{"id":205664,"date":"2024-04-26T11:02:56","date_gmt":"2024-04-26T15:02:56","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=205664"},"modified":"2024-04-26T11:02:38","modified_gmt":"2024-04-26T15:02:38","slug":"bond-modified-duration-in-excel-and-r","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/","title":{"rendered":"Bond Modified Duration in Excel and R"},"content":{"rendered":"\n

Bond duration is a basic building block for bond portfolio management and asset-liability management (ALM). This post explains the meaning of duration and calculation of this risk measure by using Excel and R.<\/p>\n\n\n\n

In this post, a bond price is calculated by discounting future cash flows using YTM<\/strong> which is the abbreviation of Yield To Maturity<\/strong>.<\/p>\n\n\n\n

Bond Price<\/h3>\n\n\n\n

Bond price with unit notional amount, coupon C, YTM y, annual frequency is as follows.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

(Modified) Duration<\/h3>\n\n\n\n

Duration is a measure of price sensitivity to interest rates. At first, we need to calculate an interest rate sensitivity of a bond price.<\/p>\n\n\n\n

The first derivative of P<\/em><\/strong> with respect to y <\/strong><\/em>is as follows.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Factoring out \"\"in the above equation yields<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

To avoid lengthy expression, we substitute STDC<\/strong> for the bracketed term. STDC<\/strong> is the abbreviation of the s<\/strong>um of multiplications of t<\/strong>ime and d<\/strong>iscounted c<\/strong>ash flow (only coupon or coupon + principal amount). Of course, this abbreviation is not official<\/p>\n\n\n\n

It is noting that the above amount is a kind of a change of bond price<\/strong>. But it is more convenient to use the expression of a percentage change<\/strong> for comparison or analysis. For this reason, let’s modify it by a ratio of its initial bond price<\/strong>.<\/p>\n\n\n\n

Through this modification, we can use this measure as a % change of bond price which resulted from a change of interest rate. Dividing<\/strong> \"\" by P<\/em><\/strong> gives the following expression.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

This is the modified duration (D)<\/strong>. Modified duration is defined without negative sign since this “minus” sign is popped out of discounting, which indicates that an increase in interest rate lowers a bond price.<\/p>\n\n\n\n

Rearranging this equation, we can find that % change of bond price results from the multiplication of modified duration and interest rate change<\/strong>.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

For example,<\/p>\n\n\n\n

1) If modified duration is 1 (year)<\/strong> and interest rate change is +25bp (= +0.25%<\/strong>), % change of bond price is equal to -0.25%<\/strong> (= -1*0.25%).<\/p>\n\n\n\n

2) If modified duration is 10 (year)<\/strong> and interest rate change is +25bp (= +0.25%<\/strong>), % change of bond price is equal to -2.5%<\/strong> (= -10*0.25%).<\/p>\n\n\n\n

In other words, the longer the duration or maturity of a bond, the more sensitive is it’s price to a change in interest rates<\/strong>. For this reason, when the central bank increases the target rate, bond portfolio managers have a tendency to make bond portfolio duration shorter to avoid subsequent capital loss due to interest rate hikes. But it is not always.<\/p>\n\n\n\n

Macaulay Duration<\/h3>\n\n\n\n

In fact, Macaulay originally invented the concept of duration. This is called as Macaulay duration<\/strong> which is the average time until receipt of a bond’s cash flows, weighted according to the present values of these cash flows, measured in years.<\/p>\n\n\n\n

Interestingly, it is already calculated in the previous equation. Macaulay duration \"\" is as follows.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The relationship between modified duration and Macaulay duration is<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

It is worth while to note that the meaning of “modified” is the modification of Macaulay duration by dividing 1 + y<\/strong>.<\/p>\n\n\n\n

As modified duration is widely used than Macaulay duration, when we use the term of duration, it is the modified duration. For this reason, we use D<\/em><\/strong> for the modified duration and Dmac<\/sub><\/em><\/strong> for Macaulay duration.<\/p>\n\n\n\n

Generalization<\/h3>\n\n\n\n

When interest conversion period is less than one year such as one quarter, duration is redefined as follows.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Here, k is the number of compounding periods per year.<\/p>\n\n\n\n

