•   Swap Agreements are agreements entered into primarily with major global financial institutions for a specified period ranging from a day to more than one year. In a standard “swap” transaction, two parties agree to exchange the return (or differentials in rates of return) earned or realized on particular predetermined investments or instruments.
DTC has advised the Trust as follows: it is a limited-purpose trust company organized under the laws of the State of New York, a member of the Federal Reserve System, a “clearing corporation” within the meaning of the New York Uniform Commercial Code and a “clearing agency” registered pursuant to the provisions of Section 17A of the 1934 Act. DTC was created to hold securities of its participants (“DTC Participants”) and to facilitate the clearance and settlement of securities transactions among the DTC Participants in such securities through electronic book-entry changes in accounts of the DTC Participants, thereby eliminating the need for physical movement of securities certificates. DTC Participants include securities brokers and dealers, banks, trust companies, clearing corporations and certain other organizations, some of whom (and/or their representatives) own DTC. More specifically, DTC is owned by a number of its DTC Participants and by the NYSE and the Financial Industry Regulatory Authority, Inc. Access to the DTC system is also available to others such as banks, brokers, dealers and trust companies that clear through or maintain a custodial relationship with a DTC Participant, either directly or indirectly (“Indirect Participants”). DTC agrees with and represents to DTC Participants that it will administer its book-entry system in accordance with its rules and by-laws and requirements of law. Beneficial ownership of Shares is limited to DTC Participants, Indirect Participants and persons holding interests through DTC Participants and Indirect Participants. Ownership of beneficial interests in Shares (owners of such beneficial interests are referred to herein as “Beneficial owners”) is shown on, and the transfer of ownership is effected only through, records maintained by DTC (with respect to DTC Participants) and on the records of DTC Participants (with respect to Indirect Participants and Beneficial owners that are not DTC Participants). Beneficial owners will receive from or through the DTC Participant a written confirmation relating to their purchase of Shares. The laws of some jurisdictions may require that certain purchasers of securities take physical delivery of such securities in definitive form. Such laws may impair the ability of certain investors to acquire beneficial interests in Shares.
Margin-trading is what provides the real reward and potential in daytrading bitcoin. You will be able to access the leverage to profit well from relatively small moves in BTC/USD price. High risk, high reward, high potential for loss. However, you need not use Futures only to speculate, hedging on lower leverage is also a great use case for Bitcoin derivatives if you just want to defend your coins. 
You can find other information about ProShares on the SEC’s website (www.sec.gov) or you can get copies of this information after payment of a duplicating fee by electronic request at publicinfo@sec.gov or by writing to the Public Reference Section of the SEC, Washington, D.C. 20549-0102. Information about ProShares, including their SAI, can be reviewed and copied at the SEC’s Public Reference Room in Washington, D.C. For information on the Public Reference Room, call the SEC at (202) 551-8090.
The Trustees, their birth date, term of office and length of time served, principal business occupations during the past five years and the number of portfolios in the Fund Complex overseen and other directorships, if any, held by each Trustee, are shown below. Unless noted otherwise, the addresses of each Trustee is: c/o ProShares Trust, 7501 Wisconsin Avenue, Suite 1000E, Bethesda, MD 20814.
Provide a list or diagram of all persons directly or indirectly controlled by or under common control with the Registrant. For any person controlled by another person, disclose the percentage of voting securities owned by the immediately controlling person or other basis of that person’s control. For each company, also provide the state or other sovereign power under the laws of which the company is organized.
  •   Futures Position Limit Risk — Limits on the amount of futures any one entity can hold may negatively impact the Fund’s ability to meet its investment objective if such limits are reached and exceptions to such limits are not granted. Currently the position limits for bitcoin futures contracts are much lower than they are for most other futures contracts.
The Trust’s website has information about the premiums and discounts for each Fund. Premiums or discounts are the differences between the NAV and market price of a Fund on a given day, generally at the time NAV is calculated. A premium is the amount that a Fund is trading above the NAV. A discount is the amount that the Fund is trading below the NAV.
In addition, the Advisor, any of its affiliates or employees and the Funds have a policy not to enter into any agreement or other understanding—whether written or oral—under which brokerage transactions or remuneration are directed to a broker to pay for distribution of a Fund’s shares. The table below sets forth the brokerage commissions paid by each Fund for the period noted for each Fund. Because each of the New Funds was not operational at the end of the Trust’s last fiscal year, information on brokerage commissions paid by the Fund is not included in this SAI.
