Pips
Most currency quotes are given to four decimal places although there are exceptions such as the U.S. Dollar against the Great British Pound (GBP) or the Euro (EUR), which are generally given to five decimal places. The Australian Dollar (AUD) is usually quoted to five decimal places as well. The USD is only given to two decimals when quoted in terms of yen. Regardless of the format, the last place holder for any quote is called a PIP, which stands for price interest point. A pip is the smallest increment that the quote currency (the currency to the right of the slash) can move and is similar to a “tick” for the stock market.
For example, in Table 2-1 the quote for the GBP/USD is 1.7478. The last decimal place holder (8 in this quote) is called a pip since that place holder represents the smallest increment that this quote could move. In other words, an increase of one pip will make the quote 1.7479 while a decrease of one pip makes it 1.7477. Because most currencies are quoted to four decimal points, a one-pip move is generally .0001 with the USD/JPY being the sole exception where each pip represents .01.
How much is a pip worth? The value depends on the size of the contract that you’re trading. This is similar for stock trading. If the stock smallest price increment that a stock’s price can move is one-cent then the value of that one-cent move depends on how many shares you’re holding.
Recall that most currencies are traded in lots of 100,000 units of the base currency. Once we know the quote and the value of the contract, we can find the value of a pip. Continuing with our earlier example, the quote for the Great British Pound in terms of Dollars is GBP/USD = 1.7478. The value of a pip is .0001 so if this quote moves up one pip to 1.7479 then that’s an increase of .0001 * $100,000 = $10.
In fact, any currency that is quoted in terms of USD (with USD on the right hand side of the slash) to four decimals will always have a pip value of $10. This is called a static pip value since it never changes. Every one pip move is always worth $10. Keep in mind that this only qualifies for currencies that are quoted to four decimal places against the Dollar. The major currencies with static pip values are the EUR/USD (Euro vs. U.S. Dollar), GBP/USD (Great British Pound vs. U.S. Dollar), and the AUD/USD (Australian Dollar vs. U.S. Dollar).
Let’s step through the motions of a trade to verify that the value of a pip is $10. Assume you believe the Great British Pound will rise against the U.S. Dollar. You now know that you would want to buy the GBP/USD currency pair. This makes you long the GBP and short the USD. We’ll assume the quote is GBP/USD = 1.7478.
By purchasing this currency pair, you are effectively buying 100,000 Pounds (remember, most contracts control 100,000 units of the base currency) and simultaneously shorting the USD equivalent. How many dollars are you shorting? If one GBP is worth 1.7478 USD, then you are shorting $174,780. Hopefully you remembered that when moving from the base currency to the quote currency (left to right) that you must multiply by the quote. Effectively, you are taking this amount of dollars and converting them into British Pounds.
Once again, by shorting $174,780, you have an obligation to deliver that money back to the bank. Since you are long the GBP/USD currency pair, you’d like to see the quote rise since that means the British Pound is getting stronger against the U.S. Dollar. Let’s assume the quote moves up one pip and is now GBP/USD = 1.7479. The British Pound has against the U.S. Dollar, just as you expected. In this case, the British Pound has risen one pip against the U.S. Dollar.
How much profit have you made? You are still holding 100,000 British Pounds as that amount never changes. So you now take those pounds and exchange them for U.S. Dollars, which is effectively done by selling the GBP/USD currency pair. Remember, we want to convert our currency back into the “home” currency of U.S. Dollars, which means we need to be “long” that currency. If you sell the GBP/USD pair, you are short the GBP and long the USD which is exactly what you need to do to bring the profits home.
The new quote tells us that GBP/USD =1.7479, which means you will receive 1.7479 USD for every British Pound that you own, or 100,000 * 1.7479 = $174,790 USD. After paying back the bank the $174,780 that you borrowed, you’re left with a $10 profit, which is exactly what our pip calculation told us. For any quote with USD as the quote currency, each pip will always be worth $10. A one-pip increase in the quote will add $10 to your account while each one-pip decrease will reduce your account value by $10.
