{"id":251,"date":"2026-07-19T16:20:31","date_gmt":"2026-07-19T16:20:31","guid":{"rendered":"https:\/\/eclass.co.ke\/class\/lesson\/3-3-relationships-among-a-bond-s-price-coupon-rate-maturity-and-market-discount-rate-yield-to\/"},"modified":"2026-07-19T17:41:25","modified_gmt":"2026-07-19T17:41:25","slug":"3-3-relationships-among-a-bond-s-price-coupon-rate-maturity-and-market-discount-rate-yield-to","status":"publish","type":"eclass_lesson","link":"https:\/\/eclass.co.ke\/class\/lesson\/3-3-relationships-among-a-bond-s-price-coupon-rate-maturity-and-market-discount-rate-yield-to\/","title":{"rendered":"3.3 Relationships among a bond&#8217;s price, coupon rate, maturity, and market discount rate (yield-to-maturity):"},"content":{"rendered":"<p>Bond Coupon Rate Maturity Price at 20% Discount Rates Go Down Discount Rates Go Up Price at 19% % Change Price at 21% % Change A 10% 10 58.075 60.950 4.95% 55.405 -4.60% B 20% 10 100.000 104.339 4.34% 95.946 -4.05% C 30% 10 141.925 147.728 4.09% 136.487 -3.83% D 10% 20 51.304 54.092 5.43% 48.776 -4.93% E 20% 20 100.000 105.101 5.10% 95.343 -4.66% F 30% 20 148.696 156.109 4.99% 141.910 -4.56%<\/p>\n<h3>3.3.1 Bond Price &#8211; Coupon Rate Relationship<\/h3>\n<p>For the same time-to-maturity, a lower-coupon bond has a greater percentage price change than a higher-coupon bond when their market discount rates change by the same amount (the coupon effect).<\/p>\n<p>Consider Bonds A, B, and C, which have 10 years to maturity. For both the decrease and increase in the yield-to-maturity, Bond A has a larger percentage price change than Bond B and Bond B has a larger change than C. The same pattern holds for the 20-year bonds. Therefore, lower- coupon bonds have more price volatility than higher-coupon bonds, other things being equal.<\/p>\n<h3>3.3.2 Bond Price &#8211; Maturity Relationship<\/h3>\n<p>For the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount (the maturity effect).<\/p>\n<p>Compare the results for Bonds A and D and for Bonds B and E. The 20-year bonds have greater percentage price changes than the 10-year bonds for either an increase or a decrease in the market discount rate.<\/p>\n<p>In general, longer-term bonds have more price volatility than shorter-term bonds, other things being equal.<\/p>\n<h3>3.3.3 Bond Price &#8211; Market Discount Rate (YTM) Relationship<\/h3>\n<p>The price of a fixed-rate bond will change whenever the market discount rate changes.<\/p>\n<ul>\n<li>The bond price is inversely related to the market discount rate. When the market discount rate increases, the bond price decreases (the inverse effect).<\/li>\n<\/ul>\n<p>All bond prices in the table go up when the rates go down from 20% to 19%, and all prices go down when the rates go up from 20% to 21%.<\/p>\n<ul>\n<li>The percentage price change is greater when the market discount rate goes down than when it goes up (the convexity effect).<\/li>\n<\/ul>\n<p>For each bond, the percentage price increases are greater in absolute value than the percentage price decreases. This implies that the relationship between bond prices and the market discount rate is not linear; instead, it is curved. It is described as being &quot;convex.&quot;<\/p>\n<h3>Lesson Wrap-Up<\/h3>\n<p>This lesson should leave you able to explain the relationships among a bond&#x27;s price, coupon rate, maturity, and market discount rate (yield-to-maturity): 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 bond price &#8211; coupon rate relationship in your own words.<\/li>\n<li>Explain bond price &#8211; maturity relationship in your own words.<\/li>\n<li>Explain bond price &#8211; market discount rate (ytm) relationship in your own words.<\/li>\n<li>State one exam-style risk, valuation, or market implication of the relationships among a bond&#x27;s price, coupon rate, maturity, and market discount rate (yield-to-maturity):.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Bond Coupon Rate Maturity Price at 20% Discount Rates Go Down Discount Rates Go Up Price at 19% % Change Price at 21% % Change A 10% 10 58.075 60.950 4.95% 55.405 -4.60% B 20% 10 100.000 104.339 4.34% 95.946 -4.05% C 30% 10 141.925 147.728 4.09% 136.487 -3.83% D 10% 20 51.304 54.092 5.43% [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-251","eclass_lesson","type-eclass_lesson","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/251","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=251"}],"version-history":[{"count":2,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/251\/revisions"}],"predecessor-version":[{"id":387,"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/eclass_lesson\/251\/revisions\/387"}],"wp:attachment":[{"href":"https:\/\/eclass.co.ke\/class\/wp-json\/wp\/v2\/media?parent=251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}