The Distribution and Service Plan is intended to permit the financing of a broad array of distribution-related activities and services, as well as shareholder services, for the benefit of investors. These activities and services are intended to make the Shares an attractive investment alternative, which may lead to increased assets, increased investment opportunities and diversification, and reduced per share operating expenses. There are currently no plans to impose distribution fees.
If you are “going long” on Bitcoin, you assume that Bitcoin prices will go up. And if you expect Bitcoin prices to go up, you are interested in buying call options – options that enable you to buy Bitcoin at a predetermined price in the future. For example, if the current Bitcoin price is 5,000 USD and you expect it to rise to 8,000 USD 6 months from now, you would certainly pay good money for a call option that allows you to purchase Bitcoin for 5000 USD in 6 months, when everyone else is buying for 8,000 USD.
So far, these derivatives market have only been a niche occupied by crypto enthusiasts. That is until one of the newcomers, Crypto Facilities, and an incumbent in the derivatives market have joined forces: Crypto Facilities and the CME Group. The CME Group (controlling, for example, the Chicago Mercantile Exchange that has been around for more than a century) is a large-scale business that is officially regulated and audited by the US financial authorities. It settles its contracts in fiat money rather than cryptocurrency, thus enabling non-crypto experts to speculate on Bitcoin.
For purchases and sales of derivatives (i.e., financial instruments whose value is derived from the value of an underlying asset, interest rate or index) the Advisor evaluates counterparties on the following factors: reputation and financial strength; execution prices; commission costs; ability to handle complex orders; ability to give prompt and full execution, including the ability to handle difficult trades; accuracy of reports and confirmations provided; reliability, type and quality of research provided; financing costs and other associated costs related to the transaction; and whether the total cost or proceeds in each transaction is the most favorable under the circumstances.
Interest Rate Risk — The Fund intends to invest a substantial portion of its assets in U.S. Treasury securities and is subject to interest rate risk. Interest rate risk is the risk that debt securities may fluctuate in value due to changes in interest rates. Commonly, investments subject to interest rate risk will decrease in value when interest rates rise and increase in value when interest rates decline. The value of securities with longer maturities may fluctuate more in response to interest rate changes than securities with shorter maturities. A wide variety of factors can cause interest rates to rise (e.g., central bank monetary
The ProShares Bitcoin/Blockchain Strategy ETF contains portfolio investments that are primarily listed on foreign markets. To the extent the Fund’s portfolio investments trade in foreign markets on days when the Fund is not open for business or when the primary exchange for its shares is not open, the value of the Fund’s assets may vary on days when shareholders may not be able to purchase or sell Fund shares and Authorized Participants may not be able to create or redeem Creation Units. Also, certain portfolio investments may not be traded on days the Fund is open for business.
The Board has not adopted a policy of monitoring for frequent purchases and redemptions of shares that appear to attempt to take advantage of potential arbitrage opportunities. The Board believes this is appropriate because ETFs, such as the Funds, are intended to be attractive to arbitrageurs, as trading activity is critical to ensuring that the market price of Fund shares remains at or close to NAV.
