{"id":17712,"date":"2021-07-14T15:10:20","date_gmt":"2021-07-14T15:10:20","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=17712"},"modified":"2026-03-19T20:03:14","modified_gmt":"2026-03-19T20:03:14","slug":"calculate-the-expected-return-on-a-bond-given-transition-in-its-credit-rating","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/calculate-the-expected-return-on-a-bond-given-transition-in-its-credit-rating\/","title":{"rendered":"Credit Migration"},"content":{"rendered":"<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Price impact of credit downgrade using modified duration\",\r\n    \"text\": \"Consider a AAA-rated corporate bond with a 5% coupon that matures in six years and has a modified duration of 5. The credit spread for AAA is 1.00% and for A is 1.50%. If the bond is downgraded to an A rating over the next year, the expected price change is closest to:\\n\\nA. -0.05%\\n\\nB. -1.30%\\n\\nC. -2.50%\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is C.\\n\\nPercentage price change = -Modified duration \u00d7 Change in credit spread = -5 \u00d7 (0.0150 \u2212 0.0100) = -0.0250, or -2.50%.\"\r\n    }\r\n  }\r\n}\r\n<\/script>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/pHEcwZjtzl8\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p>Credit rating agencies come up with transition matrixes of credit ratings based on the historical experience of issuers. A <em><strong>transition matrix<\/strong><\/em> captures the probability that a certain obligor will transition (migrate) from one credit state (rating) to another over a given time period, usually a year.<\/p>\r\n<div style=\"text-align:center; margin:22px 0;\">\r\n<a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\r\nstyle=\"display:inline-flex; align-items:center; justify-content:center; padding:10px 18px; border:2px solid #1e5bd8; color:#1e5bd8; border-radius:9999px; text-decoration:none; font-weight:600;\">\r\nPractice credit rating transition questions for CFA Level II\r\n<\/a>\r\n<\/div>\r\n<p>The table below presents an example of a rating transition matrix according to S&amp;P\u2019s rating categories:<\/p>\r\n<p>$$ \\textbf{One-year transition matrix}$$<\/p>\r\n<p>$$ \\small{\\begin{array}{l|cccccccc} \\textbf{Initial}&amp; {} &amp; \\textbf{Rating} &amp; \\textbf{at} &amp; \\textbf{Year} &amp; \\textbf{End} &amp; {} &amp; {} &amp; {} \\\\ \\textbf{Rating} &amp; \\textbf{AAA} &amp; \\textbf{AA} &amp; \\textbf{A} &amp; \\textbf{BBB} &amp; \\textbf{BB} &amp; \\textbf{B} &amp; \\textbf{CCC} &amp; \\textbf{Default}\\\\ \\hline \\text{AAA} &amp; {90.81\\%} &amp; {8.33\\%} &amp; {0.68\\%} &amp; {0.06\\%} &amp; {0.12\\%} &amp; {0.00\\%} &amp; {0.00\\%} &amp; {0.00\\%} \\\\ \\text{AA} &amp; {0.70\\%} &amp; {90.65\\%} &amp; {7.79\\%} &amp; {0.64\\%} &amp; {0.06\\%} &amp; {0.14\\%} &amp; {0.02\\%} &amp; {0.00\\%} \\\\ \\text{A} &amp; {0.09\\%} &amp; {2.27\\%} &amp; {91.05\\%} &amp; {5.52\\%} &amp; {0.74\\%} &amp; {0.26\\%} &amp; {0.01\\%} &amp; {0.06\\%} \\\\ \\text{BBB} &amp; {0.02\\%} &amp; {0.33\\%} &amp; {5.95\\%} &amp; {86.93\\%} &amp; {5.30\\%} &amp; {1.17\\%} &amp; {0.12\\%} &amp; {0.18\\%} \\\\ \\text{BB} &amp; {0.03\\%} &amp; {0.14\\%} &amp; {0.67\\%} &amp; {7.73\\%} &amp; {80.53\\%} &amp; {8.84\\%} &amp; {1.00\\%} &amp; {1.06\\%} \\\\ \\text{B} &amp; {0.00\\%} &amp; {0.11\\%} &amp; {0.24\\%} &amp; {0.43\\%} &amp; {6.48\\%} &amp; {83.46\\%} &amp; {4.07\\%} &amp; {5.20\\%} \\\\ \\text{CCC} &amp; {0.22\\%} &amp; {0.00\\%} &amp; {0.22\\%} &amp; {1.30\\%} &amp; {2.38\\%} &amp; {11.24\\%} &amp; {64.86\\%} &amp; {19.79\\%} \\\\ \\end{array}}$$<\/p>\r\n<p>The expected percentage price change due to credit migration can be calculated as:<\/p>\r\n<p>$$ {\\Delta}\\%P =\\ \u2013 (\\text{Modified duration of the bond}) \\times (\\Delta \\text{Credit spread}) $$<\/p>\r\n<p>The expected return will then be calculated as:<\/p>\r\n<p>$$ \\text{Expected return}=\\text{Yield to maturity (YTM)}+{\\Delta}\\%P $$<\/p>\r\n<h4>Example: Credit Migration<\/h4>\r\n<p>An A-rated corporate bond with a yield to maturity of 4% will have a modified duration of 6.5 at the end of the year. You have been given the following partial corporate transition matrix:<\/p>\r\n<p>$$ \\begin{align*} &amp; {\\textbf{ One-Year Transition Matrix for}} \\\\ &amp; \\textbf{A-Rated Bonds and Credit Spreads} \\end{align*} \\\\ \\begin{array}{c|c|c|c|c|c|c|c} &amp; \\bf{AAA} &amp; \\bf{AA} &amp; \\bf A &amp; \\bf{BBB} &amp; \\bf{BB} &amp; \\bf B &amp; \\bf{CCC,} \\\\ &amp; &amp; &amp; &amp; &amp; &amp; &amp; \\bf{CC,C} \\\\ \\hline {\\text{Probability}} &amp; 0.018 &amp; 0.263 &amp; 75.010 &amp; 16.704 &amp; 6.081 &amp; 1.531 &amp; 0.394 \\\\ {(\\%)} &amp; &amp; &amp; &amp; &amp; &amp; \\\\ \\hline \\text{Credit} &amp; 0.60\\% &amp; 0.90\\% &amp; 1.10\\% &amp; 1.50\\% &amp; 3.40\\% &amp; 6.50\\% &amp; 9.50\\% \\\\ \\text{Spread} &amp; &amp; &amp; &amp; &amp; &amp; \\end{array} $$<\/p>\r\n<p>The expected return of the bond over the next year is <em>closest to<\/em>:<\/p>\r\n<p><strong>Solution<\/strong><\/p>\r\n<p>The bond&#8217;s expected return over the next year is calculated as its yield to maturity, plus the expected percentage price change in the bond over the same year.<\/p>\r\n<p>$$ \\begin{align*} {\\text{Expected }} &amp; {\\text{percentage price change} } {\\left({\\Delta}\\%P\\right)} \\\\ &amp; =\\ \u2013(\\text{Modified duration of the bond} \\times {\\Delta \\text{Credit spread}} \\end{align*} $$<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c} &amp; \\bf{\\text{Expected} \\%} &amp; \\textbf{Probability} &amp; \\bf{\\text {Expected } \\%} \\\\ &amp; \\textbf{Price} &amp; &amp; \\bf{\\text{Price Change} \\times} \\\\ &amp; \\textbf{Change} &amp; &amp; \\textbf{Probability}\\\\ \\hline \\text{From A to AAA} &amp; 3.25\\% &amp; 0.018 &amp; 0.0006\\% \\\\ \\hline \\text{From A to AA} &amp; 1.30\\% &amp; 0.263 &amp; 0.0034\\% \\\\ \\hline \\text{From A to A} &amp; 0.00\\% &amp; 75.010 &amp; 0.0000\\% \\\\ \\hline \\text{From A to BBB} &amp; -2.60\\% &amp; 16.704 &amp; -0.4343\\% \\\\ \\hline \\text{From A to BB} &amp; -14.95\\% &amp; 6.081 &amp; -0.9091\\% \\\\ \\hline \\text{From A to B} &amp; -35.10\\% &amp; 1.531 &amp; -0.5375\\% \\\\ \\hline \\text{From A to CCC,CC,C} &amp; -54.60\\% &amp; 0.394 &amp; -0.2150\\% \\end{array} $$<\/p>\r\n<p>$$ \\text{Total expected percentage price change} =-2.0919\\% $$<\/p>\r\n<p>$$ \\begin{align*} \\text{Expected return} &amp; = \\text{Yield to maturity (YTM)}+ {\\Delta}\\%P \\\\\u00a0 &amp; = 4.0\\% \u2013 2.0919\\% = 1.91\\% \\end{align*} $$<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>The following is a partial one-year corporate bonds transition matrix:<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c} \\text{From\/To} &amp; \\bf{AAA} &amp; \\bf{AA} &amp; \\bf A \\\\ \\hline AAA &amp; 90.00 &amp; 8.00 &amp; 2.00 \\\\ \\hline AA &amp; 2.00 &amp; 87.00 &amp; 14.00 \\\\ \\hline A &amp; 0.60 &amp; 2.40 &amp; 83.00 \\\\ \\hline \\text{Credit Spread} &amp; 1.00\\% &amp; 1.30\\% &amp; 1.50\\% \\end{array} $$<\/p>\r\n<p>Consider an AAA-rated corporate bond with 5% coupon payments that matures in six years. The bond has a modified duration of 5. If this bond is downgraded to an A rating over the next year, its expected price change will be <em>closest to<\/em>:<\/p>\r\n<ol type=\"A\">\r\n\t<li>-0.05%.<\/li>\r\n\t<li>-1.30%.<\/li>\r\n\t<li>-2.50%.<\/li>\r\n<\/ol>\r\n<h4><strong>Solution<\/strong><\/h4>\r\n<p><strong>The correct answer is C.<\/strong><\/p>\r\n<p>The expected percentage price change is the product of the negative of the modified duration and the difference between the credit spread in the new rating and the old rating:<\/p>\r\n<p>$$ {\\Delta}\\%P = \u20135 \\times (0.0150 \u2013 0.01) = \u20130.0250, \\text{ or } \u20132.50\\% $$<\/p>\r\n<\/blockquote>\r\n<p>Reading 31: Credit Analysis Models<\/p>\r\n<p><em>LOS 31 (c) Calculate the expected return on a bond given transition in its credit rating.<\/em><\/p>\r\n<p>\r\n<\/p>\r\n<div style=\"text-align:center; margin:30px 0;\">\r\n<a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\r\nstyle=\"display:inline-flex; align-items:center; justify-content:center; padding:12px 26px; border-radius:9999px; background:#1e5bd8; color:#ffffff; font-weight:700; text-decoration:none;\">\r\nStart Free Trial \u2192\r\n<\/a>\r\n<p style=\"margin-top:12px; font-size:16px; line-height:1.5;\">\r\nMaster CFA Level II credit migration analysis with exam-style practice on transition matrices, credit spread changes, and expected bond return calculations.\r\n<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Credit rating agencies come up with transition matrixes of credit ratings based on the historical experience of issuers. A transition matrix captures the probability that a certain obligor will transition (migrate) from one credit state (rating) to another over a&#8230;<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,472],"tags":[],"class_list":["post-17712","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-fixed-income","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>Credit Migration - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Learn how to calculate expected price changes and returns on bonds based on credit rating transitions, using examples and formulas.\" \/>\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\/study-notes\/cfa-level-2\/calculate-the-expected-return-on-a-bond-given-transition-in-its-credit-rating\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Credit Migration - 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