Variable Pips
If a currency is quoted with the dollar as the base currency (the USD to the left of the slash) then it will have a variable pip value. The major currencies with variable pips are USD/JPY (U.S. Dollar vs. Japanese Yen), USD/CHF (U.S. Dollar vs. Swiss Franc), and USD/CAD (U.S. Dollar vs. Canadian Dollar).
Why do these currency pairs have variable pip values? Let’s use the USD/CAD=1.1646 quote from Table 2-1 to find out. If one lot of currency controls 100,000 units of the base currency (the currency to the left of the slash) then this lot controls 116,460 Canadian Dollars and one pip equals .0001 * 100,000 = 10 Canadian Dollars. At the current quote a one pip move equals 10/1.1646 = $8.59. When the USD is the base currency, the pip value depends on the current exchange rate.
Let’s step through the motions of an actual trade to check our answer. Assume you buy the currency pair USD/CAD=1.1646. If one lot of currency equals 100,000 units of the base currency then you are long 100,000 U.S. Dollars and short 116,460 Canadian Dollars. The $100,000 you are long never changes in amount but only in value in terms of Canadian Dollars. If the quote rises to USD/CAD=1.1647 then how much profit have you made? Since you’re short 116,460 Canadian Dollars, you must purchase that amount back to deliver to the bank. You take your $100,000 and purchase 116,460 CAD for a total cost of 116,460/1.1647 = $99,910.41 thus leaving you with a profit of $100,000 - $99,910.41 = $8.59, which is what our pip calculation showed.
It should be evident that this value will change as the exchange rate changes and that’s why it is called a variable pip. Again, the variable pip currency pairs are any with the USD as the base currency (to the left of the slash). The value of a pip, whether variable or static, is always in relation to the quote currency.
The Bid-Ask Spread
Up to this point, we have assumed that currencies could be bought and sold for one price. For example, when we referred to the quote USD/JPY = 117 that assumes that traders can buy or sell the U.S. Dollar in exchange for 117 Japanese Yen. In the real world of trading, that is not how the system works. Just as with the stock market, there is a bid-ask spread that you must contend with.
Whether you’re talking about stocks or currencies, the bid price represents the highest price that someone is willing to pay. If that’s confusing, think about the terms used at a live auction or an electronic one such as eBay. If you wish to buy a house through a realtor or decide on an antique on eBay, you would submit a bid. Buyers place bids. On the other hand, sellers place “asking” prices (also called “offers”). If you are selling your house, you would say it is “offered” at such-and-such a price. The terms bid and ask are used in the same way for the stock and currency markets.
The forex market has bid-ask spreads due to different dealers placing bids to buy and offers to sell. Rather than seeing a quote like USD/JPY = 117, you might see it as USD/JPY = 117.00/117.05. This is just a shorthand notation meaning that the bid is 117 and the asking price is 117.05.
In this example, there is a five pip spread between the bid and ask, which is common as the major currencies generally carry a three to seven pip spread.
Because the spreads are relatively small, most dealers only show the digits to the right of the decimal point for the asking price so you’d likely see this quote written as USD/JPY = 117.00/05. This means the dealer is willing to buy the USD in exchange for 117 JPY and is also willing to sell the USD in exchange for 117.05 JPY. In turn, this means that you can buy the USD in exchange for 117.05 JPY and sell the USD in exchange for 117 JPY.
For example, let’s use the quote USD/JPY = 117.00/05. When you’re first introduced to currency trading it helps to spell out what each quote means by writing out two separate statements such as this:
1) The dealer is willing to buy one USD for 117 JPY
2) The dealer is willing to sell one USD for 117.05 JPY
Let’s assume this dealer is a bank and that you are going on a business trip to Japan. If you have $5,000 and need to convert it to yen, you’re really wishing to SELL dollars and BUY yen. Keeping that in mind, you need to use the quote where the dealer is willing to BUY dollars. In this example, the first statement shows the dealer is willing to buy dollars in exchange for 117 yen. If you give the bank $5,000, you will receive $5,000 * 117 = 585,000 yen.