Example: spot BTC/USD is $500. A weekly futures contract expires in 7 days. What should it be trading at? Using a 5% APY USD rate and a 1% BTC rate, you borrow $500, invest in 1 BTC. 7 days later, you will have paid $0.48 in USD interest, and earned 0.0002 BTC ($0.10 at current spot price).  A reasonable price for the futures contract would be somewhere more than $0.38 (the difference between the $0.48 interest paid $0.10 expected interest received) above spot price. This is because you would be able to lock in the sale of the 1 BTC that is being invested at a higher price. You know you have to pay back $500 plus interest, and you earn a little interest on the bitcoin, so any futures contract trading significantly above that $0.38 deficit in the spot play would give you a great arbitrage opportunity:

The method by which Creation Units are created and traded may raise certain issues under applicable securities laws. Because new Creation Units are issued and sold by the Trust on an ongoing basis, at any point a “distribution,” as such term is used in the 1933 Act, may occur. Broker-dealers and other persons are cautioned that some activities on their part may, depending on the circumstances, result in their being deemed participants in a distribution in a manner which could render them statutory underwriters and subject them to the prospectus delivery and liability provisions of the 1933 Act. For example, a broker-dealer firm or its client may be deemed a statutory underwriter if it takes Creation Units after placing an order with the Distributor, breaks them down into constituent Shares and sells some or all of the Shares comprising such Creation Units directly to its customers; or if it chooses to couple the creation of a supply of new Shares with an active selling effort involving solicitation of secondary market demand for Shares. A determination of whether a person is an underwriter for the purposes of the 1933 Act depends upon all the facts and circumstances pertaining to that person’s activities. Thus, the examples mentioned above should not be considered a complete description of all the activities that could lead a person to be deemed an underwriter. Broker-dealer firms should also note that dealers who are effecting transactions in Shares, whether or not participating in the distribution of Shares, are generally required to deliver a prospectus. This is because the prospectus delivery exemption in Section 4(3) of the 1933 Act is not available in respect of such transactions as a result
The Fund is an actively managed exchange traded fund. The Fund seeks to achieve its investment objective by investing substantially all of its assets in a combination of short positions in bitcoin futures contracts and money market instruments. The Fund is designed to benefit when the price of bitcoin futures contracts declines. The Fund generally seeks to have 30% of the value of its portfolio invested in short positions in bitcoin futures contracts and 70% of the value of its portfolio invested in money market instruments.
On March 18, 2013, the Financial Crimes Enforcement Network (“FinCEN”) a bureau of the US Department of the Treasury, issued interpretive guidance relating to the application of the Bank Secrecy Act to distributing, exchanging and transmitting “virtual currencies.” More specifically, it determined that a user of virtual currencies (such as bitcoin) for its own account will not be considered a money service business (“MSB”) or be required to register, report and perform recordkeeping; however, an administrator or exchanger of virtual currency must be a registered money services business under FinCEN’s money transmitter regulations. As a result, Bitcoin Exchanges that deal with U.S. residents or otherwise fall under U.S. jurisdiction are required to obtain licenses and comply with FinCEN regulations. FinCEN released additional guidance clarifying that, under the facts presented, miners acting solely for their own benefit, software developers, hardware manufacturers, escrow service providers and investors in bitcoin would not be required to register with FinCEN on the basis of such activity alone, but that Bitcoin Exchanges, certain types of payment processors and convertible digital asset administrators would likely be required to register with FinCEN on the basis of the activities described in the October 2014 and August 2015 letters. FinCEN has also taken significant enforcement steps against companies alleged to have violated its regulations, including the assessment in July 2017 of a civil money penalty in excess of $110 million against BTC-e for alleged willful violation of U.S. anti-money laundering laws.
While cryptocurrencies are digital currencies that are managed through advanced encryption techniques, many governments have taken a cautious approach toward them, fearing their lack of central control and the effects they could have on financial security.[99] Regulators in several countries have warned against cryptocurrency and some have taken concrete regulatory measures to dissuade users.[100] Additionally, many banks do not offer services for cryptocurrencies and can refuse to offer services to virtual-currency companies.[101] Gareth Murphy, a senior central banking officer has stated "widespread use [of cryptocurrency] would also make it more difficult for statistical agencies to gather data on economic activity, which are used by governments to steer the economy". He cautioned that virtual currencies pose a new challenge to central banks' control over the important functions of monetary and exchange rate policy.[102] While traditional financial products have strong consumer protections in place, there is no intermediary with the power to limit consumer losses if bitcoins are lost or stolen.[103] One of the features cryptocurrency lacks in comparison to credit cards, for example, is consumer protection against fraud, such as chargebacks.
BB, B, CCC, CC, and C – Obligations rated ‘BB’, ‘B’, ‘CCC’, ‘CC’, and ‘C’ are regarded as having significant speculative characteristics. ‘BB’ indicates the least degree of speculation and ‘C’ the highest. While such obligations will likely have some quality and protective characteristics, these may be outweighed by large uncertainties or major exposures to adverse conditions.
The Code generally imposes a 3.8% Medicare contribution tax on the net investment income of certain individuals, trusts, and estates to the extent their income exceeds certain threshold amounts. For these purposes, “net investment income” generally includes, among other things, (i) distributions paid by a Fund of ordinary dividends and capital gain dividends as described above, and (ii) any net gain from the sale, redemption or exchange of Fund shares. Shareholders are advised to consult their tax advisors regarding the possible implications of this additional tax on their investment in a Fund.

