{"id":45221,"date":"2023-06-27T16:49:41","date_gmt":"2023-06-27T16:49:41","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=45221"},"modified":"2026-04-14T18:30:41","modified_gmt":"2026-04-14T18:30:41","slug":"annualized-returns","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/","title":{"rendered":"Annualized Returns"},"content":{"rendered":"<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/QIl6JH_PuW8?si=kwV2e4llhA5xaE_3\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\"><\/iframe> <!-- \/wp:post-content --> <!-- wp:paragraph -->\n\nTo compare returns over different timeframes, we need to annualize them. This means converting daily, weekly, monthly, or quarterly returns into annual figures.\n\n<!-- \/wp:paragraph --> <!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Non-Annual Compounding<\/h2>\n<!-- \/wp:heading --> <!-- wp:paragraph -->\n\nInterest may be paid semiannually, quarterly, monthly, or even daily \u2013 interest payments can be made more than once a year. Consequently, the present value formula can be expressed as follows when there are multiple compounding periods in a year:\n\n<!-- \/wp:paragraph --> <!-- wp:paragraph -->\n\n$$PV=\\ {{\\rm FV}_N\\left(1+\\frac{R_S}{m}\\right)}^{-mN}$$\n\n<!-- \/wp:paragraph --> <!-- wp:paragraph -->\n\nWhere:\n\n<!-- \/wp:paragraph --> <!-- wp:paragraph -->\n\n\\(m\\) = Number of compounding periods in a year.\n\n<!-- \/wp:paragraph --> <!-- wp:paragraph -->\n\n\\(R_s\\) = Quoted annual interest rate.\n\n<!-- \/wp:paragraph --> <!-- wp:paragraph -->\n\n\\(N\\) = Number of years.\n\n<!-- \/wp:paragraph --> <!-- wp:html -->\n<div><a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Access our CFA free trial for annualized return practice <\/a><\/div>\n<!-- \/wp:html -->\n<h4><strong>Example: Calculating the Present Value of a Lump Sum (More than One Compounding Period)<\/strong><\/h4>\nJane Doe wants to invest money today and have it become $500,000 in five years. The annual interest rate is 8%, and it&#8217;s compounded quarterly. How much should Jane invest right now?\n\nUsing the formula above:\n\n\\({FV}_N = $500,000\\).\n\n\\(R_S = 8\\%\\).\n\n\\(m = 4\\).\n\n\\(R_s\/m = \\frac{8\\%}{4} = 2\\% = 0.02\\).\n\n\\(N = 5\\).\n\n\\(mN = 4\\times 5=20\\).\n\nTherefore,\n\n$$ PV=\\ {{FV}_N\\left(1+\\frac{R_S}{m}\\right)}^{-mN}=\\$500,000\\ \\times\\left(1.02\\right)^{-20}=\\$336,485.67$$\n\n<strong><u>Using BA II <em>Plus <\/em>Calculator<\/u><\/strong><u>:<\/u>\n<ul>\n \t<li>Press the [2nd] button, then the [FV] button to clear the financial registers. The display should show \u201cCLR TVM.\u201d<\/li>\n \t<li>Enter the future value (FV). This is the amount Jane wants to have in five years, which is $500,000. To do this, type \u201c500000\u201d and press the [FV] button.<\/li>\n \t<li>Enter the interest rate (I\/Y). This is the annual interest rate, which is 8%. However, since interest is compounded quarterly, we need to divide this by 4. To do this, type \u201c8\u201d, press the [\u00f7] button, type \u201c4\u201d, then press the [ENTER] button, and finally press the [I\/Y] button.<\/li>\n \t<li>Enter the number of periods (N). This is the number of quarters in five years, which is 5*4 = 20. To do this, type \u201c20\u201d and press the [N] button.<\/li>\n \t<li>Compute the present value (PV). To do this, press the [CPT] and then the [PV] buttons. The display should show the amount Jane needs to invest today, approximately $336,485.49.<\/li>\n<\/ul>\n<h2>Annualized Returns<\/h2>\nTo annualize a return for a period shorter than a year, you need to account for how many times that period fits into a year. For example, if you have a weekly return, you would compound it 52 times because there are 52 weeks in a year.\n\nGenerally, we can annualize the returns using the following formula:\n\n$${\\text{Return}}_{\\text{annual}}=\\left(1+{\\text{Return}}_{\\text{period}}\\right)^c-1$$\n\nWhere:\n\n\\({\\text{Return}}_{\\text{period}}\\) = Quoted return for the period.\n\n\\(c\\) = Number of periods in a year.