{"id":43547,"date":"2022-12-15T12:07:04","date_gmt":"2022-12-15T12:07:04","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=43547"},"modified":"2026-04-01T02:06:43","modified_gmt":"2026-04-01T02:06:43","slug":"value-and-price-of-futures-contracts","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/value-and-price-of-futures-contracts\/","title":{"rendered":"Value and Price of Futures Contracts"},"content":{"rendered":"\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\u00a0 <iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/j97FeOxxdRk\" width=\"611\" height=\"344\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\"><\/iframe>  Recall that during the initiation of a forward commitment, no cash changes hands. Further, the forward commitment is neither a liability nor an asset to the buyer or the seller. As such, the value of both the forward contract and the futures contract is zero:\n\n $$V_0(T)=0$$\n\n Consider an underlying with no associated costs or benefits. Like forward contracts, the futures price is calculated by compounding the spot price of the underlying using the risk-free rate:\n\n $$f_T(0)=S_0(1+r)^T$$\n\n Where:\n\n \\(f_T(0)=\\) Futures forward price.\n\n \\(S_0=\\) Spot price of the underlying at time \\(t=0\\).\n\n \\(r=\\) Risk-free rate.\n\n \\(T=\\) Time to maturity.\n\n Note that, like forward contracts, we have used discrete compounding. However, continuous compounding is also preferred in futures contracts if the underlying assets comprise a portfolio, such as commodities, fixed income, and equity. Also, continuous compounding is preferred when the underlying is foreign exchange denominated in two currencies.\n\n Using continuous compounding, the future price is given by:\n\n $$f_T(0)=S_0e^{rT}$$\n\n \n<h2 class=\"wp-block-heading\">Cost of Carry and Futures Price<\/h2>\n Like forward contracts, the price of futures whose underlying has income (I) and costs (C) is adjusted as follows:\n\n $$f_T(0)=[S_0-PV_0(I)+PV_0(C)](1+r)^{T}$$\n\n Where:\n\n \\(PV_0(I)=\\) Present value of income or benefit associated with the underlying at time \\(t=0\\).\n\n \\(PV_0(C)=\\) Present value of costs associated with the underlying at time \\(t=0\\)\n\n \n<h3 class=\"wp-block-heading\">Example: Futures Price Valuation<\/h3>\n Minners Inc. enters a futures contract on an exchange via a financial intermediary to buy 80 kilos of gold. The current spot price is $52,950 per kilo.\n\n If the risk-free rate of return is 3%, what is the no-arbitrage futures price for settlement in 95 days?\n\n \n<h4 class=\"wp-block-heading\">Solution<\/h4>\n The futures price is equal to the compounded value of the spot price of the underlying at the risk-free rate for a period \\(T\\):\n\n $$\\begin{align*}f_T(T)&amp;=S_0(1+r)^T\\\\&amp;=\\$52,950(1.03)^{\\frac{95}{365}}\\\\&amp;=\\$53,358.94\\end{align*}$$\n\n \n<h2 class=\"wp-block-heading\">Mark-to-Market Valuation of a Future Contract Compared to a Forward Contract<\/h2>\n As time passes, the value of futures and forward contracts changes. However, the forward contract price remains constant until maturity.\n\n As seen previously, for the long position, the value of a forward contract during its life is calculated as the difference between the current spot price and the present value of the original forward price:\n\n $$V_t(T)=S_t-F_0(T)(1+r)^{-(T-t)}$$\n\n The MTM value of the forward contract is not settled until its expiration date, which causes counterparty risk.\n\n On the other hand, the futures price changes depending on market conditions. Moreover, the daily settlement resets the MTM value to zero. Besides, the variation margin is exchanged to cover the difference, decreasing counterparty risk.\n\n Note that the cumulative MTM gain or loss is approximately equal to that of a comparable forward contract.\n\n \n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1590\" height=\"683\" class=\"alignnone wp-image-43710 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG.jpg\" alt=\"\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG.jpg 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG-300x129.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG-1024x440.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG-768x330.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG-1536x660.jpg 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/Futures-Contracts-JPEG-400x172.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/figure>\n \n<h2 class=\"wp-block-heading\">Interest Rate Futures and Forward Contracts<\/h2>\n Remember that a forward rate agreement (FRA) uses implied forward rates as a no-arbitrage fixed rate. In this instance, the counterparties exchange fixed for floating payments at a specified time in the future.\n\n The futures contracts on short-term interest rates are more liquid and standardized than FRAs. These contracts are often available for monthly and quarterly market reference rates (MRRs).\n\n \n<h3 class=\"wp-block-heading\">Description of Interest Rate Futures<\/h3>\n As is the case in FRA, the underlying of the interest rate futures is the market reference rate on a hypothetical amount of money at a future date. However, interest rate futures trade on a price basis, given by the following formula:\n\n $$f_{A,B-A}=100-(100\\times\\text{MRR}_{A,B-A})$$\n\n Where: \\(f_{A,B-A}=\\) futures price for the market reference rate for \\(B \u2013 A\\) periods that begin in A period \\((MRR_{A, B-A})\\).