{"id":264,"date":"2026-07-19T16:20:31","date_gmt":"2026-07-19T16:20:31","guid":{"rendered":"https:\/\/eclass.co.ke\/class\/lesson\/4-6-effect-of-a-bond-s-maturity-coupon-embedded-options-and-yield-level-on-its-interest-rate-r\/"},"modified":"2026-07-19T17:41:25","modified_gmt":"2026-07-19T17:41:25","slug":"4-6-effect-of-a-bond-s-maturity-coupon-embedded-options-and-yield-level-on-its-interest-rate-r","status":"publish","type":"eclass_lesson","link":"https:\/\/eclass.co.ke\/class\/lesson\/4-6-effect-of-a-bond-s-maturity-coupon-embedded-options-and-yield-level-on-its-interest-rate-r\/","title":{"rendered":"4.6 Effect of a bond&#8217;s maturity, coupon, embedded options, and yield level on its interest rate risk"},"content":{"rendered":"<p>Bond duration is the basic measure of interest rate risk on a fixed-rate bond.<\/p>\n<p>The duration for a fixed-rate bond is a function of the following input variables.<\/p>\n<ul>\n<li>Coupon rate or payment per period<\/li>\n<li>Yield-to-maturity per period<\/li>\n<li>Time-to-maturity (as of the beginning of the period)<\/li>\n<li>Fraction of the period that has gone by<\/li>\n<li>Presence and nature of embedded options The coupon payments are made on regularly scheduled dates-for example, on 15 June and 15 December each year on a semiannual coupon paying bond. The last coupon is paid together with the face value on the maturity date. The market discount rate is also called the &quot;required yield&quot; or &quot;required rate of return.&quot;<\/li>\n<li>Coupon rate relation to Macaulay duration:<\/li>\n<li>The coupon rate is inversely related to the Macaulay duration. A lower-coupon bond has a higher duration and more interest rate risk than a higher-coupon bond. The Macaulay duration of a zero-coupon bond is equal to its time-to-maturity.<\/li>\n<li>Yield-to-Maturity relation to Macaulay duration:<\/li>\n<li>The yield-to-maturity is inversely related to the Macaulay duration. A higher yield-to- maturity reduces the weighted average of the time to receipt of cash flow. With a higher yield-to-maturity, there is more weight on the cash flows received in the near term, and less weight is on the cash flows received in the more-distant future periods if those cash flows are discounted at a higher rate.<\/li>\n<li>Time-to-Maturity relation to Macaulay duration:<\/li>\n<li>Time-to-maturity is typically directly related to the Macaulay duration. This pattern always holds for bonds trading at par value or at a premium above par. The exception is deep- discount bonds, where the relationship does not hold for a long time-to-maturity.<\/li>\n<li>Fraction of the period relation to Macaulay duration:<\/li>\n<li>Fraction of the period that has gone by (t\/T) is inversely related to the Macaulay duration.<\/li>\n<\/ul>\n<p>Macaulay duration decreases smoothly as t goes from t = 0 to t = T and then jumps upward after the coupon is paid. The duration of perpetuity (consol bond) is the constant.<\/p>\n<ul>\n<li>Bonds with embedded options:<\/li>\n<li>Bonds with embedded options (e.g., callable, putable) require the use of effective duration because Macaulay and modified yield duration statistics are not relevant.<\/li>\n<li>The yield-to-maturity for callable and putable bonds is not well defined because future cash flows are uncertain.<\/li>\n<li>When benchmark yields are high (low), the effective durations of the callable (putable) and non-callable (non-putable) bonds are very similar. There is a large discrepancy in durations for callable (putable) and non-callable (non-putable) bonds when yields are low (high).<\/li>\n<li>In summary, the presence of an embedded option reduces the sensitivity of the bond price to changes in the benchmark yield curve (lower duration), assuming no change in credit risk.<\/li>\n<li>Effective duration measures are also used for bonds with other embedded options, such as asset-backed securities.<\/li>\n<\/ul>\n<h3>Lesson Wrap-Up<\/h3>\n<p>This lesson should leave you able to explain the effect of a bond&#x27;s maturity, coupon, embedded options, and yield level on its interest rate risk in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.<\/p>\n<h3>Review Prompts<\/h3>\n<ol>\n<li>Explain effect of a bond&#x27;s maturity, coupon, embedded options, and yield level on its interest rate risk in your own words.<\/li>\n<li>State one exam-style risk, valuation, or market implication of the effect of a bond&#x27;s maturity, coupon, embedded options, and yield level on its interest rate risk.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Bond duration is the basic measure of interest rate risk on a fixed-rate bond. The duration for a fixed-rate bond is a function of the following input variables. Coupon rate or payment per period Yield-to-maturity per period Time-to-maturity (as of the beginning of the period) Fraction of the period that has gone by Presence and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-264","eclass_lesson","type-eclass_lesson","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/264","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson"}],"about":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/types\/eclass_lesson"}],"author":[{"embeddable":true,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/comments?post=264"}],"version-history":[{"count":2,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/264\/revisions"}],"predecessor-version":[{"id":400,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/264\/revisions\/400"}],"wp:attachment":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/media?parent=264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}