What is PIPS? — A Comprehensive Analysis of Pips, Pip Value, Spreads, and Their Application in Multi-Asset Trading

1.What is PIPS? — A Comprehensive Analysis of Pips, Pip Value, Spreads, and Their Application in Multi-Asset Trading
2.Comparison of PIPS Across Different Assets
3.Advanced Concepts: Pip Value and Spread

What is PIPS? — A Comprehensive Analysis of Pips, Pip Value, Spreads, and Their Application in Multi-Asset Trading

In financial markets, PIPS (points) are a crucial unit for measuring price fluctuations, particularly in forex trading. Accurately understanding what PIPS are and how to calculate them is fundamental for every trader in terms of developing strategies, managing risks, and evaluating profit potential. This article will guide readers through the definition of PIPS, calculation methods, and their practical application in various assets, from basic knowledge to advanced techniques. It should be noted that while pip value and spreads are also important concepts in trading, this article will focus on the definition and real-world application of PIPS, with later chapters addressing the roles and calculation methods of pip value and spreads for a more detailed understanding.

Definition and Basic Concept of PIPS

PIPS, or “points,” typically refer to the smallest unit of price movement in financial products. In the forex market, a common definition is that when the fourth decimal place in a currency pair quote changes, it represents a movement of one PIP. For example, if the EUR/USD quote rises from 1.1050 to 1.1051, it means the market price has moved by one PIP. Although this small price change may seem insignificant in value, it is an essential tool for precisely recording market price fluctuations.

By understanding PIPS, traders can more intuitively grasp market trends, making it easier to set stop-loss points, calculate risks, and predict potential profits. Moreover, the concept of PIPS is not limited to forex trading; it can also be extended to other asset markets, serving as a universal standard for assessing price movement magnitude.

Comparison of PIPS Across Different Assets

 

Asset Type PIP Definition Pip Value (Example) Volatility Characteristics
Forex For most non-JPY currency pairs, PIP is defined as the 4th decimal place of the quote (0.0001); for JPY currency pairs, it is the 2nd decimal place (0.01). For example, for EUR/USD, one standard lot (100,000 units) is typically worth about $10/pip. Intraday market fluctuations typically range from 50-100 pips, influenced by economic data and market news.
Stock Indices Usually calculated based on whole-point changes in the index, where one point represents a whole change in the index price, such as 1 point in the DAX. For example, for the S&P 500 index, one point change is approximately $50/pip (depending on the contract size). Stock indices are influenced by multiple factors, and extreme daily fluctuations can exceed 200+ pips, reflecting changes in overall market sentiment.
Gold Gold prices are typically calculated with a change of $0.01 per ounce as one PIP. For example, for one standard lot (100 ounces), each $0.01/ounce change is about $1/pip. Gold has moderate volatility, mainly influenced by geopolitical factors, inflation expectations, and the US dollar movement, with relatively stable price changes.
Crude Oil Crude oil prices are usually calculated with a change of $0.01 per barrel as one PIP. For example, for a 1,000-barrel contract, each $0.01/barrel change is approximately $10/pip. The crude oil market is highly volatile and often experiences large fluctuations due to OPEC decisions, inventory data, and geopolitical events.
Cryptocurrency For BTC/USD, PIP is defined as a $1 price movement. For example, for BTC/USD, a $1 price change represents $1/pip. The cryptocurrency market operates 24/7, with significant price volatility often influenced by market sentiment and news.

PIPS Calculation Method and Practical Application

1. PIPS Calculation Method

In financial markets, PIPS are the smallest unit of price movement, and the calculation method varies depending on the asset type. Below is the basic calculation process and formula for the forex market:

  • Calculation Formula:
    1. Pip Value Calculation Formula
      The value of each PIP can be calculated using the following formula:
      Pip Value = (PIP Size / Current Exchange Rate) × Trade Units
      For example, in the EUR/USD currency pair, assuming the current exchange rate is 1.1050 and the trader holds one standard lot (100,000 units):

      • PIP Size: 0.0001
      • Pip Value = (0.0001 / 1.1050) × 100,000 ≈ $9.05

In actual trading, it is typically agreed to be $10/pip, although the specific value may fluctuate slightly depending on market conditions.