Now assume that you return from your trip and are still holding all of your yen. You’d like to turn them back into dollars, which means you want to BUY dollars in exchange for yen. If the quote is still the same when you return home, the second statement shows that the dealer is willing to SELL dollars to you in exchange for 117.05 yen. You can sell your yen and receive 585,000/117.05 = $4,997.85. Notice that the bid-ask spread has created a “leak” in the exchanges that caused a loss of $2.15 for no other reason than converting your dollars to yen and then back to dollars again. It is the bid-ask spread that allows dealers to not charge commissions for currency trading. Buying at the asking price and selling at the bid price creates a nice profit for their services.
The bid-ask spread affects all traders equally and is not affected by which currency you start with. For example, assume a businessman from Japan travels to the U.S. When he lands, he has 585,000 yen that he would like to exchange for dollars. Using the same quotes, he needs to BUY dollars in exchange for yen, which means he must find the quote where the dealer is willing to SELL dollars. The second statement above shows that the dealer will sell one dollar for every 117.05 yen.
The Japanese businessman will therefore receive 585,000/117.05 = $4,997.85. When it’s time to return home, he’d like to convert his remaining dollars back into yen. At this point, he needs to SELL dollars in exchange for yen, which means he needs to find the quote where the dealer is willing to BUY dollars in exchange for yen. The first statement shows that the businessman can get $4,997.85 * 117 = 584,748.45 yen, which is less than the 585,000 yen he started with.
Whether you go through the motions the long way as we have done here or simply trade by purchasing the USD/JPY pair and then selling the USD/JPY pair the results will be exactly the same.
If reading the quotes still seems difficult, just remember that the prices are never in your favor. The reason the dealers make a profit from the bid-ask spread is because you must “buy high” and “sell low” which leaves a profit for them. Therefore, if you see a quote USD/JPY = 117.00/.05 you can figure that you must buy for 117.05 and sell for 117. The reason you can buy for 117.05 is because that quote is a seller and can therefore be executed. The reason you can sell for 117 is because that quote represents a buyer and, again, the trade can be executed.
Spread Percent
We’ve just shown how the bid-ask spread creates a hidden transaction cost for traders. We can easily find out just how big this cost is with a simple formula:
This formula just calculates the percentage change as we move down from the asking price to the bid price. If the quote is 117.00/.05, the spread percent is (117.05 – 117)/117.05 = .000427, or .0427%.
If you lose .0427% of your money between the bid and ask then that’s the same thing as saying you keep 1 - .000427 = .99957 of your money. In the first example, you ended up with $4,997.85 after converting $5,000 into yen and then back into dollars at a bid-ask spread of .0427%. We could have gone straight to the answer by taking $5,000 * .99957 = $4,997.85.
We could also calculate the Japanese businessman would end up with 585,000 * .99957 = 584,748.45 by exchanging yen for dollars and then back to yen at the same bid-ask spread. Our previous long calculation confirms this result.
The bid-ask spread depends on the volume in a particular market, the volatility, and the size of the transaction. Generally speaking, the more liquid the market (larger number of buyers and sellers, or “volume”) the smaller the spread. Therefore, the major currency pairs will have smaller bid-ask spreads when compared to the less commonly traded pairs. High volatility will create larger spreads for any given market and that’s because the dealer has a harder time spreading the risk as prices move around.
Remember that cross rates are generally more volatile since they essentially involve two separate trades against the U.S. Dollar. Because of this, cross rates usually have higher spreads. Currency pairs that are relatively quiet (low volatility) have smaller spreads. Last, larger orders will be given better prices and will therefore have smaller spreads between the bid and ask.
