can be calculated in two ways. One method is the historical <span class=\"fontstyle0\">sample covariance between two random variables \\(X_i\\)<\/span><span class=\"fontstyle2\">&nbsp;<\/span><span class=\"fontstyle0\">and \\(Y_i\\). It is <\/span><span class=\"fontstyle0\">based on a sample of past data of size n and is given by:<\/span><\/p>\n<p>$$\\text{Cov}_{X_i,Y_i}=\\frac{\\sum_{i=1}^{n}{(X_i -\\bar{X})(Y_i -\\bar{Y})}}{n-1}$$<\/p>\n<p>Alternatively, covariance can be defined as <span class=\"fontstyle0\">probability-weighted average of the cross-products of each random variable\u2019s deviation from its own expected value.<\/span> That is:<\/p>\n<p>$$\\text{Cov}_{X_i,Y_i}=E\\left[(X_i -\\bar{X})(Y_i -\\bar{Y})\\right]$$<\/p>\n<p>Consider the following example:<\/p>\n<p><!--more--><\/p>\n<h2><strong>Example<\/strong><\/h2>\n<p>Assume that we want to find the variance of each asset and the covariance between the returns of ABC and XYZ, given that the amount invested in each company is $1,000.<\/p>\n<p>This table is used to calculate the expected returns:<\/p>\n<p>$$ \\begin{array}{c|c|c|c} &amp; \\textbf{Strong Economy} &amp; \\textbf{Normal Economy} &amp; \\textbf{Week Economy} \\\\ \\hline \\text{Probability} &amp; {15\\%} &amp; {60\\%} &amp; {25\\%} \\\\ \\hline \\text{ABC Returns} &amp; {40\\%} &amp; {20\\%} &amp; {0} \\\\ \\hline \\text{XYZ Returns} &amp; {20\\%} &amp; {15\\%} &amp; {4\\%} \\\\ \\end{array} $$<\/p>\n<h3><strong><br>Solution<\/strong><\/h3>\n<p>For us to find the covariance, we must calculate the expected return of each asset as well as their variances. The assets weights are:<\/p>\n<p>$$ \\text W_{\\text{ABC}}=\\cfrac {1000}{2000} = 0.5 $$<\/p>\n<p>$$ \\text W_{\\text{XYZ}}=\\cfrac {1000}{2000} = 0.5 $$<\/p>\n<p>Next, we should calculate the individual expected returns:<\/p>\n<p>$$ \\text E(\\text R_{\\text{ABC}}) = 0.15 * 0.40 + 0.60 * 0.2 + 0.25 * 0.00 = 0.18 $$<\/p>\n<p>$$ \\text E(\\text R_{\\text{XYZ}}) = 0.15 * 0.2 + 0.60 * 0.15 + 0.25 * 0.04 = 0.13 $$<\/p>\n<p>Finally, we can compute the covariance between the returns of the two assets:<\/p>\n<p>$$ \\begin{align*}<br>\\text{Cov}(\\text R_{\\text{ABC},\\text{XYZ}}) &amp;= 0.15(0.40 \u2013 0.18)(0.20 \u2013 0.13) \\\\<br>&amp; + 0.6(0.20 \u2013 0.18)(0.15 \u2013 0.13) \\\\<br>&amp; + 0.25(0.00 \u2013 0.18)(0.04 \u2013 0.13) \\\\<br>&amp; = 0.0066<br>\\end{align*} $$<\/p>\n<p>Interpretation: since covariance is positive, the two returns show some co-movement, though it&#8217;s a weak one.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>The following table represents the estimated returns for two motor vehicle production brands \u2013 TY and Ford, in 3 industrial environments: strong (50% probability), average (30% probability) and weak (20% probability).<\/p>\n<p>$$ \\begin{array}{c|c|c|c} {} &amp; \\text{TY Returns +6%} &amp; \\text{TY Returns +3%} &amp; \\text{TY Returns -1%} \\\\ \\hline {\\text{Ford Sales }+10\\%} &amp; \\text{Strong(0.5)} &amp; {} &amp; {} \\\\ \\hline {\\text{Ford Sales }+4\\%} &amp; {} &amp; \\text{Average(0.3)} &amp; {} \\\\ \\hline {\\text{Ford Sales }-4\\%} &amp; {} &amp; {} &amp; \\text{Weak(0.2)} \\\\ \\end{array} $$<\/p>\n<p>Given the above joint probability function, the covariance between TY and Ford returns is <em>closest<\/em> to:<\/p>\n<p>A. 0.054.<\/p>\n<p>B. 0.1542.<\/p>\n<p>C. 0.1442.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is C.<\/p>\n<p>First, we must start by calculating the expected return for each brand:<\/p>\n<p>$$ \\text{Expected return for TY} = (0.5 * 6\\%) + (0.3 * 3\\%) + (0.2 * (-1\\%)) = 3\\% + 0.9\\% \u2013 0.2\\% = 3.7\\% $$<\/p>\n<p>$$ \\text{Expected return for Ford} = (0.5 * 10\\%) + (0.3 * 4\\%) + (0.2 * (-4\\%)) = 5\\% + 1.2\\% \u2013 0.8\\% = 5.4\\% $$<\/p>\n<p>Next, we can now compute the covariance:<\/p>\n<p>$$ \\begin{align*}<br>\\text{Covariance} &amp; = 0.5(6\\% \u2013 3.7\\%)(10\\% \u2013 5.4\\%) \\\\<br>&amp; + 0.3(3\\% \u2013 3.7\\%)(4\\% \u2013 5.4\\%) \\\\<br>&amp; + 0.2(-1\\% \u2013 3.7\\%)(-4\\% \u2013 5.4\\%) \\\\<br>&amp; = 5.29\\% + 0.294\\% + 8.836\\% \\\\<br>&amp; = 0.1442 \\\\<br>\\end{align*} $$<\/p>\n<p>Interpretation: the covariance is positive. This means that the returns for the two brands show some co-movement in the same direction. (This would most likely be the case in real life because the companies are in the same industry and therefore, the <strong>systematic risks<\/strong> affecting them are quite similar.)<\/p>\n<\/blockquote>\n<p><em>Reading 8 LOS 8m<\/em><\/p>\n<p><em>Calculate and interpret covariance given a joint probability function.<\/em><\/p>\n<div class=\"notes_inv\"><hr>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum-quantitative-methods\/\"><em>Quantitative Methods &#8211; Learning Sessions<\/em><\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Covariance between variables can be calculated in two ways. One method is the historical sample covariance between two random variables \\(X_i\\)&nbsp;and \\(Y_i\\). It is based on a sample of past data of size n and is given by: $$\\text{Cov}_{X_i,Y_i}=\\frac{\\sum_{i=1}^{n}{(X_i -\\bar{X})(Y_i&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-589","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Covariance &amp; Joint Probability | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn how to calculate the covariance between two random variables using their joint probability distribution. Explore formulas and key concepts here.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Covariance &amp; Joint Probability | CFA Level 1\" \/>\n<meta property=\"og:description\" content=\"Learn how to calculate the covariance between two random variables using their joint probability distribution. Explore formulas and key concepts here.