{"id":33566,"date":"2023-11-23T17:16:58","date_gmt":"2023-11-23T17:16:58","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=33566"},"modified":"2024-03-20T07:17:29","modified_gmt":"2024-03-20T07:17:29","slug":"an-approach-to-assessing-yield-curve-strategies","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/an-approach-to-assessing-yield-curve-strategies\/","title":{"rendered":"An Approach to Assessing Yield Curve Strategies"},"content":{"rendered":"<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/BGinionbfpQ\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Scenario Analysis<\/h2>\n<p>As described earlier, many factors can change the return of a fixed-income portfolio, including changes in the yield curve. These changes can involve the curve&#8217;s slope, level, shape, and underlying currencies. Scenario analysis refers to a set of tools used to measure the changes in multiple inputs into a fixed-income portfolio value, all happening simultaneously. For example, a manager may use scenario analysis to measure the impact of a curve that slopes upward, and simultaneously appreciates underlying currency. The scenario analysis would allow viewing the impact on the portfolio&#8217;s price under the new conditions without recalculating all of the offsetting effects one by one.<\/p>\n<\/p>\n<p>$$ \\begin{align*} &#038; \\text{Expected } \\Delta \\% \\text{ Bond Price} \\\\ &#038; = (-\\text{Mod Duration} \\times \\Delta \\text{Yield}) + \\left[ \\frac {1}{2} \\times \\text{Convexity} \\times (\\Delta \\text{Yield})^2) \\right] \\end{align*} $$<\/p>\n<p>$$ \\begin{array}{c|c|c}<br \/>\n\\textbf{Maturity} &#038;\t\\textbf{ModDuration} &#038;\t\\textbf{Convexity} \\\\ \\hline<br \/>\n2yr &#038;\t2.15 &#038;\t7.0 \\\\ \\hline<br \/>\n5yr &#038;\t4.08 &#038;\t20.4 \\\\ \\hline<br \/>\n10yr &#038;\t7.22 &#038;\t33.98<br \/>\n\\end{array} $$<\/p>\n<p>A manager considering scenario analysis could use the equation listed above in conjunction with the portfolio bond data to calculate a final portfolio value under two different circumstances, such as:<\/p>\n<ul>\n<li><strong>A flattening of the yield curve<\/strong> (No change in the 2-year yield, a 50bp fall in the 5-year yield, and a 75bp fall in the 10-year yield.).<\/li>\n<li><strong>A steepening of the yield curve<\/strong> (No change in the 2-year yield, a 50bp rise in the 5-year yield, and a 75bp rise in the 10-year yield.)<\/li>\n<\/ul>\n<p>If the portfolio is a bullet portfolio, <em>made up of all 5-year notes<\/em>, the final portfolio would be calculated as:<\/p>\n<p><u><strong>Flattening of the yield curve:<\/strong><\/u><\/p>\n<p>$$ \\begin{align*} &#038; \\text{Expected } \\Delta \\% \\text{ Bond Price} \\\\ &#038; = (-\\text{Mod Duration} \\times \\Delta \\text{Yield}) + \\left[\\frac{1}{2} \\times \\text{Convexity} \\times (\\Delta \\text{Yield})^2)\\right] \\end{align*} $$<\/p>\n<p><u><strong>5-year Bonds:<\/strong><\/u><\/p>\n<p>$$  \\begin{align*} (-4.08 \\times -0.005) + \\left[\\frac {1}{2} \\times 20.4 \\times (-0.005)^2 \\right] &#038; =  +  = 0.0204 +  0.005202 \\\\ &#038; = 2.5602\\%  \\end{align*} $$<\/p>\n<p><u><strong>Steepening of the yield curve:<\/strong><\/u><\/p>\n<p>$$ \\begin{align*}<br \/>\n(-4.08 \\times 0.005) + \\left[\\frac{1}{2} \\times 20.4 \\times (0.005)^2 \\right] &#038; =  +  = -0.0244 + 0.005202 \\\\ &#038; = -1.9198\\%  \\end{align*} $$<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Based on the information in the provided table, what is the anticipated effect of a yield curve flattening on a portfolio consisting of equally-weighted 2-year and 10-year notes?\n<\/p>\n<ol type=\"A\">\n<li>5.51%.<\/li>\n<li>2.75%.<\/li>\n<li>-3.15%.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p><strong>The correct answer is B.<\/strong><\/p>\n<p><p>$$ \\begin{array}{c|c|c}<br \/>\n\\textbf{Maturity} &#038;\t\\textbf{ModDuration} &#038;\t\\textbf{Convexity} \\\\ \\hline<br \/>\n2yr &#038;\t2.15 &#038;\t7.0 \\\\ \\hline<br \/>\n10yr &#038;\t7.22 &#038;\t33.98<br \/>\n\\end{array} $$<\/p>\n<p><strong>A flattening involves<\/strong> &#8211; (No change in 2-year yields, a 50bp fall in the 5-year yield, and a 75bp fall in the 10-year yield.)<\/p>\n<p>$$ \\begin{align*} &#038; \\text{Expected } \\Delta \\% \\text{ Bond Price} \\\\ &#038; = (-\\text{Mod Duration} \\times \\Delta \\text{Yield}) + \\left[\\frac{1}{2} \\times \\text{Convexity} \\times (\\Delta \\text{Yield})^2)\\right] \\end{align*} $$<\/p>\n<p><u>10-year Bonds<\/u><\/p>\n<p>$$ \\begin{align*} &#038; (-7.22 \\times -0.0075) + \\left[ \\frac{1}{2} \\times 33.98 \\times (-0.0075)^2 \\right] \\\\  = &#038;  0.05415 + 0.0009556875 \\\\    = &#038;  5.51\\% \\end{align*} $$<\/p>\n<p>Given the equal-weighted allocation of the portfolio between the 2-year and 10-year notes, the projected price adjustment will be the average of the changes in the 2-year and 10-year notes. As a result, the correct choice is B \\(\\left(\\frac {5.51\\%}{2} \\right)\\).<\/p>\n<p><strong>A is incorrect.<\/strong> The correct answer is B based on the above workings.<\/p>\n<p><strong>C is incorrect.<\/strong> It should be rejected since it implies an anticipated loss in the portfolio. This option contradicts the portfolio&#8217;s exposure, which involves either an unchanged rate in the 2-year portion or a decreasing rate in the 10-year portion. Thus, a positive portfolio change is to be expected, not a negative one.\n<\/p>\n<\/blockquote>\n<p>Reading 21: Yield Curve Strategies<\/p>\n<p>Los 21 (g) Evaluate the expected return and risks of a yield curve strategy<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Scenario Analysis As described earlier, many factors can change the return of a fixed-income portfolio, including changes in the yield curve. These changes can involve the curve&#8217;s slope, level, shape, and underlying currencies. Scenario analysis refers to a set of&#8230;<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[571],"tags":[],"class_list":["post-33566","post","type-post","status-publish","format-standard","hentry","category-cfa-level-iii","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>An Approach to Assessing Yield Curve Strategies - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Explore a scenario where a portfolio consists of equally-weighted 2-year and 10-year notes, and determine the anticipated effect of a yield curve flattening.\" \/>\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-iii\/an-approach-to-assessing-yield-curve-strategies\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An Approach to Assessing Yield Curve Strategies - 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