In an earlier section, we showed that if you know the quote for USD/JPY then you could find JPY/USD by simply taking the reciprocals of both sides of the quote. For the same reason, if you know the bid-ask spread for a particular quote, you can calculate the bid-ask spread for the reciprocal quote.
In this example, we assumed the quote for USD/JPY = 117.00/05. What are the bid and ask prices for JPY/USE? Since we know the quote for USD/JPY we know to take the reciprocals of the quotes to find JPY/USD. The reciprocal quote for the bid is 1/117 = .008547 and is 1/117.05 = .008543 for the asking price. But notice that the bid price is larger than the asking price! This will always happen when you take the reciprocals for the bid and ask for any currency pair. All you have to do is switch the two numbers and make the smaller number the bid and the larger number the asking price. In this example, the bid price for JPY/USD is .008543 and the asking price is .008547. In practice, this quote would be displayed as JPY/USD = .008543/47. After multiplying by 100 to get rid of the two leading zeros, you’d see it as JPY/USD = .8543/47.
Let’s run through the above example and check our numbers. This quote tells us the following:
1) The dealer is willing to buy one JPY for .008543 dollars
2) The dealer is willing to sell one JPY for .008547 dollars
If you were leaving for Japan and had $5,000 cash, you would need to sell dollars and buy yen. If you need to BUY yen then you need to look for the quote where the dealer will SELL yen. The second statement tells us that you can get $5,000/.008547 = 585,000.58 yen. Note that this is slightly higher than the 585,000 yen from the first example. This is strictly due to the quote not being carried out enough decimal places. When you return from your trip, you’d like to turn these yen back into dollars. This means you need to SELL yen in exchange for dollars so must find the quote where the dealer will BUY yen. The dealer will buy each of your yen for .008543, or 585,000.58 * .008547 = $4,997.65. This closely agrees with our previous ending value of $4,997.85.
It should be evident that the Japanese businessman who starts with 585,000 yen will also end up with the same loss as in the first example.
Implied Bid-Ask Spreads
In an earlier section, we found out how to calculate the cross rate from two sets of quotes against the dollar. Now that you understand bid-asks spreads, let’s not only calculate the cross rate, but let’s also find the bid-ask spread. Calculating the cross rate bid-ask spread is often called the implied bid-ask spread or the synthetic bid-ask spread. For example, assume the bid and ask prices for the following pair of quotes:
EUR/USD = 1.2096/1.2101
USD/CHF = 1.3012/1.3017
From these quotes, we can calculate the EUR/CHF cross rate by purchasing the EUR/USD and also purchasing the USD/CHF pair:
To buy the EUR/USD pair we must pay the asking price of 1.2101. For the USD/CHF pair, we must pay the asking price of 1.3017. The cross rate equation shows that we must multiply these quotes together to get 1.2101 * 1.3017 = 1.5752. This calculation gives us the asking price for the EUR/CHF pair.
By the same reasoning, we should be able to find the bid price for the EUR/CHF pair. We can sell EUR/USD at the bid price of 1.2096 and can sell the USD/CHF pair at the bid price of 1.3012. After multiplying these together we get 1.2096 * 1.3012 = 1.5739. The calculations show that the implied bid-ask spread for EUR/CHF is 1.5739/1.5752 (or 1.5739/52). Notice the relatively larger bid-ask spread for this cross rate as compared to the previous example. Even though all quotes were assumed to have a five-pip spread, the bid-ask spread is much wider for the cross rate, which is what we stated previously.
Finding the implied bid-ask spread for cross rates can be confusing for new traders because the formula depends on the quotes you are given. Sometimes you need to multiply by the quotes and sometimes you need to divide. However, there is an easy way to always understand which formula to use and that is to simply follow the currency conversions.