\n<h4><strong>Example<\/strong>: <strong>Annualizing Returns<\/strong><\/h4>\nIf the monthly return is 0.7%, then the compound annual return is:\n\n$$\\begin{align}{\\text{Return}}_{\\text{annual}}&amp;=\\left(1+{\\text{Return}}_{\\text{monthly}}\\right)^{12}-1\\\\&amp;=\\left(1.007\\right)^{12}-1=0.0873=8.73\\%\\end{align}$$\n\nFor a period of more than one year, for example, a 15-month return of 16% can be annualized as:\n\n$$\\begin{align}{\\text{Return}}_{\\text{annual}}&amp;=\\left(1+{\\text{Return}}_{15\\ \\text{month}}\\right)^\\frac{12}{15}-1\\\\&amp;=\\left(1.16\\right)^\\frac{4}{5}-1=12.61\\%\\end{align}$$\n\nWe may apply the same procedure to convert weekly returns to annual returns for comparison with weekly returns.\n\n$${\\text{Return}}_{\\text{annual}}=\\left(1+{\\text{Return}}_{\\text{weekly}}\\right)^{52}-1$$\n\nFor comparison with weekly returns, we can convert annual returns to weekly returns by making \\({(\\text{Return}}_{\\text{weekly}})^{52}\\) the subject of the formula.\n<h4><strong>Example: Comparing Investments by Annualizing Returns<\/strong><\/h4>\nAn investor is evaluating the returns of two recently formed bonds. Selected return information on the bonds is presented below:\n\n$$\\begin{array}{c|c|c}\\text{Bond}&amp;\\text{Time Since Issuance}&amp;\\text{Return Since Issuance (%)}\\\\ \\hline \\text{A}&amp;\\text{120 days}&amp;2.50\\\\ \\hline \\text{B}&amp;\\text{8 months}&amp;6.00\\\\ \\end{array}$$\n<h2>Annualized Return Calculation<\/h2>\nTo compare the annualized rate of return for both bonds, you can use the formula for annualizing returns based on different time periods:\n\n<strong>Annualized Return<\/strong> = \\(\\left(1 + \\frac{\\text{Return Since Issuance}}{100}\\right)^\\frac{365}{\\text{Time Since Issuance}} &#8211; 1\\)\n\nLet&#8217;s calculate the annualized returns for both bonds:\n\n<strong>For Bond A:<\/strong>\n\nTime Since Issuance = 120 days.\n\nReturn Since Issuance = 2.50%.\n\nAnnualized Return for Bond A = \\(\\left(1 + \\frac{2.50}{100}\\right)^\\frac{365}{120} &#8211; 1\\).\n\nAnnualized Return for Bond A = \\(\\left(1 + 0.025\\right)^{3.0417} &#8211; 1\\).\n\nAnnualized Return for Bond A = 1.07799 &#8211; 1 = 0.07799 or 7.80%.\n\n<strong>For Bond B:<\/strong>\n\nTime Since Issuance = 8 months .\n\nReturn Since Issuance = 6.00%.\n\nAnnualized Return for Bond B = \\(\\left(1 + \\frac{6.00}{100}\\right)^\\frac{12}{8} &#8211; 1\\).\n\nAnnualized Return for Bond B = \\(\\left(1 + 0.06\\right)^{1.5} &#8211; 1\\).\n\nAnnualized Return for Bond B = 1.09133 &#8211; 1 = 0.09133 or 9.13%.\n\nComparing the annualized returns:\n\nBond A has an annualized return of approximately 7.80%.\n\nBond B has an annualized return of approximately 9.13%.\n\nTherefore, Bond B has a higher annualized rate of return compared to Bond A.\n<h2>Continuously Compounded Returns<\/h2>\nThe continuously compounded return is calculated by taking the natural logarithm of one plus the holding period return. For example, if the monthly return is 1.2%, you&#8217;d calculate it as ln(1.012), which equals approximately 0.01192.\n\nGenerally, continuously compounded from \\(t\\) to \\(t+1\\) is given by:\n\n$$r_{t,t+1}=\\ln{\\left(\\frac{P_{t+1}}{P_t}\\right)=\\ln{\\left(1+R_{t,t+1}\\right)}}$$\n\nAssume now that the investment horizon is from time \\(t=0\\) to time \\(t=T\\) then the continuously compounded return is given by:\n\n$$r_{0,T}=\\ln{\\left(\\frac{P_T}{P_0}\\right)}$$\n\nIf we apply the exponential function on both sides of the equation, we have the following:\n\n$$P_T=P_0e^{r_{0,T}}$$\n\nNote that \\(\\frac{P_T}{P_0}\\) can be written as:\n\n$$\\frac{P_T}{P_0}=\\left(\\frac{P_T}{P_{T-1}}\\right)\\left(\\frac{P_{T-1}}{P_{T-2}}\\right)\\ldots\\left(\\frac{P_1}{P_0}\\right)$$\n\nIf we take natural logarithm on both sides of the above equation:\n\n\\begin{align*} \\ln{\\left(\\frac{P_T}{P_0}\\right)} &amp;= \\ln{\\left(\\frac{P_T}{P_{T-1}}\\right)} + \\ln{\\left(\\frac{P_{T-1}}{P_{T-2}}\\right)} + \\ldots + \\ln{\\left(\\frac{P_1}{P_0}\\right)}\\\\\\Rightarrow r_{0,T} &amp;= r_{T-1,T} + r_{T-2,T-1} + \\ldots + r_{0,1} \\end{align*}\n\nTherefore, the continuously compounded return to time T is equivalent to the sum of one-period continuously compounded returns.