Bitcoin is a relatively new type of currency—a digital or cryptocurrency secured through cryptography, or codes that can’t be read without a key. Traditional currencies are made up of paper bills and coins. Unlike traditional currencies, the bitcoin is not issued by any central government. Rather, a computer algorithm determines how many bitcoins are produced and added to the economy. This is much different than a traditional currency, where central banks typically determine how much money to print.


You could imagine the spread going the other way, though. If everyone really was clamoring to short bitcoin, and if the futures offered a more convenient way to do it than the bitcoin exchanges, then you'd expect the short sellers to pay a premium to short via futures. Instead of selling a bitcoin at $18,000 today, they'd be willing to sell a synthetic bitcoin for $17,500, paying the spread to an arbitrageur who was willing to do the actual shorting for them. But the fact that the spread is mostly positive, and that bitcoin's price has been mostly going up, suggests that the demand has mostly been for synthetic long positions, not short.
  3. Make loans to other persons, except that the acquisition of bonds, debentures or other corporate debt securities and investment in government obligations, commercial paper, pass-through instruments, certificates of deposit, bankers’ acceptances and repurchase agreements and purchase and sale contracts and any similar instruments shall not be deemed to be the making of a loan, and except, further, that the Fund may lend its portfolio securities, provided that the lending of portfolio securities may be made only in accordance with applicable law and the guidelines set forth in the Prospectus and this SAI, as they may be amended from time to time.
This website is published in the United States for residents of specified countries. Investors are subject to securities and tax regulations within their applicable jurisdictions that are not addressed on this website. Nothing on this website should be considered a solicitation to buy or an offer to sell shares of any investment in any jurisdiction where the offer or solicitation would be unlawful under the securities laws of such jurisdiction, nor is it intended as investment, tax, financial, or legal advice. Investors should seek such professional advice for their particular situation and jurisdiction.
The Board oversight of the Trust and the Funds extends to the Trust’s risk management processes. The Board and its Audit Committee consider risk management issues as part of their responsibilities throughout the year at regular and special meetings. The Advisor and other service providers prepare regular reports for Board and Audit Committee meetings that address a variety of risk-related matters, and the Board as a whole or the Audit Committee may also receive special written reports or presentations on a variety of risk issues at the request of the Board or the Audit Committee. For example, the portfolio managers of the Funds meet regularly with the Board to discuss portfolio performance, including investment risk, counterparty risk and the impact on the Funds of investments in particular securities or derivatives. As noted above, given the relatively small size of the Board, the Board determined it is not necessary to adopt a complex leadership structure in order for the Board to effectively exercise its risk oversight function.
  •   Inverse Correlation Risk — Since a portion of the Fund’s assets are invested in short positions in bitcoin futures contracts, the Fund will likely decline in value when the price of bitcoin futures contracts goes up (unless such losses are offset by gains in the value of the Fund’s positions in other investments), a result that is the opposite from the results of taking long positions in bitcoin futures contracts.
The value of such Creation Unit for the MSCI Europe Dividend Growers ETF, the S&P 500 Ex-Energy ETF, the S&P 500 Ex-Financials ETF, the S&P 500 Ex-Health Care ETF, the S&P 500 Ex-Technology ETF, High Yield—Interest Rate Hedged, the Investment Grade—Interest Rate Hedged, the Short Term USD Emerging Markets Bond ETF, the UltraPro Short S&P500® ETF, the UltraPro Short QQQ® ETF, the UltraPro Short Dow30SM ETF, the UltraPro Short MidCap400 ETF, the UltraPro Short Russell2000 ETF, the Short High Yield ETF, the UltraPro S&P500® ETF, the UltraPro QQQ® ETF, the UltraPro Dow30SM ETF, the UltraPro MidCap400 ETF and the UltraPro Russell2000 ETF as of each such Fund’s inception was $4,000,000.
It can often be confusing to traders who are using multiple futures exchanges with different contract types -- inverse and qunato, dailies or quarterlies, 5x or 100x -- so people wonder: what should I trade? Well, it depends on what your goals are. If you are trying to do a little hedge for a medium term, you would want to use a quarterlies expiration contract instead, because otherwise you'd have to reopen shorter-term contracts after they expire and settle. 

