{"id":17230,"date":"2021-07-08T23:05:39","date_gmt":"2021-07-08T23:05:39","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=17230"},"modified":"2024-04-06T11:01:28","modified_gmt":"2024-04-06T11:01:28","slug":"explain-how-a-bonds-exposure-to-each-of-the-factors-driving-the-yield-curve-can-be-measured-and-how-these-exposures-can-be-used-to-manage-yield-curve-risks","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/explain-how-a-bonds-exposure-to-each-of-the-factors-driving-the-yield-curve-can-be-measured-and-how-these-exposures-can-be-used-to-manage-yield-curve-risks\/","title":{"rendered":"Measuring Bond Exposure"},"content":{"rendered":"\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/ovQh3D6WBOw\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p><em><strong>Shaping risk<\/strong> <\/em>is the sensitivity of a bond\u2019s price to changes in the shape of the yield curve. An active bond investor trades based on the predicted shape of the yield curve.<\/p>\r\n<p><em><strong>Yield curve<\/strong> <strong>risk<\/strong> <\/em>is the bond portfolio exposure to shifts in the yield curve. Yield curve movements can be explained by independent changes along any of its different dimensions, including level, steepness, and curvature.<\/p>\r\n<h2>Level, Steepness, and Curvature<\/h2>\r\n<ul>\r\n\t<li><em><strong>Level:<\/strong><\/em> Relates to the parallel up or down movement of the yield curve. Empirical evidence shows that up and downshifts in the yield curve explain more than 75% of the yield curve\u2019s total change.<\/li>\r\n\t<li><em><strong>Steepness:<\/strong> <\/em>Relates to the non-parallel shift in the yield curve, i.e., an increase in the long-term interest rates with a decrease in the short-term interest rates.<\/li>\r\n\t<li><em><strong>Curvature:<\/strong> <\/em>The rise in the long-term and short-term parts of the yield curve with the middle part falling or vice versa.<\/li>\r\n<\/ul>\r\n<p>Let \\(D_L\\), \\(D_S\\), and \\(D_C\\) be a given portfolio\u2019s sensitivities to small changes in the level, slope, and curvature factors, respectively.<\/p>\r\n<p>A small change in the level factor, slope factor, and curvature factor would result in a proportional change in the portfolio value as given below:<\/p>\r\n<p>$$ \\cfrac {\\Delta P}{P}\\approx -D_L \\Delta x_L-D_S \\Delta x_S-D_C \\Delta x_C $$<\/p>\r\n<p>Where \\(\\Delta x\\) is the change in the respective factors.<\/p>\r\n<h4>Example: Level, Steepness, and Curvature<\/h4>\r\n<p>The yield curve risk of a certain bond portfolio is expressed as:<\/p>\r\n<p>$$ \\cfrac {\\Delta P}{P}\\approx -2\\Delta x_L-3\\Delta x_S-\\Delta x_C $$<\/p>\r\n<p>Given that the following yield curve changes occurred: \\(\\Delta x_L=0.003, \\Delta x_S=-0.002,\\Delta x_C=-0.004\\), calculate the percentage change in the value of the portfolio.<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$ \\cfrac {\\Delta P}{P}\\approx-2\u00d70.003-3\u00d7-0.002&#8211;0.004=0.004=0.4\\% $$<\/p>\r\n<p>Therefore, 0.4% is the predicted increase in the portfolio\u2019s value resulting from shifts in the yield curve.<\/p>\r\n<p>The yield curve risk can also be measured and managed using effective duration and key rate duration measures as discussed below:<\/p>\r\n<h2>Effective Duration<\/h2>\r\n<p>The <em><strong>effective duration<\/strong><\/em> measures the price sensitivity to a small parallel shift in the benchmark yield curve, assuming that the bond\u2019s credit spread remains constant.<\/p>\r\n<p>The effective duration of a zero-coupon bond is equivalent to its maturity. This measure is inappropriate for identifying and managing the yield curve risk associated with non-parallel shifts.<\/p>\r\n<h2>Key Rate Duration<\/h2>\r\n<p>The <em><strong>key rate duration<\/strong><\/em> measures a bond\u2019s sensitivity to a small change in a benchmark yield curve at a specific spot rate, keeping all else constant.<\/p>\r\n<p>Unlike effective duration, this measure allows for identifying and managing risk, i.e., interest rate sensitivity to non-parallel shifts in the yield curve.<\/p>\r\n<p>The formula for key rate duration is the following:<\/p>\r\n<p>$$ \\cfrac {\\Delta P}{P}\\approx -D_1 \\Delta r_1-D_2 \\Delta r_2-D_3\\Delta r_3 $$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(D_i\\) is the key rate duration of the portfolio to the i<sup>th<\/sup> rate.<\/p>\r\n<p>\\(r_i\\) is the i<sup>th<\/sup> key rate.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Which yield curve risk measures is <em>least<\/em> appropriate for measuring shaping risk?<\/p>\r\n<ol type=\"A\">\r\n\t<li>Effective duration.<\/li>\r\n\t<li>Key rate duration.<\/li>\r\n\t<li>A model that decomposes yield curve movements into changes in level, steepness, and curvature.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is A.<\/strong><\/p>\r\n<p>Shaping risk can be addressed by key rate durations and a measure based on sensitivities to level, slope, and curvature movements.<\/p>\r\n<p>However, the effective duration is not an accurate measure of interest rate sensitivity to non-parallel shifts in the yield curve.<\/p>\r\n<\/blockquote>\r\n<p>Reading 28: The Term Structure and Interest Rate Dynamics.<\/p>\r\n<p><em>LOS 28 (i) Explain how a bond\u2019s exposure to each of the factors driving the yield curve can be measured and how these exposures can be used to manage yield curve risks.<\/em><\/p>\r\n\n            <div \n                class=\"elfsight-widget-pricing-table elfsight-widget\" \n                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An active bond investor trades based on the predicted shape of the yield curve. Yield curve risk is the bond portfolio exposure&#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-17230","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>Measuring Bond Exposure - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Yield curve movements can be explained by independent changes along any of its different dimensions, including level, steepness, and curvature\" \/>\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\/explain-how-a-bonds-exposure-to-each-of-the-factors-driving-the-yield-curve-can-be-measured-and-how-these-exposures-can-be-used-to-manage-yield-curve-risks\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Measuring Bond Exposure - 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