\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\nThe weekly return of an investment that produces an annual compounded return of 23% is <em>closest to<\/em>:\n\nA. 0.40%.\n\nB. 0.92%.\n\nC. 0.41%.\n\n<strong>The correct answer is A.<\/strong>\n\nRecall that:\n\n$${\\text{Return}}_{\\text{annual}}=\\left(1+{\\text{Return}}_{\\text{weekly}}\\right)^{52}-1$$\n\nWe can rewrite the above equation as follows:\n\n\\begin{align}\n\\text{Return}_{\\text{weekly}} &amp;= \\left(1 + \\text{Return}_{\\text{annual}}\\right)^{\\frac{1}{52}} &#8211; 1 \\\\\n&amp;= \\left(1 + 0.23\\right)^{\\frac{1}{52}} &#8211; 1 \\\\\n&amp;\\approx 0.40\\%\n\\end{align}<\/blockquote>\n<!-- wp:html -->\n<div><a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>Build confidence in quantitative methods with CFA exam-style practice on annualized returns, compounding, and time-value-of-money concepts.\n\n<\/div>\n<!-- \/wp:html -->","protected":false},"excerpt":{"rendered":"<p>To compare returns over different timeframes, we need to annualize them. This means converting daily, weekly, monthly, or quarterly returns into annual figures. Non-Annual Compounding Interest may be paid semiannually, quarterly, monthly, or even daily \u2013 interest payments can be&#8230;<\/p>\n","protected":false},"author":15,"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-45221","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Annualized Returns - AnalystPrep | CFA\u00ae Exam Study Notes<\/title>\n<meta name=\"description\" content=\"Learn to annualize returns, comparing investments over different timeframes. Explore examples and formulas for annualized returns.\" \/>\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\/annualized-returns\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Annualized Returns - AnalystPrep | CFA\u00ae Exam Study Notes\" \/>\n<meta property=\"og:description\" content=\"Learn to annualize returns, comparing investments over different timeframes. Explore examples and formulas for annualized returns.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/\" \/>\n<meta property=\"og:site_name\" content=\"AnalystPrep | CFA\u00ae Exam Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-27T16:49:41+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-14T18:30:41+00:00\" \/>\n<meta name=\"author\" content=\"Kosikos Tuitoek\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Kosikos Tuitoek\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 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\\\/annualized-returns\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/\"},\"author\":{\"name\":\"Kosikos Tuitoek\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#\\\/schema\\\/person\\\/73df713e3b6e82ee139e1eff20cebe20\"},\"headline\":\"Annualized Returns\",\"datePublished\":\"2023-06-27T16:49:41+00:00\",\"dateModified\":\"2026-04-14T18:30:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/\"},\"wordCount\":1074,\"articleSection\":[\"Quantitative Methods\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/\",\"url\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/\",\"name\":\"Annualized Returns - AnalystPrep | CFA\u00ae Exam Study Notes\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#website\"},\"datePublished\":\"2023-06-27T16:49:41+00:00\",\"dateModified\":\"2026-04-14T18:30:41+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/#\\\/schema\\\/person\\\/73df713e3b6e82ee139e1eff20cebe20\"},\"description\":\"Learn to annualize returns, comparing investments over different timeframes. Explore examples and formulas for annualized returns.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/quantitative-methods\\\/annualized-returns\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Annualized Returns\"}]},{\"@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\\\/73df713e3b6e82ee139e1eff20cebe20\",\"name\":\"Kosikos Tuitoek\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8260edaa3f7ba04cf6b536b3f7fd769007ecb789b3289ac0cc4c3ab8b3f7f061?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8260edaa3f7ba04cf6b536b3f7fd769007ecb789b3289ac0cc4c3ab8b3f7f061?