{"id":2582,"date":"2008-08-11T18:40:40","date_gmt":"2008-08-11T22:40:40","guid":{"rendered":"http:\/\/www.prefblog.com\/?p=2582"},"modified":"2008-08-11T18:40:40","modified_gmt":"2008-08-11T22:40:40","slug":"perpetualdiscount-duration-calculation","status":"publish","type":"post","link":"https:\/\/prefblog.com\/?p=2582","title":{"rendered":"PerpetualDiscount Duration Calculation"},"content":{"rendered":"<p>Very simple.<\/p>\n<p>Given that the yield is &#8220;r&#8221; per period and that the first payment is received exactly one period hence:<\/p>\n<p>Macaulay Duration = (1+r) \/ r<\/p>\n<p>Modified Duration = 1 \/ r<\/p>\n<p>And <a href=\"http:\/\/www.prefblog.com\/wp-content\/uploads\/2008\/08\/derivedurperp.tif\">here&#8217;s the proof<\/a> (TIF file).<\/p>\n<p>Note that, strictly speaking, these are the durations of a perpetual annuity; the assumption of perpetuity gets shakier as redemption becomes more likely.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Very simple. Given that the yield is &#8220;r&#8221; per period and that the first payment is received exactly one period hence: Macaulay Duration = (1+r) \/ r Modified Duration = 1 \/ r And here&#8217;s &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-2582","post","type-post","status-publish","format-standard","hentry","category-primers"],"_links":{"self":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/posts\/2582","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2582"}],"version-history":[{"count":0,"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/posts\/2582\/revisions"}],"wp:attachment":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2582"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2582"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}