What is a consol bond? What is the duration of a consol bond that sells at a yield to maturity of 8 percent? 10percent? 12percent? Would a consol trading at a yield to maturity of 10 percent have a greater duration than a 20-year zero-coupon bond trading at the same yield to maturity? Why?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n A consol bond<\/strong> is a type of perpetuity bond that pays a fixed coupon indefinitely, without ever maturing. Instead of repaying the principal, the issuer pays interest payments forever. Its price can be calculated using the formula:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n The duration<\/strong> of a consol bond is its Macauley duration<\/strong>, which measures the sensitivity of the bond’s price to changes in interest rates. For a perpetuity, the duration is calculated as:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n The duration of a zero-coupon bond equals its time to maturity, i.e., 20 years. A consol bond trading at a 10% YTM has a duration of 11 years<\/strong>, which is significantly less than the duration of the 20-year zero-coupon bond.<\/p>\n\n\n\n The duration of a zero-coupon bond is equal to its maturity because all the cash flow occurs at the end. In contrast, the duration of a consol bond is determined by its infinite series of fixed coupon payments, making it less sensitive to changes in interest rates over long horizons. This reflects the time-weighted average of receiving cash flows, which is shorter for a consol bond than for a long-dated zero-coupon bond. Thus, the consol bond has less interest rate risk.<\/p>\n","protected":false},"excerpt":{"rendered":" What is a consol bond? What is the duration of a consol bond that sells at a yield to maturity of 8 percent? 10percent? 12percent? Would a consol trading at a yield to maturity of 10 percent have a greater duration than a 20-year zero-coupon bond trading at the same yield to maturity? Why? The […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-183936","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183936","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=183936"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183936\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183936"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183936"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}What is a Consol Bond?<\/h3>\n\n\n\n
P = \\frac{C}{r}
]<\/p>\n\n\n\n\n
\n\n\n\nDuration of a Consol Bond<\/h3>\n\n\n\n
D = \\frac{1 + r}{r}
]<\/p>\n\n\n\n\n
Calculations:<\/h4>\n\n\n\n
\n
[
D = \\frac{1 + 0.08}{0.08} = \\frac{1.08}{0.08} = 13.5 \\text{ years}
]<\/li>\n\n\n\n
[
D = \\frac{1 + 0.10}{0.10} = \\frac{1.10}{0.10} = 11 \\text{ years}
]<\/li>\n\n\n\n
[
D = \\frac{1 + 0.12}{0.12} = \\frac{1.12}{0.12} = 9.33 \\text{ years}
]<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nComparison with a 20-Year Zero-Coupon Bond<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n