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8260edaa3f7ba04cf6b536b3f7fd769007ecb789b3289ac0cc4c3ab8b3f7f061?s=96&d=mm&r=g\",\"caption\":\"Kosikos Tuitoek\"},\"url\":\"https:\\\/\\\/analystprep.com\\\/cfa-level-1-exam\\\/author\\\/kosikos-tuitoek-enockanalystprep-com\\\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/QIl6JH_PuW8\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"3658\" \/>\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=\"2023-06-27T16:49:41+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Annualized Returns - AnalystPrep | CFA\u00ae Exam Study Notes","description":"Learn to annualize returns, comparing investments over different timeframes. Explore examples and formulas for annualized returns.","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\/annualized-returns\/","og_locale":"en_US","og_type":"article","og_title":"Annualized Returns - AnalystPrep | CFA\u00ae Exam Study Notes","og_description":"Learn to annualize returns, comparing investments over different timeframes. Explore examples and formulas for annualized returns.","og_url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/","og_site_name":"AnalystPrep | CFA\u00ae Exam Study Notes","article_published_time":"2023-06-27T16:49:41+00:00","article_modified_time":"2026-04-14T18:30:41+00:00","author":"Kosikos Tuitoek","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Kosikos Tuitoek","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/"},"author":{"name":"Kosikos Tuitoek","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/73df713e3b6e82ee139e1eff20cebe20"},"headline":"Annualized Returns","datePublished":"2023-06-27T16:49:41+00:00","dateModified":"2026-04-14T18:30:41+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/"},"wordCount":1074,"articleSection":["Quantitative Methods"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/","url":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/","name":"Annualized Returns - AnalystPrep | CFA\u00ae Exam Study Notes","isPartOf":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#website"},"datePublished":"2023-06-27T16:49:41+00:00","dateModified":"2026-04-14T18:30:41+00:00","author":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/#\/schema\/person\/73df713e3b6e82ee139e1eff20cebe20"},"description":"Learn to annualize returns, comparing investments over different timeframes. Explore examples and formulas for annualized returns.","breadcrumb":{"@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/annualized-returns\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/cfa-level-1-exam\/"},{"@type":"ListItem","position":2,"name":"Annualized Returns"}]},{"@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\/73df713e3b6e82ee139e1eff20cebe20","name":"Kosikos Tuitoek","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/8260edaa3f7ba04cf6b536b3f7fd769007ecb789b3289ac0cc4c3ab8b3f7f061?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/8260edaa3f7ba04cf6b536b3f7fd769007ecb789b3289ac0cc4c3ab8b3f7f061?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8260edaa3f7ba04cf6b536b3f7fd769007ecb789b3289ac0cc4c3ab8b3f7f061?s=96&d=mm&r=g","caption":"Kosikos Tuitoek"},"url":"https:\/\/analystprep.com\/cfa-level-1-exam\/author\/kosikos-tuitoek-enockanalystprep-com\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/QIl6JH_PuW8","og_video_type":"text\/html","og_video_duration":"3658","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2023-06-27T16:49:41+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/45221","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\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/comments?post=45221"}],"version-history":[{"count":21,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/45221\/revisions"}],"predecessor-version":[{"id":60383,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/posts\/45221\/revisions\/60383"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/media?parent=45221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/categories?post=45221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-json\/wp\/v2\/tags?post=45221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}