# Calculating Profit and Loss in Interest Rate Futures

As you have likely discovered, the term commodity can be used to describe a wide array of assets. The formal definition of a commodity is a physical substance or asset that is “interchangeable” in trade. From a more general standpoint, a commodity is any product that trades on a futures exchange. Along with grains such as corn and wheat, commodities also come in the form of financial assets such as interest rate products and currencies. Just as you wouldn’t prefer one bar of gold over another, you likely wouldn’t have a preference between one T-bill over another. The Chicago Board of Trade (CBOT) division of the CME Group futures exchange has recognized this; therefore the CBOT exchange offers standardized contracts to represent each of the government issued fixed income securities known as Treasuries. Similarly, the Chicago Mercantile Exchange division of the CME Group, offers futures trading in a short term interest rate product known as a Eurodollar.

There are several widely traded contracts in the realm of interest rate futures trading. Each of these futures contracts carry slightly differing market characteristics, and in some cases contract sizes, point values, etc. For those unfamiliar with the futures markets, these discrepancies can be overwhelming. However, I hope to deliver the pertinent information clearly in order to make your journey into financial futures trading as pleasant as possible.

Before we cover the basic specifications of each contract, it is important to be aware of a few facts regarding Treasury bond valuation. First, longer maturities will react quicker and more violently to changes in interest rates than shorter maturities. Additionally, the value of a bond (the price in which it is trading) is inversely correlated with interest rates or yields. Accordingly, if interest rates go up bond price will drop and vice versa. Keep these points in mind as you review the details of each contract; it will help you to determine which avenue best suits your risk tolerance and personality.

Interest Rate Futures

## Treasury Futures

Several years ago the 30-year Treasury bond was the primary interest rate product traded on the Chicago Board of Trade (CBOT). During its prime, it was considered the only Treasury futures contract for experienced commodity traders to involve themselves with. However, the Federal Reserve’s failure to issue new 30-Year bond contracts on a regular basis has worked against the popularity of the contract. In the meantime, shorter maturities such as the 10-Year note benefited in terms of volume and open interest.

Similar to the other financial futures contracts, all interest rate products are on a quarterly cycle. This means that there are four differing expiration months based on a calendar year. Thos months are; March, June, September and December.

### 30-Year T-Bond Futures

**Symbol: ZB**

The 30-year bond is often referred to as the long bond due to its lengthy maturity and its spot on the infamous yield curve. You might also know it simply as “the bond” as other Treasury issues are known as Notes or Bills (to be discussed later).

The face value of a T-Bond at maturity is $100,000; therefore the contract size of one futures contract with the 30-year Treasury bond as an underlier is also $100,000. Knowing this, it is easy to see that a contract can be looked at as 1,000 points, or trading handles, worth $1,000 a piece. What is unlikely to be obvious is that each full point or handle can then be looked at as a fraction. In trading, the term handle is used to describe the stem of a quote. This usage began in reference to currency futures to describe a penny move. For example, if the Euro rallies from 131.00 to 132.00, some may say that it has moved a handle. In the case of the 30-year Treasury futures, a rally from 156’0 to 157’0 is equivalent to a price increase of one handle.

The discussion of the relationship between Treasury futures prices and interest rates is to extensive to be included here, but to clarify pricing here is a general explanation of the relationship between the current Treasury price relative to it’s par value. If a futures contract is trading in excess of its par value of 100’0, interest rates have gone down since the issuance of the underlying Treasury securities. If the futures contract is trading below par, interest rates have gone up.

The long bond trades in fractions of a full point; specifically, ticks equivalent to 1/32 of a full point or $31.25 figured by dividing $1,000 by 32. Treasury bond futures are quoted in handles, and fractions of a handle. Further, by the number of full points (worth $1,000) and an incremental fraction of such. Thus a typical bond quote may be 152-24. This is read as 152 handles and 24/32nds. At this quote, the futures contract has a value of $152,750. This is calculated by multiplying 152 by $1000 and 24 by the tick value of $31.25.

If you are comfortable with the idea of adding and subtracting fractions you will be able to easily calculate profit, loss and risk in Treasury futures. For those that are “fractionally” challenged, you may want to trade Eurodollars which are valued in decimals and will be discussed subsequently. However, I am confident that everyone will quickly become proficient bond futures calculations after looking at the examples below.

Reading the contract size and point value likely isn’t going to help you to remember or even understand bond futures pricing but looking at a few examples should add some clarity to the details. If a commodity trader goes long a September bond futures contract at 155’22 and is later able to sell the at 156’24 would be profitable by 1’02 or 1 2/32. In dollar terms this is equivalent to $1,062.50 ((1 x $1,000) + (2 x $31.25)).

The multiplication is relatively standard but people tend to be unjustifiably intimidated by fractions. If you recall the concept of borrowing, you will be fine. In the example above, it wasn’t necessary to borrow. You could have simply subtracted the numerator (top number in fraction) of the buy price from the numerator of the sell price and multiplied the result by $31.25. Likewise, you would have subtracted the handle of the buy price from the handle of the sell price and multiplied the result by $1,000.