Ripple is an open-source digital payment network, and it’s already being used by some of the world’s largest banks – such as the bank of Tokyo and Santandar. XRP has shown significant potential recently and has been turning a lot of heads. Ripple aims to become the go-to tool for banks on a global scale, while still giving an exciting investment opportunity to crypto advocates and solo investors. Ripple has many haters and I’ve been burned by it myself in the past – I sold 30,000 XRP at 20 cents… painful. Still, I did buy them at 3 cents a pop, so it could have been worse. I hold 10,000 XRP today and will hold until 2022.
“Qualified dividend income” received by an individual is taxed at the rates applicable to net capital gain. In order for some portion of the dividends received by a Fund shareholder to be qualified dividend income, the Fund must meet holding period and other requirements with respect to some portion of the dividend-paying stocks in its portfolio and the shareholder must meet holding period and other requirements with respect to the Fund’s Shares. A dividend will not be treated as qualified dividend income (at either the Fund or shareholder level) (1) if the dividend is received with respect to any share of stock held for fewer than 61 days during the 121-day period beginning on the date which is 60 days before the date on which such share becomes ex-dividend with respect to such dividend (or, in the case of certain preferred stock, 91 days during the 181-day period beginning 90 days before such date), (2) to the extent that the recipient is under an obligation (whether pursuant to a short sale or otherwise) to make related payments with respect to positions in substantially similar or related property, (3) if the recipient elects to have the dividend income treated as investment income for purposes of the limitation on deductibility of investment interest, or (4) if the dividend is received from a foreign corporation that is (a) not eligible for the benefits of a comprehensive income tax treaty with the United States (with the exception of dividends paid on stock of such a foreign corporation that is readily tradable on an established securities market in the United States) or (b) treated as a passive foreign investment company. In general, distributions of investment income reported by a Fund as derived from qualified dividend income will be treated as qualified dividend income in the hands of a shareholder taxed as an individual, provided the shareholder meets the holding period and other requirements described above with respect to the Fund’s Shares.
Bitcoin futures contracts are a new type of futures contract that began trading in December 2017. Unlike the established futures markets for traditional physical commodities, the market for bitcoin futures contracts is in the developmental stage and has very limited volume, trading and operational history. Bitcoin and other cryptocurrencies are a new and developing asset class subject to both developmental and regulatory uncertainty. Ownership of bitcoin is thought to be very concentrated and the supply and liquidity of bitcoin is limited. The price of bitcoin could drop precipitously for a variety of reasons including but not limited to regulatory changes, a crisis of confidence in the bitcoin network or a change in user preference to competing cryptocurrencies. As such, bitcoin futures contracts and the market for bitcoin futures contracts may be riskier, less liquid, more volatile and more vulnerable to economic, market, industry, regulatory and other changes than more established futures contracts and futures markets. There is no assurance that a liquid market will emerge or be sustained for bitcoin futures contracts. The liquidity of the market for bitcoin futures contracts will depend on, among other things, the supply and demand for bitcoin futures contracts, the adoption of bitcoin and the commercial and speculative interest in the market for bitcoin futures contracts. The price of bitcoin has been subject to periods of sudden and high volatility and, as a result, the price of bitcoin futures contracts also may experience periods of sudden and high volatility. Margin requirements for bitcoin futures contracts currently are, and may continue to be, materially higher than the typical margin requirements for more established types of futures contracts. Each of these factors could have a negative impact on the performance of the Fund and the market for Fund shares.
The NAV of each Fund is typically determined each business day at 3:00 p.m., Eastern Time on days when                    is open for trading. The [            ] Exchange is open every week, Monday through Friday, except when the following holidays are celebrated: New Year’s Day, Martin Luther King, Jr. Day (the third Monday in January), Presidents’ Day (the third Monday in February), Good Friday, Memorial Day (the last Monday in May), Independence Day, Labor Day (the first Monday in September), Thanksgiving Day (the fourth Thursday in November) and Christmas Day. An Exchange may close early on the business day before each of these holidays and on the day after Thanksgiving Day. Exchange holiday schedules are subject to change without notice. If the exchange or market on which a Fund’s investments are primarily traded closes early, the NAV may be calculated prior to its normal calculation time. Creation/ redemption transaction order time cutoffs would also be accelerated.