  1. PIPS Calculation for Other Assets
    • Gold: Gold prices move by $0.01 per ounce as one PIP, and for a standard lot of 100 ounces, the pip value is about $1.
    • Crude Oil: Crude oil prices move by $0.01 per barrel as one PIP, and for a contract size of 1,000 barrels, the pip value is about $10.
    • Cryptocurrency: For BTC/USD, if a $1 price change represents one PIP, then the pip value is $1.
  • Process:
    1. Confirm Asset Type and PIP Definition: Understand the smallest price movement unit based on the asset being traded.

    2. Determine Trade Size: For forex, a standard lot is typically 100,000 units.

    3. Calculate Pip Value: Apply the relevant calculation formula to determine the monetary value of each PIP.

    4. Assess Risk and Potential Profit/Loss: Based on expected price fluctuations (measured in pips), calculate possible losses or gains, providing the basis for risk management and strategy adjustments.

2. Practical Application of PIPS

Using PIPS for trading risk management and decision-making is an essential tool for traders. Below is a specific example showing how PIPS can be applied to control risk and plan trading strategies.

  • Case Background:
    Assume a trader is trading the EUR/USD currency pair, with the current exchange rate at 1.1050, and decides to open a position of one standard lot.
  • Calculating Pip Value:
    Based on the formula mentioned earlier, the value of each PIP is about $10.
  • Setting Risk Parameters:
    • Stop-Loss Setting:

f the trader sets the stop-loss point at 50 pips, the maximum loss will be:

50 pips × $10/pip = $500.

This value allows the trader to limit the loss within an acceptable range when the market moves unfavorably.

  • Take-Profit Setting:

If the trader expects the price to rise by 80 pips, the potential profit will be:

80 pips × $10/pip = $800.

This profit/loss ratio helps the trader assess the risk and reward of entering the trade, ensuring the strategy has a positive expected value.

  • Risk Management Application:
    Through the above calculations, traders can determine the appropriate position size based on the value of each PIP. For example:

    • If market volatility increases or the trader becomes more cautious about risk, they can choose to reduce the position size to lower the overall risk of each trade.
    • On the other hand, if market volatility is relatively stable, traders can increase their position size to enhance profit potential.
  • Decision Making:
    Once the value of each PIP is understood, traders can make more accurate trading decisions based on technical analysis, fundamental data, and market sentiment. For example:

    • When expecting the market to break a certain technical support or resistance level, the trader can use PIPS calculations to set entry or exit points.
    • Before news announcements or the release of important economic data, traders can use PIPS to predict the potential price fluctuation range and choose more reasonable stop-loss and take-profit strategies.

In summary, by calculating the value of each PIP in detail, traders can not only accurately estimate potential profits and losses but also adjust trading strategies flexibly based on market fluctuations and personal risk tolerance. This PIPS-based scientific calculation and application method provides solid data support and risk management foundations for successful trading operations.

Advanced Concepts: Pip Value and Spread

1. Pip Value

Pip value refers to the monetary value that each PIP represents in actual trading, directly affecting the trader’s profit and loss calculations as well as risk management. Specifically, the pip value depends on the size of the trading contract and the current market price. The calculation formula is typically:

Pip Value = (PIP Size / Current Price) × Trade Units

For example, in forex trading, with the EUR/USD pair and assuming the current exchange rate is 1.1050 and the trader is operating a standard lot (100,000 units), the value of each PIP (0.0001) would be approximately $10. When the trade size changes (such as a mini lot or micro lot), the pip value will adjust accordingly. Mastering pip value helps traders set stop-loss and take-profit levels based on personal risk tolerance and perform precise money management.

2. Spread

The spread refers to the difference between the bid price and the ask price, representing the implicit cost traders bear in each transaction. The size of the spread is primarily influenced by the following factors:

  • Market Liquidity: Highly liquid markets typically have lower spreads; conversely, markets with insufficient liquidity tend to have wider spreads.
  • Supply and Demand: When market demand surges or supply is insufficient, spreads may widen.
  • Broker Pricing Strategy: Different trading platforms or brokers’ pricing mechanisms can also result in spread differences.

The size of the spread is directly related to trading costs, especially for day traders, where a high spread might place the trade in an unfavorable position right at the opening, affecting profitability. Therefore, understanding and monitoring the spread is a critical element in formulating an effective trading strategy.

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How to Help Understand the True Meaning of PIPS

The advanced concepts of pip value and spread enrich the understanding of PIPS from different perspectives:

  • Pip value enables traders to clearly understand the actual currency change represented by each PIP, helping to accurately calculate potential profits and losses and adjust position sizes.
  • The spread helps traders understand the market entry cost, preventing high spreads from eroding expected profits.

