{"id":46793,"date":"2023-09-25T03:32:12","date_gmt":"2023-09-25T03:32:12","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=46793"},"modified":"2026-04-06T08:44:19","modified_gmt":"2026-04-06T08:44:19","slug":"cross-rates","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/economics\/cross-rates\/","title":{"rendered":"Cross Rates"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Exchange Rate Calculations (2025 CFA\u00ae Level I Exam \u2013 Economics \u2013 Learning Module 8)\",\n  \"description\": \"This lesson covers exchange rate calculations for the 2025 CFA\u00ae Level I Economics curriculum. It explains spot and forward exchange rates, currency cross rates, and triangular arbitrage, with step-by-step examples. The video also covers forward discounts and premiums, forward points and pips, covered interest parity, and how interest rate differentials affect exchange rates and currency risk in exam-style problems.\",\n  \"uploadDate\": \"2023-11-17T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/JyrmJH0MVWg\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/JyrmJH0MVWg\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/JyrmJH0MVWg\",\n  \"duration\": \"PT33M16S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"A forex trader noticed the USD\/EUR spot rate is 1.3960. Similarly, the CHF\/USD spot rate is 0.9587. Calculate the spot CHF\/EUR cross-rate.\",\n    \"text\": \"A forex trader noticed the USD\/EUR spot rate is 1.3960. Similarly, the CHF\/USD spot rate is 0.9587. Calculate the spot CHF\/EUR cross-rate.\\n\\n1. 1.7422.\\n2. 1.3383.\\n3. 1.4561.\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B.\\n\\nThe spot rate is:\\n\\nCHF\/EUR = CHF\/USD \u00d7 USD\/EUR = 1.3960 \u00d7 0.9587 = 1.3383.\"\n    }\n  }\n}\n<\/script>\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/JyrmJH0MVWg\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>It is possible to back out cross rates given two exchange rates involving three currencies. Consider a foreign exchange market with the exchange rate between the Chinese Yuan and the South African rand (ZAR\/CNY). This market can also quote the exchange rate between the South African rand and the Russian ruble (RUB\/ZAR). It is, therefore, possible to back out the cross-rates between the Chinese yuan and the Russian ruble, which is quoted as (RUB\/CNY) according to market conventions and can be represented as follows:<\/p>\n<p>$$ \\frac{RUB}{ZAR}\\times\\frac{ZAR}{CNY}=\\frac{RUB}{CNY}$$<\/p>\n<p>For example, the RUB\/ZAR exchange rate is 1.4876, and the ZAR\/CNY exchange rate is 1.6459. We can calculate the RUB\/CNY exchange rate using sample spot exchange rates as follows:<\/p>\n<p>$$\\frac{RUB}{ZAR}\\times\\frac{ZAR}{CNY}=1.4876\\times1.6459=2.4484\\ \\text{Russian Rubble per Chinese Yuan}$$<\/p>\n<div style=\"margin: 20px 0;\"><a style=\"display: block; width: 100%; text-align: center; padding: 10px; border: 2px solid #2f5bea; border-radius: 40px; font-size: 16px; color: #2f5bea; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Practice cross rate questions with our free trial. <\/a><\/div>\n<h3>Inversion<\/h3>\n<p>Sometimes, it is important to invert one of the quotes to get the intermediary currency to cancel out the equation and get the cross rate. For example, to get the Russian ruble\u2013Japanese yen (JPY\/RUB) quote, we first invert the South African rand\u2013Russia ruble (RUB\/ZAR) quote before multiplying it by the South African rand\u2013Japanese yen (JPY\/ZAR) quote.