{"id":1388,"date":"2022-10-15T07:01:56","date_gmt":"2022-10-15T07:01:56","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1388"},"modified":"2026-01-21T17:36:46","modified_gmt":"2026-01-21T17:36:46","slug":"arbitrage-relationship-forward-spot-rates","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/economics\/arbitrage-relationship-forward-spot-rates\/","title":{"rendered":"Relationship Among Forward, Interest and Spot Rates"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Theory linking interest rate differences to inflation differences\",\n    \"text\": \"Which of the following theories states that the interest rate differences between two countries reflect the difference in the inflation rates of these two countries?\\n\\nA. The interest rate parity (IRP).\\n\\nB. The international Fisher effect.\\n\\nC. The purchasing power parity (PPP).\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"B. The international Fisher effect.\\n\\nThe international Fisher effect suggests that differences in nominal interest rates between countries reflect differences in expected inflation rates, and that currency appreciation or depreciation is proportional to these interest rate differentials.\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"A. The interest rate parity (IRP).\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"C. The purchasing power parity (PPP).\"\n      }\n    ]\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Currency Exchange Rates (2025 Level I CFA\u00ae Exam \u2013 Economics \u2013 Module 8)\",\n  \"description\": \"This video lesson covers currency exchange rates, explaining key concepts such as nominal vs. real exchange rates, spot vs. forward exchange rates, and arbitrage relationships. It also covers calculations for percentage changes in currency values, cross-rates, forward discounts\/premiums, and the effects of exchange rates on trade and capital flows.\",\n  \"uploadDate\": \"2022-03-29T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/Kh3Lq2F_D3Q\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/Kh3Lq2F_D3Q\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/Kh3Lq2F_D3Q\",\n  \"duration\": \"PT31M26S\"\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/Kh3Lq2F_D3Q?si=kpoQ-DlPQYDsPv1d\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n<p>The interest rate difference between two countries affects the spot and forward rates. Using a single period analogy, an investor who has funds to invest in treasury securities, has two alternatives:<\/p>\n<p><!--more--><\/p>\n<ul>\n<li>Invest at the domestic risk-free rate (\\(i_d\\)).<\/li>\n<li>Invest at the foreign risk-free rate (\\(i_f\\)).<\/li>\n<\/ul>\n<p>If the investor takes the former option, the fund held at the end of the period would be (\\(1 + i_d\\)). Alternatively, the investor could convert the domestic currency to be invested in a foreign currency using the spot rate \\(S_{f\/d}\\). It is important to note that (\\(f\/d\\)) is the currency quoting convention that expresses the number of foreign units per single domestic unit.<\/p>\n<p>At the end of the investment period, the investor would hold \\(S_{f\/d}(1 + i_f)\\) units of foreign currency. Then, the funds would have to be converted back into the domestic currency using the initial forward rate. Note that the two investment alternatives are risk-free because they are invested in risk-free assets.<\/p>\n<p>Since these investment alternatives are equal, considering the risk characteristics, the returns must also be equal. As such, we have the following relationship:<\/p>\n<p>$$1+i_d =S_{f\/d}(1 + i_f)(\\frac {1}{F_{f\/d}})$$<\/p>\n<p>Note that \\(\\frac{1}{F_{f\/d}}\\) is the number of units of domestic currency for each unit of foreign sold forward.<\/p>\n<p>The relationship above can be rearranged to get the formula for a forward rate as:<\/p>\n<p>$$F_{f\/d}=S_{f\/d} (\\frac{1 + i_f}{1+i_d})$$<\/p>\n<p>This formula shows the relationship among the spot rate, the forward rate, and the interest rate in foreign and domestic countries.<\/p>\n<h3><strong>Example: Relationship Among Forward<\/strong>,<strong> Interest<\/strong>,<strong> and Spot Rates<\/strong><\/h3>\n<p>Given that the spot exchange \\(S_{f\/d}\\) is 1.502, the domestic risk-free rate for 12 months is 4%, and the 12-month foreign risk-free rate is 6.2%, the forward rate \\(F_{f\/d}\\) is:<\/p>\n<p>$$F_{f\/d}=S_{f\/d} (\\frac{1 + i_f}{1+i_d})$$<\/p>\n<p>$$F_{f\/d}=1.502 (\\frac{1+0.062}{1+0.04})=1.5338$$<\/p>\n<h2><strong>International Fisher Effect in Spot vs. Forward Rates<\/strong><\/h2>\n<p>According to the Fisher effect, interest rate differences between two countries reflect the difference in the inflation rates of these two countries. High-interest rate countries experience higher inflation rates, and so the same uninvested dollar today is worth much less in the future. Therefore, there is the need to have a higher interest rate to compensate for the loss of purchasing power.<\/p>\n<h2><strong>Interest Rate Parity (IRP) in Spot vs. Forward<\/strong><\/h2>\n<p>The interest rate parity is a theory which states that the difference between the interest rates of two countries is the same as the difference between the spot exchange rate and the forward exchange rate. This theory plays a major role in foreign exchange markets since it connects the dots among the interest rates, the spot exchange rates, and the foreign exchange rates.<\/p>\n<h2><strong>Purchasing Power Parity (PPP) in Spot Rates vs. Forward Rates<\/strong><\/h2>\n<p>According to the purchasing power parity principle, a country\u2019s currency fluctuates as the inflation rate of another country fluctuates. Therefore, the depreciation rate in a currency is roughly equal to the excess inflation rate in the domestic country over another country&#8217;s inflation rate.<\/p>\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\n<p>Which of the following theories states that the interest rate differences between two countries reflect the difference in the inflation rates of these two countries?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">The interest rate parity (IRP).<\/li>\n<li data-tadv-p=\"keep\">The international Fisher effect.<\/li>\n<li data-tadv-p=\"keep\">The purchasing power parity (PPP).<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>The international Fisher effect suggests\u00a0that the estimated appreciation or depreciation of two countries\u2019 currencies is proportional to the difference in their nominal interest rates.<\/p>\n<\/blockquote>\n<div class=\"notes_inv\"><hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/economics\/learning-sessions-curriculum-economics\/\"><em>Economics &#8211; Learning Sessions<\/em><\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The interest rate difference between two countries affects the spot and forward rates. Using a single period analogy, an investor who has funds to invest in treasury securities, has two alternatives:<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[],"class_list":["post-1388","post","type-post","status-publish","format-standard","hentry","category-economics","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Forward, Interest &amp; Spot Rates | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Understand the relationship between spot rates, forward rates, and interest rates, including interest rate parity and exchange rate dynamics.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/economics\/arbitrage-relationship-forward-spot-rates\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Forward, Interest &amp; Spot Rates | CFA Level 1 - 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