By combining these two aspects of analysis, traders can not only more accurately assess market volatility but also formulate more scientific risk management and trading strategies based on different asset types and market conditions. These advanced concepts ultimately help improve trading efficiency and profitability, truly reflecting the core value of PIPS in trading.

FAQs

  • How do you correctly calculate the value of each PIP?
    The method for calculating the value of each PIP varies slightly across different assets, but the basic formula is based on the PIP size, current price, and trade units. For example:

    • In the forex market, if the EUR/USD quote is 1.1050, for a standard lot (100,000 units), the value of each PIP (0.0001) is approximately $10.

It is recommended that traders confirm the specific definition and calculation formula of the asset they are trading before opening a position and perform precise calculations based on their position size.

  • Why do the PIP definitions and pip values differ across different assets?
    Each asset market sets its own minimum price movement unit based on the quote format and market characteristics. For example:

    • In forex, non-JPY currency pairs are calculated to the fourth decimal place, while JPY currency pairs are calculated to the second decimal place;
    • Gold uses $0.01 per ounce and crude oil uses $0.01 per barrel as the standard;
    • Cryptocurrency may define a PIP as a $1 movement.

Understanding these differences helps traders adjust strategies based on different market characteristics.

  • How can you use PIPS for risk control during market volatility?
    When the market is highly volatile, PIPS is an intuitive tool that helps traders set reasonable stop-loss and take-profit levels. Experts suggest:

    • Set stop-loss points based on historical volatility ranges to ensure risk control during extreme market conditions;
    • Regularly adjust position sizes to avoid excessive losses caused by short-term market fluctuations.
  • Do all brokers use the same PIP definition?
    Not all brokers use the same PIP definition. Different platforms or brokers may have slight differences in their pricing rules. Traders should carefully read the trading specifications to confirm the exact PIP definition and calculation method to avoid misunderstandings when trading across platforms.

Glossary

Get started or expand your knowledge of trading at any level with a wealth of financial industry terms and definitions that you won’t find anywhere else.

Bookmarked Trading Term(s)

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  • AMM (Automated Money Market)

    A decentralized system that uses algorithms to automatically manage liquidity and trading in financial markets without traditional market makers.

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    The yearly interest rate a trader pays on borrowed funds or e arns on investments, excluding compounding.

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    The yearly interest rate a trader earns, including compounding, which reflects the real return on an investment.

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  • Asymmetric Cryptography

    A security method using two different keys (public and private) to encrypt and decrypt data, ensuring secure transactions.

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    The apportionment of premiums and discounts on forward exchange transactions that relate directly to deposit swap (interest arbitrage) deals, over the period of each deal.

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    A direct peer-to-peer exchange of different cryptocurrencies without the need for intermediaries, reducing counterparty risk.

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  • Balance Of Trade

    The value of a country's exports minus its imports.

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  • Bar Chart

    A type of chart which consists of four significant points: the high and the low prices, which form the vertical bar; the opening price, which is marked with a horizontal line to the left of the bar; and the closing price, which is marked with a horizontal line to the right of the bar.

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  • Barrier Level

    A certain price of great importance included in the structure of a Barrier Option. If a Barrier Level price is reached, the terms of a specific Barrier Option call for a series of events to occur.

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  • Barrier Option

    Any number of different option structures (such as knock-in, knock-out, no touch, double-no-touch-DNT) that attaches great importance to a specific price trading. In a no-touch barrier, a large defined payout is awarded to the buyer of the option by the seller if the strike price is not 'touched' before expiry. This creates an incentive for the option seller to drive prices through the strike level and creates an incentive for the option buyer to defend the strike level.

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  • Base Currency

    The first currency in a currency pair. It shows how much the base currency is worth as measured against the second currency. For example, if the USD/CHF (U.S. Dollar/Swiss Franc) rate equals 1.6215, then one USD is worth CHF 1.6215. In the forex market, the US dollar is normally considered the base currency for quotes, meaning that quotes are expressed as a unit of $1 USD per the other currency quoted in the pair. The primary exceptions to this rule are the British pound, the euro and the Australian dollar.