In this example, we were trying to figure out the EUR/CHF cross rate based on the EUR/USD and USD/CHF quotes. Think about what the problem is asking for. It is asking you to take EUR and convert it to CHF. Based on the two quotes, we can convert EUR to USD by multiplying by the quote. Remember, we multiply whenever we convert the base currency to the quote currency (moving from the left currency to the right). Once we do that, we’re now holding USD and want to convert that to EUR which we can do by the second set of quotes. That quote is USD/EUR which means we must multiply by the quote again. If you just follow the conversions from one currency to the next in the proper order, you will always be able to figure out whether you should multiply or divide. For example, assume that you had been given the following quotes instead and asked to find the implied EUR/CHF bid-ask spread:
EUR/USD = 1.2096/1.2101
CHF/USD = 0.7682/0.7685
As before, the question is asking us to convert currency from EUR to CHF so we only need to focus on that path based on these quotes. Start by converting EUR to USD, which is done by multiplying. Next, covert the USD to CHF by using the CHF/USD quote but this time we must divide by the quote since we’re moving from the quote currency to the base currency. So to find the implied bid-ask spread we would buy the EUR/USD pair at the asking price of 1.2101. In order to convert those dollars to CHF we must divide by the bid price of 0.7682 and get 1.2101/0.7682 = 1.5752.
We can also find the price for selling the EUR/CHF pair. Start by selling EUR/USD and the 1.2096 bid. Next, covert those dollars to CHF by buying the CHF/USD pair at the 1.2096 bid. Now take those dollars and covert them to CHF by dividing by the 0.7685 asking price, which give 1.2096/0.7685 = 1.5739. As before, the implied bid-ask spread is 1.5739/1.5752 but we had to use a different set of calculations to get there. If you just remember to follow the conversion from where you want to start to where you want to finish you’ll have no trouble remembering how to perform the calculation. Regardless of which calculation is used, the bid price will always be the smaller of the two answers.
Triangular Arbitrage
The previous sections showed how we can calculate cross rates from two other currency quotes. This shows that there is a connection between currency pairs and cross rates. Are there any procedures set in place to be sure the cross rate quotes do not get out of line from the rest? The answer is yes. The people in charge of making sure the prices do not get too far out of line are called arbitrageurs. Arbitrage is from the French arbitrer, which means “to judge.” It is also where we get the word arbitrator from.
Arbitrageurs are speculators in the market who make “free” money by judging the relative values between assets. And free money is a powerful incentive for someone to keep a watchful eye on prices. By placing simultaneous trades, arbitrageurs can capture money for no risk (called an arbitrage profit) in the marketplace.To qualify as an arbitrage profit, two conditions must be met. First, the profit must be guaranteed. Second, there can be no cash outlay on the part of the arbitrageur. This second condition is necessary otherwise an investment in a government bond would count as arbitrage since it results in a risk-free profit. For the arbitrageurs, they must gain this profit by not spending any money.
The classic form of arbitrage involves the simultaneous buying and selling of the same security on two different exchanges. The arbitrageur buys the relatively cheap asset and, at the same time, sells the relatively expensive one. For instance, assume that IBM is trading for $100 on the New York Stock Exchange and is also trading for $100.10 on the Philadelphia Exchange.
Realizing that the same asset is trading for two different prices, arbitrageurs would buy shares on the New York and simultaneously sell them on the Philly for a guaranteed 10-cent profit. You might be wondering why anybody would bother for a 10-cent profit but arbitrageurs will send in orders for potentially tens of thousands of shares thus magnifying tiny price discrepancies into considerable gains. Their actions put buying pressure in New York (where IBM prices are low) and selling pressure in Philly (where IBM prices are high) thus bringing both prices closer together. The arbitrage opportunities cease to exist once IBM is trading for the same price on both exchanges.
In the currency markets, arbitrageurs do a similar, although more complicated, process called triangular arbitrage. The word “triangular” is used to denote the fact that the arbitrageur must convert one currency into another on one exchange, then into another at another exchange, and then convert the currency back to the base currency at yet another exchange. This three step process represents each leg of a triangle.