Excel Illustration<\/strong><\/p>\n\n\n\n

Excel provides MDURATION()<\/strong> function for the calculation of modified duration.<\/p>\n\n\n\n

    MDURATION (settlement, maturity, coupon, yld, freq)<\/strong><\/p>\n\n\n\n

Arguments of MDURATION() are pricing date, maturity date, coupon rate, YTM, compounding frequency<\/strong> in order.<\/p>\n\n\n\n

Besides MDURATION(), we calculate duration by using definition and numerical differentiation for clear understanding.<\/p>\n\n\n\n

The following Excel spreadsheet shows the case of k=1.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The following Excel spreadsheet shows the case of k=4.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

R code<\/h3>\n\n\n\n

No sooner had we explained the concept of duration than we made the following R code.<\/p>\n\n\n\n

#========================================================#\n# Quantitative ALM, Financial Econometrics & Derivatives \n# ML\/DL using R, Python, Tensorflow by Sang-Heon Lee \n#\n# https:\/\/shleeai.blogspot.com\n#--------------------------------------------------------#\n# Bond Modified Duration Calculation\n#========================================================#\n \ngraphics.off()  # clear all graphs\nrm(list = ls()) # remove all files from your workspace\n \n#-------------------------------------------------------\n# Input\n#-------------------------------------------------------\n    C  <- 0.05       # coupon rate\n    y  <- 0.03       # YTM\n    m  <- 5          # maturity\n    dr <- 0.000001   # interest rate change\n \n#-------------------------------------------------------\n# Duration by Definition (k=1)\n#-------------------------------------------------------\n    \n    # data.frame for calculation\n    df <- data.frame(T = 1:m, \n                     CF = C + c(0,0,0,0,1))\n    \n    df$DF <- 1\/(1+y)^(df$T)\n    df$DC <- df$DF*df$CF\n    \n    P0 <- sum(df$DC) # initial bond price\n    \n    df$TDC <- df$T*df$DC # time * discounted CF\n    \n    STDC <- sum(df$TDC)\n    \n    # duration\n    D_mac_dk1 <- STDC\/P0         # Macaulay Dur\n    D_mod_dk1 <- D_mac_dk1\/(1+y) # Modified Dur\n    \n#-------------------------------------------------------\n# Duration by Numerical Differentiation (k=1)\n#-------------------------------------------------------\n    \n    df <- data.frame(T = 1:m, \n                     CF = C + c(rep(0,m-1),1))\n    \n    df$DFu <- 1\/(1+y-dr)^(df$T)\n    df$DCu <- df$DFu*df$CF\n    \n    Pu <- sum(df$DCu) # price up\n    \n    df$DFd <- 1\/(1+y+dr)^(df$T)\n    df$DCd <- df$DFd*df$CF\n    \n    Pd <- sum(df$DCd) # price down\n    \n    # duration\n    D_mod_nk1 <- (Pu-Pd)\/(2*dr)\/P0 # Modified Dur\n    \n#-------------------------------------------------------\n# Duration by Definition (k=4)\n#-------------------------------------------------------\n    \n    k  <- 4 # Compouding period = Q\n    \n    df <- data.frame(T = seq(1\/k,m,1\/k), \n                     CF = C\/k + c(rep(0,k*m-1),1))\n    \n    df$DF <- 1\/(1+y\/k)^(df$T*k)\n    df$DC <- df$DF*df$CF\n    \n    P0 <- sum(df$DC)\n    \n    df$TDC <- df$T*df$DC\n    STDC <- sum(df$TDC)\n    \n    D_mac_dk4 <- STDC\/P0           # Macaulay Dur\n    D_mod_dk4 <- D_mac_dk4\/(1+y\/k) # Modified Dur\n    \n#-------------------------------------------------------\n# Duration by Numerical Differentiation (k=4)\n#-------------------------------------------------------\n \n    df <- data.frame(T = seq(1\/k,m,1\/k),\n                     CF = C\/k + c(rep(0,k*m-1),1))\n \n    df$DFu <- 1\/(1+(y-dr)\/k)^(df$T*k)\n    df$DCu <- df$DFu*df$CF\n \n    Pu <- sum(df$DCu)\n \n    df$DFd <- 1\/(1+(y+dr)\/k)^(df$T*k)\n    df$DCd <- df$DFd*df$CF\n \n    Pd <- sum(df$DCd)\n    D_mod_nk4 <- (Pu-Pd)\/(2*dr)\/P0 # Modified Dur\n \n    \n    # Print\n    cat(paste0(\"\\nDuration Calculation Results \\n\\n\",\n        \"Macaulay Dur (k=1) def = \", D_mac_dk1, \"\\n\",\n        \"Modified Dur (k=1) def = \", D_mod_dk1, \"\\n\",\n        \"Modified Dur (k=1) num = \", D_mod_nk1, \"\\n\",\n        \"\\n\",\n        \"Macaulay Dur (k=4) def = \", D_mac_dk4, \"\\n\",\n        \"Modified Dur (k=4) def = \", D_mod_dk4, \"\\n\",\n        \"Modified Dur (k=4) num = \", D_mod_nk4))<\/pre>\n\n\n\n
The above R code produces the same results as those of Excel exercises.<\/p>\n\n\n\n
Duration Calculation Results \n \nMacaulay Dur (k=1) def = 4.56806046946571\nModified Dur (k=1) def = 4.43501016452982\nModified Dur (k=1) num = 4.43501016417148\n \nMacaulay Dur (k=4) def = 4.48393573818857\nModified Dur (k=4) def = 4.45055656395888\nModified Dur (k=4) num = 4.45055656459531<\/pre>\n\n\n\n
Concluding Remarks<\/h3>\n\n\n\n