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  • Cable

    The GBP/USD (Great British Pound/U.S. Dollar) pair. Cable earned its nickname because the rate was originally transmitted to the US via a transatlantic cable beginning in the mid 1800s when the GBP was the currency of international trade.

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  • Cad

    The Canadian dollar, also known as Loonie or Funds.

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  • Call Option

    A currency trade which exploits the interest rate difference between two countries. By selling a currency with a low rate of interest and buying a currency with a high rate of interest, the trader will receive the interest difference between the two countries while this trade is open.

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  • Canadian Ivey Purchasing Managers (Cipm) Index

    A monthly gauge of Canadian business sentiment issued by the Richard Ivey Business School.

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  • Candlestick Chart

    A chart that indicates the trading range for the day as well as the opening and closing price. If the open price is higher than the close price, the rectangle between the open and close price is shaded. If the close price is higher than the open price, that area of the chart is not shaded.

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  • Day Trader

    Speculators who take positions in commodities and then liquidate those positions prior to the close of the same trading day.

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  • Day Trading

    Making an open and close trade in the same product in one day.

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  • Deal

    A term that denotes a trade done at the current market price. It is a live trade as opposed to an order.

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  • Dealer

    An individual or firm that acts as a principal or counterpart to a transaction. Principals take one side of a position, hoping to earn a spread (profit) by closing out the position in a subsequent trade with another party. In contrast, a broker is an individual or firm that acts as an intermediary, putting together buyers and sellers for a fee or commission.

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  • Dealing Spread

    The difference between the buying and selling price of a contract.

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  • Ecb

    European Central Bank, the central bank for the countries using the euro.

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  • Economic Indicator

    A government-issued statistic that indicates current economic growth and stability. Common indicators include employment rates, Gross Domestic Product (GDP), inflation, retail sales, etc.

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  • End Of Day Order (eod)

    An order to buy or sell at a specified price that remains open until the end of the trading day.

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  • Est/Edt

    The time zone of New York City, which stands for United States Eastern Standard Time/Eastern Daylight time.

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  • Estx50

    A name for the Euronext 50 index.

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  • Factory Orders

    The dollar level of new orders for both durable and nondurable goods. This report is more in depth than the durable goods report which is released earlier in the month.

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  • Fed

    The Federal Reserve Bank, the central bank of the United States, or the FOMC (Federal Open Market Committee), the policy-setting committee of the Federal Reserve.

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  • Fed Officials

    Refers to members of the Board of Governors of the Federal Reserve or regional Federal Reserve Bank Presidents.

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  • Figure/The Figure

    Refers to the price quotation of '00' in a price such as 00-03 (1.2600-03) and would be read as 'figure-three.' If someone sells at 1.2600, traders would say 'the figure was given' or 'the figure was hit.

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  • Fill

    When an order has been fully executed.

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  • G7

    Group of 7 Nations - United States, Japan, Germany, United Kingdom, France, Italy and Canada.

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  • G8

    Group of 8 - G7 nations plus Russia.

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  • Gap Gapping

    A quick market move in which prices skip several levels without any trades occurring. Gaps usually follow economic data or news announcements.

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  • Gearing (Also Known As Leverage)

    Gearing refers to trading a notional value that is greater than the amount of capital a trader is required to hold in his or her trading account. It is expressed as a percentage or a fraction.

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    An index of the top 30 companies (by market capitalization) listed on the German stock exchange – another name for the DAX.

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    Every 100 pips in the FX market starting with 000.

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  • Hawk/Hawkish

    A country's monetary policymakers are referred to as hawkish when they believe that higher interest rates are needed, usually to combat inflation or restrain rapid economic growth or both.

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    A position or combination of positions that reduces the risk of your primary position.

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  • Hit The Bid

    To sell at the current market bid.

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    Names for the Hong Kong Hang Seng index.

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    Little volume being traded in the market; a lack of liquidity often creates choppy market conditions. 

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    The IMM, or International Monetary Market, is a part of the Chicago Mercantile Exchange (CME) that deals with trading currency and interest rate futures and options.

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    A traditional futures contract based on major currencies against the US dollar. IMM futures are traded on the floor of the Chicago Mercantile Exchange.

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    8:00am - 3:00pm New York.

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    Abbreviation for the Dow Jones Industrial Average.

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  • Japanese Economy Watchers Survey

    Measures the mood of businesses that directly service consumers such as waiters, drivers and beauticians. Readings above 50 generally signal improvements in sentiment.