<\/p>\n<h4><strong>Example: Currency Cross-Rates<\/strong><\/h4>\n<p>Let&#8217;s assume we have spot exchange rates of RUB\/ZAR =1.4876 and JPY\/ZAR \u00a0= 70.74. The South African rand\u2013Russia ruble (RUB\/ZAR) \u00a0ruble exchange rate of 1.4876 inverts to:<\/p>\n<p>$$\\left(\\frac{RUB}{ZAR}\\right)^{-1}=\\left(\\frac{ZAR}{RUB}\\right)=\\ \\frac{1}{1.4876}=0.6722$$<\/p>\n<p>Multiplying this figure with the JPY\/ZAR quote of 70.74 gives us the JPY\/RUB.<\/p>\n<p>$$\\left(\\frac{ZAR}{RUB}\\right)\\times\\left(\\frac{JPY}{ZAR}\\right)=0.6722\\ \\times\\ 70.74\\ =\\ 47.5531\\ \\text{JPY per RUB}$$<\/p>\n<h3><strong>Triangular Arbitrage in Cross Rate Calculations<\/strong><\/h3>\n<p>Market participants can access both cross-rate quotes (e.g., JPY\/CAD for Japan yen\u2013Canada) and the underlying component exchange rate quotes (e.g., CAD\/USD for dollar\u2013Canada and JPY\/USD for dollar\u2013yen). These cross rates must align with their respective calculations; if not, traders will exploit the discrepancy through arbitrage. This type of profit-seeking, termed <strong>triangular arbitrage<\/strong> (given its involvement with three currencies), would persist until the price imbalance is corrected.<\/p>\n<h4><strong>Example: Illustrating Triangular Arbitrage<\/strong><\/h4>\n<p>To illustrate, consider a JPY\/CAD rate derived at 85.98 based on the underlying CAD\/USD and JPY\/USD rates of 1.3020 and 111.94, respectively:<\/p>\n<p>$$\\frac{JPY}{CAD}=\\left(\\frac{CAD}{USD}\\right)^{-1}\\times\\left(\\frac{JPY}{USD}\\right)={(1.3020)}^{-1}\\times111.94=85.98$$<\/p>\n<p>If a misinformed dealer simultaneously offers a JPY\/CAD rate of 86.20, it presents a different price for the same service, which, in this case, is converting yen to Canadian dollars. A savvy trader could purchase CAD1 for JPY85.98 and immediately sell it for JPY86.20, making a risk-free profit of JPY0.22 per CAD1.<\/p>\n<p>In practice, such discrepancies in cross-rates are infrequent. Both human traders and automated trading algorithms vigilantly monitor the markets for any pricing inefficiencies, ensuring swift corrections.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>A forex trader noticed the USD\/EUR spot rate is 1.3960. Similarly, the CHF\/USD \u00a0spot rate is 0.9587. Calculate the spot CHF\/EUR cross-rate.<\/p>\n<ol>\n<li>1.7422.<\/li>\n<li>1.3383.<\/li>\n<li>1.4561.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>The spot rate is:<\/p>\n<p>$$\\frac{CHF}{EUR}=\\frac{CHF}{USD}\\times\\frac{USD}{EUR}=1.3960\\times0.9587=1.3383$$<\/p>\n<\/blockquote>\n<div style=\"text-align: center; margin: 40px 0;\"><a style=\"display: inline-block; padding: 10px 26px; background: #3f78d7; color: #fff; border-radius: 40px; font-size: 16px; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a>\n<p style=\"margin-top: 10px; max-width: 600px; margin-left: auto; margin-right: auto; font-size: 14px;\">Solve CFA-style questions on cross rates, currency inversion, and triangular arbitrage in foreign exchange markets.<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>It is possible to back out cross rates given two exchange rates involving three currencies. Consider a foreign exchange market with the exchange rate between the Chinese Yuan and the South African rand (ZAR\/CNY). This market can also quote the&#8230;<\/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-46793","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>Cross Rates Calculation | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Learn how to calculate cross exchange rates using spot rates and understand the inversion process in foreign exchange markets.\" \/>\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\/cross-rates\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cross Rates Calculation | CFA Level 1 - 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