From this post, we can understand the meaning of duration, in particular modified duration, by using intuitive derivations and Excel illustrations. Finally we can easily implement R code for the calculation of duration. Upon this work, we can build up the advanced risk management or portfolio optimization model.<\/p>\n\n\n\n
But care is taken with some limitation of duration so that duration is the first derivative of highly non-linear bond price function, in other words, or the first order or linearly approximation<\/strong>. To make up for this shortcoming, the second order derivative (convexity<\/strong>) can be considered when the first approximation shows poor result. It depends on the product types and specifications.<\/p>\n\n\n\n
Originally posted on SHLee AI Financial Model<\/a> blog.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"
This post explains the meaning of duration and calculation of this risk measure by using Excel and R.<\/p>\n","protected":false},"author":662,"featured_media":205705,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[339,343,338,341,342],"tags":[45,806,5878,17052,487,6591],"contributors-categories":[13728],"class_list":{"0":"post-205664","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"category-programing-languages","9":"category-ibkr-quant-news","10":"category-quant-development","11":"category-r-development","12":"tag-bonds","13":"tag-data-science","14":"tag-excel","15":"tag-macaulay-duration","16":"tag-r","17":"tag-rstats","18":"contributors-categories-sh-fintech-modeling"},"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"\nBond Modified Duration in Excel and R | IBKR Quant<\/title>\n<meta name=\"description\" content=\"This post explains the meaning of duration and calculation of this risk measure by using Excel and R.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.interactivebrokers.com\/campus\/wp-json\/wp\/v2\/posts\/205664\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bond Modified Duration in Excel and R\" \/>\n<meta property=\"og:description\" content=\"This post explains the meaning of duration and calculation of this risk measure by using Excel and R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/\" \/>\n<meta property=\"og:site_name\" content=\"IBKR Campus US\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-26T15:02:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1000\" \/>\n\t<meta property=\"og:image:height\" content=\"563\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Sang-Heon Lee\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Sang-Heon Lee\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\n\t    \"@context\": \"https:\\\/\\\/schema.org\",\n\t    \"@graph\": [\n\t        {\n\t            \"@type\": \"NewsArticle\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/#article\",\n\t            \"isPartOf\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/\"\n\t            },\n\t            \"author\": {\n\t                \"name\": \"Sang-Heon Lee\",\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/person\\\/0a959ff9de7f0465a07baa1fe1ae0200\"\n\t            },\n\t            \"headline\": \"Bond Modified Duration in Excel and R\",\n\t            \"datePublished\": \"2024-04-26T15:02:56+00:00\",\n\t            \"mainEntityOfPage\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/\"\n\t            },\n\t            \"wordCount\": 818,\n\t            \"commentCount\": 0,\n\t            \"publisher\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#organization\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/#primaryimage\"\n\t            },\n\t            \"thumbnailUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/04\\\/market-charts-coins-light-blue.jpg\",\n\t            \"keywords\": [\n\t                \"bonds\",\n\t                \"Data Science\",\n\t                \"Excel\",\n\t                \"Macaulay Duration\",\n\t                \"R\",\n\t                \"rstats\"\n\t            ],\n\t            \"articleSection\": [\n\t                \"Data Science\",\n\t                \"Programming Languages\",\n\t                \"Quant\",\n\t                \"Quant Development\",\n\t                \"R Development\"\n\t            ],\n\t            \"inLanguage\": \"en-US\",\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"CommentAction\",\n\t                    \"name\": \"Comment\",\n\t                    \"target\": [\n\t                        \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/#respond\"\n\t                    ]\n\t                }\n\t            ]\n\t        },\n\t        {\n\t            \"@type\": \"WebPage\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/\",\n\t            \"url\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/\",\n\t            \"name\": \"Bond Modified Duration in Excel and R | IBKR Campus US\",\n\t            \"isPartOf\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#website\"\n\t            },\n\t            \"primaryImageOfPage\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/#primaryimage\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/#primaryimage\"\n\t            },\n\t            \"thumbnailUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/04\\\/market-charts-coins-light-blue.jpg\",\n\t            \"datePublished\": \"2024-04-26T15:02:56+00:00\",\n\t            \"description\": \"This post explains the meaning of duration and calculation of this risk measure by using Excel and R.\",\n\t            \"inLanguage\": \"en-US\",\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"ReadAction\",\n\t                    \"target\": [\n\t                        \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/\"\n\t                    ]\n\t                }\n\t            ]\n\t        },\n\t        {\n\t            \"@type\": \"ImageObject\",\n\t            \"inLanguage\": \"en-US\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/ibkr-quant-news\\\/bond-modified-duration-in-excel-and-r\\\/#primaryimage\",\n\t            \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/04\\\/market-charts-coins-light-blue.jpg\",\n\t            \"contentUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/04\\\/market-charts-coins-light-blue.jpg\",\n\t            \"width\": 1000,\n\t            \"height\": 563,\n\t            \"caption\": \"Quant\"\n\t        },\n\t        {\n\t            \"@type\": \"WebSite\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#website\",\n\t            \"url\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/\",\n\t            \"name\": \"IBKR Campus US\",\n\t            \"description\": \"Financial Education from Interactive Brokers\",\n\t            \"publisher\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#organization\"\n\t            },\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"SearchAction\",\n\t                    \"target\": {\n\t                        \"@type\": \"EntryPoint\",\n\t                        \"urlTemplate\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/?s={search_term_string}\"\n\t                    },\n\t                    \"query-input\": {\n\t                        \"@type\": \"PropertyValueSpecification\",\n\t                        \"valueRequired\": true,\n\t                        \"valueName\": \"search_term_string\"\n\t                    }\n\t                }\n\t            ],\n\t            \"inLanguage\": \"en-US\"\n\t        },\n\t        {\n\t            \"@type\": \"Organization\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#organization\",\n\t            \"name\": \"Interactive Brokers\",\n\t            \"alternateName\": \"IBKR\",\n\t            \"url\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/\",\n\t            \"logo\": {\n\t                \"@type\": \"ImageObject\",\n\t                \"inLanguage\": \"en-US\",\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/logo\\\/image\\\/\",\n\t                \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/05\\\/ibkr-campus-logo.jpg\",\n\t                \"contentUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/05\\\/ibkr-campus-logo.jpg\",\n\t                \"width\": 669,\n\t                \"height\": 669,\n\t                \"caption\": \"Interactive Brokers\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/logo\\\/image\\\/\"\n\t            },\n\t            \"publishingPrinciples\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/about-ibkr-campus\\\/\",\n\t            \"ethicsPolicy\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/cyber-security-notice\\\/\"\n\t        },\n\t        {\n\t            \"@type\": \"Person\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/person\\\/0a959ff9de7f0465a07baa1fe1ae0200\",\n\t            \"name\": \"Sang-Heon Lee\",\n\t            \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/author\\\/sang-heonlee\\\/\"\n\t        }\n\t    ]\n\t}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Bond Modified Duration in Excel and R | IBKR Quant","description":"This post explains the meaning of duration and calculation of this risk measure by using Excel and R.