{"id":7828,"date":"2025-12-06T10:24:10","date_gmt":"2025-12-06T06:24:10","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=7828"},"modified":"2026-04-11T08:29:47","modified_gmt":"2026-04-11T04:29:47","slug":"portfolio-insurance-with-index-option","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/","title":{"rendered":"<span class=\"eon-recovered-georgian-title\" data-no-translation=\"\">\u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8\u10e1 \u10d3\u10d0\u10d6\u10d5\u10d4\u10d5\u10d0 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1-\u10dd\u10e4\u10ea\u10d8\u10d4\u10d1\u10d8\u10d7<\/span>"},"content":{"rendered":"<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">A diversified portfolio\u2019s value can be insured using options written on a corresponding index (e.g., the S&#038;P 500). If we assume that the portfolio closely replicates the index, that its dividends match the index dividends, and that its beta equals 1, then by purchasing an appropriate number of put options, it becomes possible to insure the portfolio\u2019s value against falling below a chosen lower bound.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s take an example and assume we want to insure the portfolio\u2019s value over a 3-month horizon:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"379\" height=\"131\" data-attachment-id=\"7836\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/image-622\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-4.png?fit=379%2C131&amp;ssl=1\" data-orig-size=\"379,131\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-4.png?fit=379%2C131&amp;ssl=1\" class=\"wp-image-7836\" style=\"width: 350px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-4.png?resize=379%2C131&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Based on these figures, we can derive that <strong>5 put options with a strike price of 900 index points<\/strong> are sufficient to insure the portfolio against a drop below the target protection level.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"454\" data-attachment-id=\"7838\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/image-623\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-5.png?fit=1021%2C454&amp;ssl=1\" data-orig-size=\"1021,454\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-5.png?fit=1021%2C454&amp;ssl=1\" class=\"wp-image-7838\" style=\"width: 700px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-5.png?resize=1021%2C454&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The calculations become slightly more complex when the portfolio\u2019s beta differs from 1, because beta affects the portfolio\u2019s expected return relative to the risk-free rate. For this reason, it becomes necessary to determine the appropriate strike price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In such cases, we use the <strong>CAPM formula<\/strong> to establish the relationship between the portfolio\u2019s expected future value and the strike price of the put option.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In our example, we obtain that <strong>when the index level becomes 960<\/strong>, the portfolio\u2019s expected value equals the protection floor ($450,000):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1215\" height=\"455\" data-attachment-id=\"7843\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/image-624\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-6.png?fit=1215%2C455&amp;ssl=1\" data-orig-size=\"1215,455\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-6.png?fit=1024%2C383&amp;ssl=1\" class=\"wp-image-7843\" style=\"width: 700px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-6.png?resize=1215%2C455&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, we need <strong>5 put options with a 960 strike price<\/strong>. In the end, we arrive at the following structure:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1224\" height=\"461\" data-attachment-id=\"7845\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/image-625\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-7.png?fit=1224%2C461&amp;ssl=1\" data-orig-size=\"1224,461\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-7.png?fit=1024%2C386&amp;ssl=1\" class=\"wp-image-7845\" style=\"width: 700px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-7.png?resize=1224%2C461&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/16.1-index-option.xlsx\">Excel File: Index Option<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u10d0\u10d3\u10d0\u10de\u10e2\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d8\u10d0 \u10ec\u10e7\u10d0\u10e0\u10dd\u10d3\u10d0\u10dc:<br \/><em>Options, Futures &#038; Other Derivatives<\/em> \u2014 John C. Hull<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>","protected":false},"excerpt":{"rendered":"<p>\u10d3\u10d8\u10d5\u10d4\u10e0\u10e1\u10d8\u10e4\u10d8\u10ea\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d8 \u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8\u10e1 \u10e6\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d4\u10d1\u10d8\u10e1 \u10d3\u10d0\u10d6\u10e6\u10d5\u10d4\u10d5\u10d0 \u10e8\u10d4\u10e1\u10d0\u10eb\u10da\u10d4\u10d1\u10d4\u10da\u10d8\u10d0 \u10e8\u10d4\u10e1\u10d0\u10d1\u10d0\u10db\u10d8\u10e1 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1\u10d6\u10d4 (\u10db\u10d0\u10d2. S&#038;P500) \u10d2\u10d0\u10ea\u10d4\u10db\u10e3\u10da\u10d8 \u10dd\u10e4\u10ea\u10d8\u10d8\u10d7. \u10d7\u10e3 \u10d3\u10d0\u10d5\u10e3\u10e8\u10d5\u10d4\u10d1\u10d7, \u10e0\u10dd\u10db \u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8 \u10d9\u10d0\u10e0\u10d2\u10d0\u10d3 \u10d0\u10ee\u10d3\u10d4\u10dc\u10e1 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1\u10d8\u10e1 \u10e0\u10d4\u10de\u10da\u10d8\u10d9\u10d0\u10ea\u10d8\u10d0\u10e1, \u10db\u10d8\u10e1\u10d2\u10d0\u10dc \u10db\u10d8\u10e6\u10d4\u10d1\u10e3\u10da\u10d8 \u10d3\u10d8\u10d5\u10d8\u10d3\u10d4\u10dc\u10d3\u10d4\u10d1\u10d8 \u10e2\u10dd\u10da\u10d8\u10d0 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1\u10d8\u10e1 \u10d3\u10d8\u10d5\u10d8\u10d3\u10d4\u10dc\u10d3\u10d4\u10d1\u10d8\u10e1 \u10d3\u10d0 \u10d1\u10d4\u10e2\u10d0 = 1, \u10db\u10d0\u10e8\u10d8\u10dc \u10e8\u10d4\u10e1\u10d0\u10d1\u10d0\u10db\u10d8\u10e1\u10d8 \u10e0\u10d0\u10dd\u10d3\u10d4\u10dc\u10dd\u10d1\u10d8\u10e1 [\u2026]<\/p>","protected":false},"author":12998525,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_eon_insights_quality":"","_eon_insights_decision":"","_eon_insights_destination":"","_eon_insights_merge_group":"","_eon_insights_required_changes":"","_eon_insights_start_order":0,"_eon_featured_insight":0,"_eon_insights_map_version":"","_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[31110612,784237235,106538530],"tags":[],"eon_topic":[],"eon_learning_path":[],"eon_collection":[],"eon_level":[],"eon_content_type":[],"eon_source":[],"eon_idea":[784445705],"eon_framework":[],"class_list":["post-7828","post","type-post","status-publish","format-standard","hentry","category-excel-models","category-options-futures-other-derivatives-john-c-hull-ka","category-derivatives","eon_idea-derivatives"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Portfolio Insurance with Index Option - Eon Investment<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/\" \/>\n<meta property=\"og:locale\" content=\"ka_GE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Portfolio Insurance with Index Option - Eon Investment\" \/>\n<meta property=\"og:description\" content=\"\u10d3\u10d8\u10d5\u10d4\u10e0\u10e1\u10d8\u10e4\u10d8\u10ea\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d8 \u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8\u10e1 \u10e6\u10d8\u10e0\u10d4\u10d1\u10e3\u10da\u10d4\u10d1\u10d8\u10e1 \u10d3\u10d0\u10d6\u10e6\u10d5\u10d4\u10d5\u10d0 \u10e8\u10d4\u10e1\u10d0\u10eb\u10da\u10d4\u10d1\u10d4\u10da\u10d8\u10d0 \u10e8\u10d4\u10e1\u10d0\u10d1\u10d0\u10db\u10d8\u10e1 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1\u10d6\u10d4 (\u10db\u10d0\u10d2. S&amp;P500) \u10d2\u10d0\u10ea\u10d4\u10db\u10e3\u10da\u10d8 \u10dd\u10e4\u10ea\u10d8\u10d8\u10d7. \u10d7\u10e3 \u10d3\u10d0\u10d5\u10e3\u10e8\u10d5\u10d4\u10d1\u10d7, \u10e0\u10dd\u10db \u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8 \u10d9\u10d0\u10e0\u10d2\u10d0\u10d3 \u10d0\u10ee\u10d3\u10d4\u10dc\u10e1 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1\u10d8\u10e1 \u10e0\u10d4\u10de\u10da\u10d8\u10d9\u10d0\u10ea\u10d8\u10d0\u10e1, \u10db\u10d8\u10e1\u10d2\u10d0\u10dc \u10db\u10d8\u10e6\u10d4\u10d1\u10e3\u10da\u10d8 \u10d3\u10d8\u10d5\u10d8\u10d3\u10d4\u10dc\u10d3\u10d4\u10d1\u10d8 \u10e2\u10dd\u10da\u10d8\u10d0 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1\u10d8\u10e1 \u10d3\u10d8\u10d5\u10d8\u10d3\u10d4\u10dc\u10d3\u10d4\u10d1\u10d8\u10e1 \u10d3\u10d0 \u10d1\u10d4\u10e2\u10d0 = 1, \u10db\u10d0\u10e8\u10d8\u10dc \u10e8\u10d4\u10e1\u10d0\u10d1\u10d0\u10db\u10d8\u10e1\u10d8 \u10e0\u10d0\u10dd\u10d3\u10d4\u10dc\u10dd\u10d1\u10d8\u10e1 [\u2026]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/eoninvestment.com\/ka\/2025\/12\/06\/portfolio-insurance-with-index-option\/\" \/>\n<meta property=\"og:site_name\" content=\"Eon Investment\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/facebook.com\/eoninvestment\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-06T06:24:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-11T04:29:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/eoninvestment.com\/wp-content\/uploads\/2025\/12\/image-4.png\" \/>\n<meta name=\"author\" content=\"neoinsight\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"neoinsight\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 \u10ec\u10e3\u10d7\u10d8\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/eoninvestment.com\\\/ka\\\/wp-json\\\/wp\\\/v2\\\/posts\\\/7828\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/eoninvestment.com\\\/ka\\\/#website\"},\"author\":{\"name\":\"neoinsight\",\"@id\":\"https:\\\/\\\/eoninvestment.com\\\/ka\\\/#\\\/schema\\\/person\\\/9bb6a82e15a5231535d10233395afa89\"},\"headline\":\"\u10de\u10dd\u10e0\u10d7\u10e4\u10d4\u10da\u10d8\u10e1 \u10d3\u10d0\u10d6\u10d5\u10d4\u10d5\u10d0 \u10d8\u10dc\u10d3\u10d4\u10e5\u10e1-\u10dd\u10e4\u10ea\u10d8\u10d4\u10d1\u10d8\u10d7\",\"datePublished\":\"2025-12-06T06:24:10+00:00\",\"dateModified\":\"2026-04-11T04:29:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/eoninvestment.com\\\/2025\\\/12\\\/06\\\/portfolio-insurance-with-index-option\\\/\"},\"wordCount\":238,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/eoninvestment.com\\\/ka\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/eoninvestment.com\\\/2025\\\/12\\\/06\\\/portfolio-insurance-with-index-option\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/eoninvestment.com\\\/wp-content\\\/uploads\\\/2025\\\/12\\\/image-4.png\",\"articleSection\":[\"Excel Models\",\"Options, Futures & Other Derivatives, - John C. 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