{"id":3473,"date":"2019-09-06T12:00:00","date_gmt":"2019-09-06T12:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=3473"},"modified":"2026-03-04T13:52:37","modified_gmt":"2026-03-04T13:52:37","slug":"term-structure-yield-volatility-intrest-rate-risk","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/term-structure-yield-volatility-intrest-rate-risk\/","title":{"rendered":"Term Structure of Yield Volatility and Interest Rate Risk"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"How should the bonds be ranked in terms of interest rate risk?\",\n    \"text\": \"An investment bank needs to rank three bonds based on interest rate risk.\\n\\nBond Data:\\nBond A \u2014 Modified Duration: 3.50, Convexity: 100, Yield change: 0.25%\\nBond B \u2014 Modified Duration: 5.25, Convexity: 350, Yield change: 0.15%\\nBond C \u2014 Modified Duration: 5.30, Convexity: 250, Yield change: 0.10%\\n\\nModified duration and convexity are annualized. Based on the predicted change in yield for each bond, how should the bonds be ranked from highest interest rate risk to lowest?\\n\\nA. Bond A, Bond B, Bond C\\n\\nB. Bond B, Bond C, Bond A\\n\\nC. Bond C, Bond B, Bond A\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. Using duration and convexity to approximate the percentage price change:\\n\\nBond A: %\u0394P \u2248 (\u22123.50 \u00d7 0.0025) + (0.5 \u00d7 100 \u00d7 0.0025\u00b2) \u2248 \u22120.0084375\\nBond B: %\u0394P \u2248 (\u22125.25 \u00d7 0.0015) + (0.5 \u00d7 350 \u00d7 0.0015\u00b2) \u2248 \u22120.0074813\\nBond C: %\u0394P \u2248 (\u22125.30 \u00d7 0.0010) + (0.5 \u00d7 250 \u00d7 0.0010\u00b2) \u2248 \u22120.005175\\n\\nBecause Bond A experiences the largest estimated price change, it has the highest interest rate risk, followed by Bond B, and then Bond C.\"\n    }\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54e-j.png\",\n  \"caption\": \"Key Rate Duration\",\n  \"width\": 974,\n  \"height\": 641,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Understanding Fixed-Income Risk and Return (2025 Level I CFA\u00ae Exam \u2013 Fixed Income \u2013 Module 5)\",\n  \"description\": \"This video lesson covers fixed-income return analysis and interest rate risk. It explains how to calculate and interpret duration measures like Macaulay, modified, and effective duration, as well as convexity. Viewers also learn portfolio duration, price value of a basis point (PVBP), key rate durations, and the impact of credit spreads and yield volatility.\",\n  \"uploadDate\": \"2022-06-01T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/ys7hMfL_EIs\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=ys7hMfL_EIs\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/ys7hMfL_EIs\",\n  \"duration\": \"PT1H1M0S\"\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/ys7hMfL_EIs?si=HUpcBzKKb6AJdToE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n<p>Time horizon is an important aspect of understanding interest rate risk and the return characteristics of a fixed-rate investment. The primary concern for an investor is the change in the price of a bond given a sudden change in its yield-to-maturity. Therefore, reinvestment of coupon interest is a key factor in the investor\u2019s horizon yield.<\/p>\n<p>Prices of fixed income securities are affected not only by the level of interest rates but also the volatility of interest rates. The risk of a default-free security emanates from two sources: interest rate shift and the risk of changes in interest rate volatility.<\/p>\n<h2><strong>Risk of Interest Rate Shift <\/strong><\/h2>\n<p>To manage this type of risk, analysts have to measure it first. In this regard, duration becomes a particularly important tool since it helps the analyst establish the sensitivity of a portfolio to changes in interest rates.<\/p>\n<h2><strong>Risk of Changes in Interest Rate Volatility<\/strong><\/h2>\n<p>This type of risk is less obvious but represents a major component of the total risk of a fixed income security. For a given duration and current value of a position, the interest rate and the expected yield volatility increase simultaneously.<\/p>\n<h2><strong>Investment Horizon and Interest Rate Risk<\/strong><\/h2>\n<p>When the government par-curve is shifted up or down by some amount to calculate effective duration and effective convexity, it is described as a \u201cparallel\u201d yield curve shift. Yield curves are rarely straight lines, so this shift may also be described as a \u201cshape-preserving\u201d shift to the yield curve.