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  • Japanese Machine Tool Orders

    Measures the total value of new orders placed with machine tool manufacturers. Machine tool orders are a measure of the demand for companies that make machines, a leading indicator of future industrial production. Strong data generally signals that manufacturing is improving and that the economy is in an expansion phase.

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  • Jpn225

    A name for the NEKKEI index.

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  • Keep The Powder Dry

    To limit your trades due to inclement trading conditions. In either choppy or extremely narrow markets, it may be better to stay on the sidelines until a clear opportunity arises.

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    Nickname for NZD/USD (New Zealand Dollar/U.S. Dollar).

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  • Knock-Ins

    Option strategy that requires the underlying product to trade at a certain price before a previously bought option becomes active. Knock-ins are used to reduce premium costs of the underlying option and can trigger hedging activities once an option is activated.

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  • Knock-Outs

    Option that nullifies a previously bought option if the underlying product trades a certain level. When a knock-out level is traded, the underlying option ceases to exist and any hedging may have to be unwound.

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  • Last Dealing Day

    The last day you may trade a particular product.

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  • Last Dealing Time

    The last time you may trade a particular product.

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  • Leading Indicators

    Statistics that are considered to predict future economic activity.

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  • Level

    A price zone or particular price that is significant from a technical standpoint or based on reported orders/option interest.

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  • Leverage

    Also known as margin, this is the percentage or fractional increase you can trade from the amount of capital you have available. It allows traders to trade notional values far higher than the capital they have. For example, leverage of 100:1 means you can trade a notional value 100 times greater than the capital in your trading account.*

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  • Macro

    The longest-term trader who bases their trade decisions on fundamental analysis. A macro trade’s holding period can last anywhere from around six months to multiple years.

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  • Manufacturing Production

    Measures the total output of the manufacturing aspect of the Industrial Production figures. This data only measures the 13 sub-sectors that relate directly to manufacturing. Manufacturing makes up approximately 80% of total Industrial Production.

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  • Market Call

    A request from a broker or dealer for additional funds or other collateral on a position that has moved against the customer.

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  • Market Maker

    A dealer who regularly quotes both bid and ask prices and is ready to make a two-sided market for any financial product.

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  • Market Order

    An order to buy or sell at the current price.

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    An abbreviation for the NASDAQ 100 index.

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  • Net Position

    The amount of currency bought or sold which has not yet been offset by opposite transactions.

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  • New York Session

    8:00am – 5:00pm (New York time).

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  • No Touch

    An option that pays a fixed amount to the holder if the market never touches the predetermined Barrier Level.

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    Symbol for NYSE Composite index.

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  • Offer (Also Known As The Ask Price)

    The price at which the market is prepared to sell a product. Prices are quoted two-way as Bid/Offer. The Offer price is also known as the Ask. The Ask represents the price at which a trader can buy the base currency, which is shown to the right in a currency pair. For example, in the quote USD/CHF 1.4527/32, the base currency is USD, and the ask price is 1.4532, meaning you can buy one US dollar for 1.4532 Swiss francs. 

    In CFD trading, the Ask represents the price a trader can buy the product. For example, in the quote for UK OIL 111.13/111.16, the product quoted is UK OIL and the ask price is £111.16 for one unit of the underlying market.

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  • Offered

    If a market is said to be trading offered, it means a pair is attracting heavy selling interest, or offers.

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  • Offsetting Transaction

    A trade that cancels or offsets some or all of the market risk of an open position.

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  • On Top

    Attempting to sell at the current market order price.

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  • One Cancels The Other Order (oco)

    A designation for two orders whereby if one part of the two orders is executed, then the other is automatically cancelled.

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  • Paid

    Refers to the offer side of the market dealing.

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  • Pair

    The forex quoting convention of matching one currency against the other.

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  • Paneled

    A very heavy round of selling.

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  • Parabolic

    A market that moves a great distance in a very short period of time, frequently moving in an accelerating fashion that resembles one half of a parabola. Parabolic moves can be either up or down.

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  • Partial Fill

    When only part of an order has been executed.

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  • Quantitative Easing

    When a central bank injects money into an economy with the aim of stimulating growth.

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  • Quarterly Cfds

    When a central bank injects money into an economy with the aim of stimulating growth.

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  • Quote

    An indicative market price, normally used for information purposes only.

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  • Rally

    A recovery in price after a period of decline.