Let’s take a look at an example, which we’ll make easier by not considering the bid-ask spreads. Assume the following three sets of hypothetical quotes:
New York: USD/CAD = 1.1651
Frankfurt: CAD/CHF = 1.1176
London: USD/CHF = 1.3008
Using computer programs, arbitrageurs would find that there are discrepancies among these quotes. To capitalize on these discrepancies, the arbitrageur may take the following steps:
- Sell 1,000,000 USD and buy 1,165,100 CAD in New York
(Remember, if we exchange the base currency for the quote currency we multiply by the quote.)
- Sell the 1,165,100 CAD and buy 1,302,116 CHF in Frankfurt
(Again, moving from CAD to CHF we must multiply by the quote.)
- Sell 1,302,116 CHF and buy 1,001,012 USD in London
(As we move from quote currency to base currency we must divide by the quote.)
These actions can be better understood by Figure 2-4, which demonstrates the process of triangular arbitrage:
Figure 2-4: Triangular Arbitrage
The arbitrageur nets a profit of $1,012 by going through the above three legs of the triangle. In reality, each step will not be taken individually as the arbitrageur would be exposed to execution risk – the risk of the quotes moving adversely during the time to set up the next trade. Instead, once the computer program flags the opportunity, the arbitrageur would enter the following trades simultaneously:
- Sell 1,000,000 USD/CAD in New York
- Sell 1,165,100 CAD/CHF in Frankfurt
- Buy 1,001,102 USD/CHF in London
These actions put the following pressures into action:
1. Selling pressure on the USD in New York. The quote will eventually FALL below USD/CAD = 1.1651
2. Selling pressure on the CAD in Frankfurt. The quote will eventually FALL below CAD/CHF = 1.1176
3. Buying pressure on the USD in London. The quote will eventually RISE above USD/CAD = 1.3008
The arbitrageurs are exchanging USD for CAD, then CAD for CHF, and then CHF for USD. These actions leave the arbitrageur back with same currency unit that he stated with:
As these buying and selling pressures start to move their respective markets, the arbitrage opportunity quickly disappears. Now let’s see if the theory or triangular arbitrage holds in practice. Notice the actual quotes from Table 2-1, which has been reproduced below, for these three pair: USD/CAD, CAD/CHF. USD/CHF, which are highlighted below:
Table 2-1 (Reproduced)
The actual quote for USD/CAD is 1.1646, which is lower than the 1.1648 quote we used in the arbitrage example. This would be due to the selling pressure in New York in our hypothetical example.
- The actual quote for CAD/CHF is 1.1173, which is also lower than the 1.1176 quote we assumed in the arbitrage example. This reduction would be due to the selling pressure we assumed in Frankfurt.
- The actual quote for USD/CHF is 1.3012, which is higher than the 1.3008 exchange rate we used, which is due to the assumed buying pressure in London.
So even though the numbers we chose for the arbitrage example were hypothetical, they still show an important point. That is, if those hypothetical numbers were real, they would be forced toward the actual values we find in Table 2-1. Arbitrageurs will make sure of it.
Are the quotes in Table 2-1 perfectly in line at the given quotes? If we run through the same steps using the actual quotes in Table 2-1, we find that the arbitrage profit has been reduced to only $6:
- Take 1,000,000 USD and exchange them for 1,164,600 CAD in New York
- Take the 1,164,600 CAD and exchange them for 1,301,208 CHF in Frankfurt
- Take the 1,301,208 CHF and exchange them for 1,000,006 USD in London
The reason for this small discrepancy is that we haven’t taken into consideration the bid-ask spreads for these quotes. If we did, you can be sure that there are no significant arbitrage opportunities in Table 2-1. Arbitrage is not possible at the retail level because the size of the necessary transactions would be very large and you would need proprietary computer programs to find and exploit the opportunities. Arbitrage is still important to understand since it is the process that keeps prices “in line” with theoretical prices and therefore makes all cross rates fairly priced.