\n\n <div class=\"wp-block-image aligncenter size-full wp-image-43883\">\n<figure class=\"size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1295\" height=\"470\" class=\"alignnone wp-image-43643 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/image-8.png\" alt=\"CFA Level 1 Interest Futures Contracts\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/image-8.png 1295w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/image-8-300x109.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/image-8-1024x372.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/image-8-768x279.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/image-8-400x145.png 400w\" sizes=\"auto, (max-width: 1295px) 100vw, 1295px\" \/><\/figure>\n<\/div> Note that the formula \\(f_{A, B-A}=100-(100\\times\\text{MRR}_{A, B-A})\\) can be written as \\(f_{A, B-A}=100-\\text{yield}\\).\n\n Intuitively, the (100 \u2013 Yield) price convention leads to an inverse price versus yield relationship that differs from the price of a zero-coupon bond at a contract rate. As such, a long futures position receives MRR in A period while the short position pays MRR in A period.\n\n In summary, the long position (lender) gains as prices rise and future MRR falls. In contrast, the short position (borrower) gains as prices fall and future MRR rises.\n\n \n<h3 class=\"wp-block-heading\">Interest Rate Futures Settlement<\/h3>\n The <strong>daily settlement<\/strong> of the interest futures occurs depending on the price changes, regarded as <strong>futures contract basis point value<\/strong> (BPV) and calculated as follows:\n\n $$\\text{Futures contract BPV}=\\text{Notional principlal}\\times0.01\\%\\times\\text{Period}$$\n\n For instance, consider USD 50 million for a 6-month MRR of 3% (assuming actual\/360 convention). The futures contract BPV is:\n\n $$\\text{Futures contract BPV}=50,000,000\\times0.01\\%\\times\\bigg(\\frac{180}{360}\\bigg)=\\$2,500$$\n\n \n<h4 class=\"wp-block-heading\">Example: Calculating Futures Contracts Gains or Losses<\/h4>\n A&amp;M Bank has issued its clients a USD 10 million three-month loan at a fixed rate.\u00a0To finance the loan, the bank has borrowed a one-month variable MRR. To hedge against interest rate risk, the bank sells futures contracts on two-month MRR. Assume that the bank agrees to sell the futures at $97.75, but the actual settlement price is $96.75.\n\n The cumulative gain\/loss to the contract from the bank\u2019s perspective is <em>closest<\/em> to:\n\n \n<h4 class=\"wp-block-heading\">Solution<\/h4>\n We need to start by calculating the contract\u2019s BPV:\n\n $$\\begin{align*}\\text{Futures contract BPV}&amp;=\\text{Notional principal}\\times0.01\\%\\times\\text{Period}\\\\&amp;=10,000,000\\times0.01\\%\\times\\frac{2}{12}\\\\&amp;=\\$166.67\\end{align*}$$\n\n We need to calculate corresponding market reference rates (MRRs) for both prices. \u00a0Note that\n\n $$f_{A, B-A}=100-(100\\times\\text{MRR}_{A, B-A}) $$\n\n Therefore;\n\n $$ \\begin{align*}96.75&amp;=100-(100\\times\\text{MRR}_{A, B-A})\\rightarrow MRR_{1,2}=3.25\\%\\\\ 97.75&amp;= 100-(100\\times\\text{MRR}_{A, B-A})\\rightarrow\\text{MRR}_{1,2}=2.25\\%\\end{align*} $$\n\n The bank has made a 100bps gain \\((=3.25\\%-2.25\\%)\\). In monetary terms, the bank has made a cumulative gain of \\(\\$16,667 (= \\text{Futures contract BPV} \\times \\text{100bps})\\) on the contract.\n\n <div class=\"wp-block-image aligncenter wp-image-43884\">\n<figure class=\"size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"263\" class=\"alignnone wp-image-43722 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/cfa-level-1-swap.png\" alt=\"CFA Level 1 Futures Contracts Gains or Losses\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/cfa-level-1-swap.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/cfa-level-1-swap-300x77.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/cfa-level-1-swap-768x197.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2022\/12\/cfa-level-1-swap-400x103.png 400w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div> \n<blockquote>\n<h2>Question<\/h2>\nWhich of the following <em>best describes<\/em> the difference between the price of a futures contract and its value?\n\nA. The price determines the profit to the buyer, and the value determines the profit to the seller.\n\nB. The futures price is fixed at the start, and the value starts at zero and changes throughout the contract\u2019s life.\n\nC. The futures contract value is a benchmark against which the price is compared to determine whether a trade is advisable.\n<h3>Solution<\/h3>\nThe correct answer is <strong>B<\/strong>.\n\nThe futures price is fixed at the start, whereas the value starts at zero and then changes, either positively or negatively, throughout the contract\u2019s life.<\/blockquote>\n<\/div><\/div>\n \n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Recall that during the initiation of a forward commitment, no cash changes hands. Further, the forward commitment is neither a liability nor an asset to the buyer or the seller. As such, the value of both the forward contract and&#8230;<\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[42],"class_list":["post-43547","post","type-post","status-publish","format-standard","hentry","category-derivatives","tag-value-and-price-of-futures-contracts","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>Value &amp; Pricing of Futures Contracts | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Futures contracts are standardized and liquid, using implied forward rates to price agreements. 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