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"974\" height=\"641\" class=\"aligncenter size-full wp-image-10111\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54e-j.png\" alt=\"key-rate-duration\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54e-j.png 974w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54e-j-300x197.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54e-j-768x505.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54e-j-400x263.png 400w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/p>\n<p>In case of a parallel shift of the yield curve, the yield-to-maturity and coupon reinvestment rates are assumed to have changed by the same amount and in the same direction. Macaulay duration is particularly important because it identifies the investment horizon such that losses (or gains) from coupon reinvestment offset gains (or losses) from changes in market prices.<\/p>\n<p>The term structure of yield volatility is the relationship between the volatility of bond yields-to-maturity and times-to-maturity. The term structure of bond yields (also called the \u201cterm structure of interest rates\u201d) is typically upward sloping. However, it can be different depending on some factors, including government policy.<\/p>\n<p>For instance, a central bank engaging in an expansionary monetary policy might cause the yield curve to steepen by reducing short-term interest rates. However, this policy might result in greater volatility in short-term bond yields to maturity than in longer-term bonds. This is because longer-term bond yields are mainly determined by future inflation and economic growth expectations. Such expectations are often less volatile.<\/p>\n<blockquote>\n<h3 class=\"Style2AltBaslik\" style=\"margin-bottom: 12.0pt; line-height: 130%;\"><strong><span lang=\"EN-US\">Question<\/span><\/strong><\/h3>\n<p class=\"Text001\" style=\"margin-bottom: 6.0pt;\"><span lang=\"EN-US\">An investment bank needs to rank 3 bonds in terms of interest rate risk.<\/span><\/p>\n<p>$$<br \/>\\begin{array}{l|c|c|c}<br \/>\\textbf{Bond} &amp; \\textbf{Modified Duration} &amp; \\textbf{Convexity} &amp; \\textbf{Yield} \\\\<br \/>\\hline<br \/>\\text{A} &amp; \\text{3.50} &amp; \\text{100} &amp; \\text{25} \\\\<br \/>\\text{B} &amp; \\text{5.25} &amp; \\text{350} &amp; \\text{15} \\\\<br \/>\\text{C} &amp; \\text{5.30} &amp; \\text{250} &amp; \\text{10} \\\\<br \/>\\end{array}<br \/>$$<\/p>\n<p>The modified duration and convexity statistics are annualized. Given the predicted change in yield in each of these bonds, how should the bonds be ranked in terms of interest rate risk (from the highest risk to the lowest)?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">Bond A has the highest degree of interest rate risk, followed by Bond B, and Bond C.<\/li>\n<li data-tadv-p=\"keep\">Bond B has the highest degree of interest rate risk, followed by Bond C, and Bond A.<\/li>\n<li data-tadv-p=\"keep\">Bond C has the highest degree of interest rate risk, followed by Bond B, and Bond A.<\/li>\n<\/ol>\n<p class=\"Style2AltBaslik\" style=\"line-height: 130%; margin: 12.0pt 0cm 12.0pt 0cm;\"><strong><span lang=\"EN-US\">Solution<\/span><\/strong><\/p>\n<p class=\"Text001\"><span lang=\"EN-US\">The correct answer is <strong>A<\/strong>. <\/span><\/p>\n<p>Based on the assumed changes in the yields and given measures of modified duration and convexity, Bond A has the highest degree of interest rate risk followed by Bond B, and then Bond C.<\/p>\n<p>Bond A: %\u0394PV<sup>FULL<\/sup> \u2248 (-3.50\u00d70.0025) + (1\/2\u00d7100\u00d7(0.0025)<sup>2<\/sup>) \u2248 -0.0084375<\/p>\n<p>Bond B: %\u0394PV<sup>FULL<\/sup> \u2248 (-5.25\u00d70.0015) + (1\/2\u00d7350\u00d7(0.0015)<sup>2<\/sup>) \u2248 -0.0074813<\/p>\n<p>Bond C: %\u0394PV<sup>FULL<\/sup> \u2248 (-5.30\u00d70.0010) + (1\/2\u00d7250\u00d7(0.0010)<sup>2<\/sup>) \u2248 -0.005175<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Time horizon is an important aspect of understanding interest rate risk and the return characteristics of a fixed-rate investment. The primary concern for an investor is the change in the price of a bond given a sudden change in its&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-3473","post","type-post","status-publish","format-standard","hentry","category-fixed-income","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>Term Structure &amp; Interest Rate Risk | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand how changes in yield-to-maturity impact bond prices and explore the term structure of interest rates.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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