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.interactivebrokers.com\/campus\/wp-json\/wp\/v2\/posts\/205664\/","og_locale":"en_US","og_type":"article","og_title":"Bond Modified Duration in Excel and R","og_description":"This post explains the meaning of duration and calculation of this risk measure by using Excel and R.","og_url":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/","og_site_name":"IBKR Campus US","article_published_time":"2024-04-26T15:02:56+00:00","og_image":[{"width":1000,"height":563,"url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg","type":"image\/jpeg"}],"author":"Sang-Heon Lee","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Sang-Heon Lee","Est. reading time":"7 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"NewsArticle","@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/#article","isPartOf":{"@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/"},"author":{"name":"Sang-Heon Lee","@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/person\/0a959ff9de7f0465a07baa1fe1ae0200"},"headline":"Bond Modified Duration in Excel and R","datePublished":"2024-04-26T15:02:56+00:00","mainEntityOfPage":{"@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/"},"wordCount":818,"commentCount":0,"publisher":{"@id":"https:\/\/ibkrcampus.com\/campus\/#organization"},"image":{"@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/#primaryimage"},"thumbnailUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg","keywords":["bonds","Data Science","Excel","Macaulay Duration","R","rstats"],"articleSection":["Data Science","Programming Languages","Quant","Quant Development","R Development"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/","url":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/","name":"Bond Modified Duration in Excel and R | IBKR Campus US","isPartOf":{"@id":"https:\/\/ibkrcampus.com\/campus\/#website"},"primaryImageOfPage":{"@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/#primaryimage"},"image":{"@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/#primaryimage"},"thumbnailUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg","datePublished":"2024-04-26T15:02:56+00:00","description":"This post explains the meaning of duration and calculation of this risk measure by using Excel and R.","inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/ibkrcampus.com\/campus\/ibkr-quant-news\/bond-modified-duration-in-excel-and-r\/#primaryimage","url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg","contentUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg","width":1000,"height":563,"caption":"Quant"},{"@type":"WebSite","@id":"https:\/\/ibkrcampus.com\/campus\/#website","url":"https:\/\/ibkrcampus.com\/campus\/","name":"IBKR Campus US","description":"Financial Education from Interactive Brokers","publisher":{"@id":"https:\/\/ibkrcampus.com\/campus\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ibkrcampus.com\/campus\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/ibkrcampus.com\/campus\/#organization","name":"Interactive Brokers","alternateName":"IBKR","url":"https:\/\/ibkrcampus.com\/campus\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/logo\/image\/","url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/05\/ibkr-campus-logo.jpg","contentUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/05\/ibkr-campus-logo.jpg","width":669,"height":669,"caption":"Interactive Brokers"},"image":{"@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/logo\/image\/"},"publishingPrinciples":"https:\/\/www.interactivebrokers.com\/campus\/about-ibkr-campus\/","ethicsPolicy":"https:\/\/www.interactivebrokers.com\/campus\/cyber-security-notice\/"},{"@type":"Person","@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/person\/0a959ff9de7f0465a07baa1fe1ae0200","name":"Sang-Heon Lee","url":"https:\/\/www.interactivebrokers.com\/campus\/author\/sang-heonlee\/"}]}},"jetpack_featured_media_url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/04\/market-charts-coins-light-blue.jpg","_links":{"self":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/posts\/205664","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/users\/662"}],"replies":[{"embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/comments?post=205664"}],"version-history":[{"count":0,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/posts\/205664\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/media\/205705"}],"wp:attachment":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/media?parent=205664"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/categories?post=205664"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/tags?post=205664"},{"taxonomy":"contributors-categories","embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/contributors-categories?post=205664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}