Fundamental securities analysis is not used by ProShare Advisors in seeking to correlate a Matching Fund’s investment returns with its index. Rather, ProShare Advisors primarily uses a passive or mathematical approach to determine the investments a Matching Fund makes and techniques it employs. While ProShare Advisors attempts to minimize any “tracking error,” certain factors tend to cause a Matching Fund’s investment results to vary from a perfect correlation to its index, as applicable. See “Special Considerations” below for additional details.
Other countries are not as accommodative of bitcoin. For example, the Chinese government on December 3, 2013 issued a notice that classified bitcoin as legal and “virtual commodities;” however, the same notice restricted the banking and payment industries from using bitcoin, creating uncertainty and limiting the ability of Bitcoin Exchanges to operate in the then-second largest bitcoin market. Then on September 15, 2017, the Chinese government and local financial regulators officially requested some Chinese Bitcoin Exchanges and digital asset trading platforms to shut down by the end of September 2017. In addition, the Central Bank of Bolivia banned the use of bitcoin as a means of payment in May 2014. Further, in July 2016, the Russian Ministry of Finance indicated it supports a proposed law that bans bitcoin domestically but allows for its use as a foreign currency. In September 2017 the head of the Russian central bank stated that it is categorically against regulating cryptocurrencies as money, as a means by which payment can be made for goods and services, and against equating them with foreign currency. Most recently, South Korea’s Office for Government Policy Coordination released a wide variety of proposed regulations which range from the imposition of capital gains taxes on profits realized from cryptocurrency trading, to banning minors from registering on South Korean bitcoin exchanges, and even prohibiting financial institutions from investing in digital assets. These restrictive stances towards digital assets may reduce the rate of expansion of bitcoin use or even eliminate the use of bitcoin entirely in these geographies.
Upon entering into a futures contract, each Fund will be required to deposit with the broker an amount of cash or cash equivalents in the range of approximately 5% to 10% of the contract amount for equity index futures and in the range of approximately 1% to 3% of the contract amount for treasury futures (these amounts are subject to change by the exchange on which the contract is traded). This amount, known as “initial margin,” is in the nature of a performance bond or good faith deposit on the contract and is returned to the Fund upon termination of the futures contract, assuming all contractual obligations have been satisfied. Subsequent payments, known as “variation margin,” to and from the broker will be made daily as the price of the index underlying the futures contract fluctuates, making the long and short positions in the futures contract more or less valuable, a process known as “marking-to-market.” At any time prior to expiration of a futures contract, a Fund may elect to close its position by taking an opposite position, which will operate to terminate the Fund’s existing position in the contract.

As of February 2018, the Chinese Government halted trading of virtual currency, banned initial coin offerings and shut down mining. Some Chinese miners have since relocated to Canada.[43] One company is operating data centers for mining operations at Canadian oil and gas field sites, due to low gas prices.[44] In June 2018, Hydro Quebec proposed to the provincial government to allocate 500 MW to crypto companies for mining.[45] According to a February 2018 report from Fortune,[46] Iceland has become a haven for cryptocurrency miners in part because of its cheap electricity. Prices are contained because nearly all of the country’s energy comes from renewable sources, prompting more mining companies to consider opening operations in Iceland. The region’s energy company says bitcoin mining is becoming so popular that the country will likely use more electricity to mine coins than power homes in 2018. In October 2018 Russia will become home to one of the largest legal mining operations in the world, located in Siberia. More than 1.5 million Russians are engaged in home mining. Russia’s energy resources and climate provide some of the best conditions for crypto mining.[47]
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Crypto Facilities and the CME Group  have been calculating and publishing the Bitcoin Reference Rate (BRR) since November 2016. Such an official rate is a prerequisite of options trading in the traditional markets. The BRR is calculated based on the rates from the biggest exchanges: Bitstamp, GDAX, itBit, and Kraken. More concretely, it is calculated based on all Bitcoin vs. USD trades on the participating exchanges between 3 and 4 p.m. London time. To calculate the BRR, the hour between 3 and 4 is divided into 12 intervals of 5 minutes. For each interval, the volume-weighted median of the Bitcoin price is calculated (statistically, the median, in contrast to the average, prevents single outliers from distorting the price). The BRR is then the average of these 12 median values. More details about the calculation of the BRR can be found in the BRR whitepaper.
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