{"id":176,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=176"},"modified":"2026-02-10T09:37:58","modified_gmt":"2026-02-10T09:37:58","slug":"yield-conversion","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/yield-conversion\/","title":{"rendered":"Yield Conversions"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Discounted Cash Flow Applications (2019 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n  \"description\": \"This video lesson covers discounted cash flow applications in quantitative methods. It includes capital budgeting techniques like NPV and IRR, holding period returns, money and time-weighted returns, and short-term financial metrics such as bank discount yield, effective annual yield, and bond equivalent yield, with practical examples for deeper understanding.\",\n  \"uploadDate\": \"2019-06-06T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/lYpi92G13U4\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/lYpi92G13U4\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/lYpi92G13U4\",\n  \"duration\": \"PT27M31S\"\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\": \"A project has an effective annual yield (EAY) of 16%. Calculate its bond equivalent yield (BEY):\",\n    \"text\": \"A project has an effective annual yield (EAY) of 16%. Calculate its bond equivalent yield (BEY):\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"15.4%.\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"107.7%.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"7.7%.\"\n      }\n    ]\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/lYpi92G13U4?rel=0&#038;modestbranding=1&#038;playsinline=1&#038;vq=hd1080\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>Yield conversion is basically the process of changing from one type of yield to the other. We have already established the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/4-types-yield-money-market-instruments\/\">4 main types of yields <\/a>and their formulae &#8211; r<sub>BD, <\/sub>HPY, EAY, and r<sub>MM<\/sub>.<\/p>\n\n\n\n<p>Given any one of these yields, we can easily find the other two by considering the following important points.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p>&#8211; HPY represents the actual return on a money market instrument assuming that it\u2019s held until maturity.<\/p>\n\n\n\n<p>-When we annualize HPY on the basis of a 365-day year and carry out compounding, the result is the EAY.<\/p>\n\n\n\n<p>-r<sub>MM <\/sub>is the annualized version of HPY on the basis of a 360-day year and assuming simple interest.<\/p>\n\n\n\n<!-- TOP CTA \u2013 Full Width Outline Button -->\n<div style=\"margin:24px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:block;\n       width:100%;\n       padding:14px 0;\n       border:2px solid #3b6fd8;\n       border-radius:50px;\n       font-size:18px;\n       font-weight:500;\n       text-align:center;\n       text-decoration:none;\n       color:#3b6fd8;\n       background-color:#f4f6f9;\n       box-sizing:border-box;\n     \">\n     Practice yield conversion questions with free trial access.\n  <\/a>\n<\/div>\n\n\n\n<h2><strong>Yield Conversion Formula Guide <\/strong><\/h2>\n<p>The following are direct results from the yield formula studied <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/4-types-yield-money-market-instruments\/\">here<\/a>.<\/p>\n<ol>\n<li>r<sub>MM <\/sub>= HPY * (360\/t)<\/li>\n<\/ol>\n<p>Alternatively, HPY = r<sub>MM<\/sub> * (t\/360)<\/p>\n<ol start=\"2\">\n<li>EAY = (1 + HPY)<sup> 365\/t<\/sup> \u2013 1<\/li>\n<\/ol>\n<p>Similarly,\\( \\text{HPY} = (1 + EAY)^{\\frac {t}{365}} \u2013 1\\)<\/p>\n<h2><strong>Example<\/strong><\/h2>\n<p>Assume you purchased a $10,000 U.S. T-bill maturing in 150 days for $9,800. The money market yield is quoted at 4.898%. How do you go about computing the HPY and the EAY?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>First, you should note that in this particular case, we can compute the HPY directly from the question:<\/p>\n<p>$$ \\text{HPY} = \\cfrac {(10,000 \u2013 9,800)}{9,800} = 2.041\\% $$<\/p>\n<p>However, we can still use the money market return given above to get our HPY:<\/p>\n<p>$$ \\text{HPY} = = r_{MM} * \\left( \\frac {t}{360} \\right)= 0.04898 * \\frac {150}{360} = 2.041\\% $$<\/p>\n<p>For the Effective annual yield:<\/p>\n<p>$$ \\text{EAY} = (1 + HPY)^{\\frac {365}{t}} \u2013 1 = (1 + 0.02041)^{ \\frac {365}{150}} \u2013 1 = 5.039\\% $$<\/p>\n<h2><strong>Bond Equivalent Yield<\/strong><\/h2>\n<p>It refers to an annualized periodic yield calculated by multiplying the periodic yield by the number of periods in a year. U.S. bonds usually have two semi-annual coupon payments. As such, yields are quoted as twice the semi-annual rate. Thus;<\/p>\n<p>Bond Equivalent Yield\u00a0(BEY) = 2 * semi-annual discount rate.<\/p>\n<p><strong>Example<\/strong><\/p>\n<p>Assume you have a 3-month loan that has a holding period of 4%. Its bond equivalent yield will be calculated as follows;<\/p>\n<p>First, we convert the 3- month HPY to an effective semi-annual yield:<\/p>\n<p>$$ 1.04^2 \u2013 1 = 8.16\\% $$<\/p>\n<p>Secondly, we double it and this will give us the BEY:<\/p>\n<p>$$ 2 * 8.16 = 16.32\\% $$<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>A project has an EAY of 16%. Calculate its BEY;<\/p>\n<p>A. 107.7%<\/p>\n<p>B. 7.7%<\/p>\n<p>C. 15.4%<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is C.<\/p>\n<p>Step 1: Convert the EAY to an effective semi-annual yield.<\/p>\n<p>$$ 1.16^{0.5} \u2013 1 = 0.077 \\text{ or } 7.7\\% $$<\/p>\n<p>Step 2: Double it!<\/p>\n<p>$$ 2 * 7.7 = 15.4\\% $$<\/p>\n<\/blockquote>\n<p><em>Reading 7 LOS 7f<\/em><\/p>\n<p><em>Convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.<\/em><\/p>\n<div class=\"notes_inv\"><hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum\/\"><em>Quantitative Methods \u2013 Learning Sessions<\/em><\/a><\/p>\n<\/div>\n\n\n<!-- BOTTOM CTA \u2013 Refined Version -->\n<div style=\"text-align:center; background-color:#f4f6f9; padding:35px 20px; border-radius:12px; margin-top:40px;\">\n\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:inline-block;\n       padding:14px 34px;\n       background-color:#3b6fd8;\n       color:#ffffff;\n       border-radius:50px;\n       font-size:16px;\n       font-weight:600;\n       text-decoration:none;\n       margin-bottom:18px;\n     \">\n     Start Free Trial\n  <\/a>\n\n  <p style=\"max-width:700px; margin:0 auto; font-size:16px; line-height:1.6; color:#333;\">\n    Strengthen your CFA Level I quantitative skills with exam-style yield conversion problems, clear step by step explanations, and timed practice designed to improve calculation speed and accuracy.\n  <\/p>\n\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Yield conversion is basically the process of changing from one type of yield to the other. We have already established the 4 main types of yields and their formulae &#8211; rBD, HPY, EAY, and rMM. Given any one of these&#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-176","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>Yield Conversion Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Yield conversion changes a quoted yield into another type, such as bond equivalent yield (BEY) or effective annual yield (EAY). 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