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\" \/>\n<meta property=\"og:site_name\" content=\"AnalystPrep | CFA\u00ae Exam Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2019-10-10T13:27:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-01-26T06:30:56+00:00\" \/>\n<meta name=\"author\" content=\"Ngari Joseph\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ngari Joseph\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\"},\"author\":{\"name\":\"Ngari Joseph\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914\"},\"headline\":\"Calculating Covariance Given a Joint Probability Function\",\"datePublished\":\"2019-10-10T13:27:00+00:00\",\"dateModified\":\"2026-01-26T06:30:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\"},\"wordCount\":510,\"articleSection\":[\"Quantitative Methods\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\",\"name\":\"Covariance & Joint Probability | CFA Level 1\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#website\"},\"datePublished\":\"2019-10-10T13:27:00+00:00\",\"dateModified\":\"2026-01-26T06:30:56+00:00\",\"author\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914\"},\"description\":\"Learn how to calculate the covariance between two random variables using their joint probability distribution. Explore formulas and key concepts here.\",\"breadcrumb\":{\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculating Covariance Given a Joint Probability Function\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#website\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/\",\"name\":\"AnalystPrep | CFA\u00ae Exam Study Notes\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914\",\"name\":\"Ngari Joseph\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png\",\"contentUrl\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png\",\"caption\":\"Ngari Joseph\"},\"url\":\"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/ngari-joseph\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"2914\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2019-10-10T13:27:00+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Covariance & Joint Probability | CFA Level 1","description":"Learn how to calculate the covariance between two random variables using their joint probability distribution. Explore formulas and key concepts here.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/","og_locale":"en_US","og_type":"article","og_title":"Covariance & Joint Probability | CFA Level 1","og_description":"Learn how to calculate the covariance between two random variables using their joint probability distribution. Explore formulas and key concepts here.","og_url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/","og_site_name":"AnalystPrep | CFA\u00ae Exam Study Notes","article_published_time":"2019-10-10T13:27:00+00:00","article_modified_time":"2026-01-26T06:30:56+00:00","author":"Ngari Joseph","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Ngari Joseph","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/"},"author":{"name":"Ngari Joseph","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914"},"headline":"Calculating Covariance Given a Joint Probability Function","datePublished":"2019-10-10T13:27:00+00:00","dateModified":"2026-01-26T06:30:56+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/"},"wordCount":510,"articleSection":["Quantitative Methods"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/","name":"Covariance & Joint Probability | CFA Level 1","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website"},"datePublished":"2019-10-10T13:27:00+00:00","dateModified":"2026-01-26T06:30:56+00:00","author":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914"},"description":"Learn how to calculate the covariance between two random variables using their joint probability distribution. Explore formulas and key concepts here.","breadcrumb":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/covariance-joint-probability\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/cfa-level-1-exam\/"},{"@type":"ListItem","position":2,"name":"Calculating Covariance Given a Joint Probability Function"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/","name":"AnalystPrep | CFA\u00ae Exam Study Notes","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/cfa-level-1-exam\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/ddbf15286b86900dfa9f8ac2603c3914","name":"Ngari Joseph","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/image\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png","contentUrl":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2016\/08\/male3-512-150x150.png","caption":"Ngari Joseph"},"url":"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/ngari-joseph\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw","og_video_type":"text\/html","og_video_duration":"2914","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2019-10-10T13:27:00+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/589","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/comments?post=589"}],"version-history":[{"count":33,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/589\/revisions"}],"predecessor-version":[{"id":58312,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/589\/revisions\/58312"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/media?parent=589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/categories?post=589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/tags?post=589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}