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  • Range

    When a price is trading between a defined high and low, moving within these two boundaries without breaking out from them.

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  • Rate

    The price of one currency in terms of another, typically used for dealing purposes.

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  • Rba

    Reserve Bank of Australia, the central bank of Australia.

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  • Rbnz

    Reserve Bank of New Zealand, the central bank of New Zealand.

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  • Sec

    The Securities and Exchange Commission.

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  • Sector

    A group of securities that operate in a similar industry.

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  • Sell

    Taking a short position in expectation that the market is going to go down.

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  • Settlement

    The process by which a trade is entered into the books, recording the counterparts to a transaction. The settlement of currency trades may or may not involve the actual physical exchange of one currency for another.

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    Symbol for the Shanghai A index

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  • Takeover

    Assuming control of a company by buying its stock.

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  • Technical Analysis

    The process by which charts of past price patterns are studied for clues as to the direction of future price movements.

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  • Technicians/techs

    Traders who base their trading decisions on technical or charts analysis.

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  • Ten (10) Yr

    US government-issued debt which is repayable in ten years. For example, a US 10-year note.

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  • Thin

    A illiquid, slippery or choppy market environment. A light-volume market that produces erratic trading conditions.

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  • Ugly

    Describing unforgiving market conditions that can be violent and quick.

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  • Uk Average Earnings Including Bonus/ Excluding Bonus

    Measures the average wage including/excluding bonuses paid to employees. This is measured quarter-on-quarter (QoQ) from the previous year.

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  • Uk Claimant Count Rate

    Measures the number of people claiming unemployment benefits. The claimant count figures tend to be lower than the unemployment data since not all of the unemployed are eligible for benefits.

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  • Uk Hbos House Price Index

    Measures the relative level of UK house prices for an indication of trends in the UK real estate sector and their implication for the overall economic outlook. This index is the longest monthly data series of any UK housing index, published by the largest UK mortgage lender (Halifax Building Society/Bank of Scotland).

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  • Uk Jobless Claims Change

    Measures the change in the number of people claiming unemployment benefits over the previous month.

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  • Value Date

    Also known as the maturity date, it is the date on which counterparts to a financial transaction agree to settle their respective obligations, i.e., exchanging payments. For spot currency transactions, the value date is normally two business days forward.

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  • Variation Margin

    Funds traders must hold in their accounts to have the required margin necessary to cope with market fluctuations.

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  • Vix Or Volatility Index

    Shows the market's expectation of 30-day volatility. It is constructed using the implied volatilities of a wide range of S&P 500 index options. The VIX is a widely used measure of market risk and is often referred to as the "investor fear gauge."

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  • Volatility

    Referring to active markets that often present trade opportunities.

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  • Wedge Chart Pattern

    Chart formation that shows a narrowing price range over time, where price highs in an ascending wedge decrease incrementally, or in a descending wedge, price declines are incrementally smaller. Ascending wedges typically conclude with a downside breakout and descending wedges typically terminate with upside breakouts.

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  • Whipsaw

    Slang for a highly volatile market where a sharp price movement is quickly followed by a sharp reversal.

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  • Wholesale Price

    Measures the changes in prices paid by retailers for finished goods. Inflationary pressures typically show earlier than the headline retail.

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  • Working Order

    Where a limit order has been requested but not yet filled.

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  • Wsj

    Acronym for The Wall Street Journal.

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  • Xag/Usd

    Symbol for Silver Index.

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  • Xau/Usd

    Symbol for Gold Index.

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  • Xax.X

    Symbol for AMEX Composite Index.

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  • YER

    Yemeni Rial. The currency of Yemen. It is subdivided into 100 fils.

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  • Yemeni Rial

    See YER.

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  • Yen

    See JPY.

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  • Yield

    Yield is the return on an investment and is usually expressed as a percentage.

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  • Yuan Renminbi

    See CNY

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  • ZAR

    Rand. The currency of South Africa. It is subdivided into 100 cents.

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  • ZMW

    Zambian Kwacha. The currency of Zambia. It is subdivided into 100 Ngwee.

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  • ZWL

    Zimbabwe Dollar. The currency of Zimbabwe. It is subdivided into 100 cents.

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  • Zambian Kwacha

    See ZMW.

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  • ZigZag

    A technical indicator that draws tops and bottoms - filtering out noise.

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  • Zimbabwe Dollar

    See ZWL.

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