24/32 – 22/32 = 2/32, 2 x $31.25 = $62.50

156 – 155 = 1 x $1,000 = $1,000

Total Gain = $1,000 + $62.50 = $1,062.50 minus commissions and fees

The math isn’t always this convenient. There will be times in which you will need to borrow from the handle to bring the fraction to a level in which you can properly figure the profit or loss. For example, a trader that sells a September bond futures contract at 158’12 and buys the contract back at 156’27 may have a difficult time calculating her trading profit. In this case it is easy to see that the trade was profitable. We know this because the handle at the time of the sell was 118 and the buy was 116 but unless you have been doing this for a while it will take a little work to derive the exact figure.

The denominator of the sell price, 12, is much smaller than the denominator of the buy price, 27. Therefore we know that we must borrow from the handle to properly net the fractions. In this example, we could reduce the selling price handle to 157 and increase the fraction by 32/32nds. Thus, the new selling price is 157’44. This is a number that can be easily worked with.

44/32 – 27/32 = 17/32, 17 x $31.25 = $531.25

157 – 156 = 1 x $1,000 = $1,000

Total Profit = $1,531.25 minus commissions and fees

The purpose of these examples is to give you an idea of how T-Bond futures traders can calculate their trading results. Obviously, not all bond futures trades or traders will make money.

### 10-Year Note Futures

**Symbol: ZN**

The 10-year note futures, or simply “the note”, has many similarities to the 30-year bond futures contract. The contract size and the point value are all common characteristics. Similarly, if you were able to come to peace with the 30-year bond futures calculations the 10-year note won’t be an issue.

To reiterate, the contract size of the note is $100,000 which is split into 1,000 handles equivalent to $1,000 and a tick value of 1/32nds or $31.25. Unlike the 30-year bond futures contract, the T-note trades in half ticks (.5/32) valued at $15.625.

Calculating profit, loss and risk in the 10-year note is identical to that of the 30-year bond. To demonstrate, if a trader goes short the 10-year note futures from 123’29.5 and places a buy stop to protect him from an adverse move at 125’15.0 the risk on the trade would be 1’17.5 or 1,546.87. This is calculated by subtracting the entrance price of the short from the potential fill price of the buy stop at 125’15.0. Once again, the math requires borrowing from the handle in order to properly subtract the fractions. This is done by adjusting the stop price from 125’15.0 to 124’47 ((125 – 1) + (15/32 + 32/32)).

47/32 – 29.5/32 = 17.5/32, 17.5 x $31.25 = $546.87

124 – 123 = 1, 1 x $1,000 = $1,000

Total Risk = $1,531.25 plus commissions and fees

### 5-Year Note Futures

The 5-year note futures contract is identical to the T-bond and the 10-year in terms of contract size. Each 5-year note futures contract represents a face value of $100,000 of the underlying security. Once again, the contract is comprised of handles valued at $1,000 and each handle is divided into 32nds. However, in the case of the 5-year note each 32nd is broken into 4 minimum increments. In other words, each 32nd moves in quarter increments or .25/32. If you recall, the 10-year note has a minimum price fluctuation of .5/32, and the 30-year bond has a minimum tick value of 1/32nds. If 1/32 is equal to $31.25, and .5.32 is worth $15.625, then we know that .25/32 must be $7.8125. Nobody said this would be easy. The futures markets can be potentially lucrative but there is no such thing as “easy money”.

There aren’t any surprises when it comes to 5-year note futures calculations, other than the fact that they trade in quarter ticks. However, this only requires an additional digit to be typed into your calculator as the process remains the same.

A trader that goes short a 5-year note futures from 119’10.25 and places a limit order to take profits at 117’05.50 will be profitable by 2’04.75 or $2,148.43. This is figured by subtracting the limit order price from the original sell price.

10.25/32 – 5.5/32 = 4.75/32, 4.75 x $31.25 = $148.43

119 – 117 = 2, 2 x $1,000 = $2,000

Total Profit if Limit Order Filled = $2,148.43

2-Year Note Futures

The 2-year note futures contract is the “oddball” of the Treasury complex. Unlike the others, this contract has a face value at maturity of $200,000. Thus, the value of a point (handle) is $2,000 and 1/32 is equivalent to $62.50. Like the 5-year note, the minimum tick is a quarter of a 32nd, or simply .25/32. In dollar terms this is $15.625.

The difference in the face value of the 2-year note relative to the other Treasury futures contracts is due to fact that the U.S. government issues significantly more debt in the 2-year maturity than any of the others. Accordingly, there are more 2-year Treasury notes traded in the underlying cash market. In other words, the CBOT opted to list the contract with a $200,000 maturity face value to provide “economies of scale” for market participants. This translates into saving the hassle of paying an additional commission which is interesting and noble logic for an organization that survives on trading volume.

Due to diversity in contract size and point value relative to the other Treasury futures, calculating profit and loss in the 2-year note must be slightly adjusted. A trader that is long a September 2 year note futures at 109’11.75 and is later stopped out of the trade at 108’02.25 would have realized a loss of 1’9.5/32 or $2,593.75 (remember, 1/32 = $62.50).

11.75/32 – 2.25/32 = 9.5/32, 9.5 x $62.50 = 593.75

109 – 108 = 2, 1 x $2,000 = $2,000

Total Loss = $2,593.75

Eurodollar Futures

Many traders confuse Eurodollars with the Forex currency pair Euro/Dollar. They may sound the same, but that is where the similarities end. A Eurodollar futures contract is written on a 3-month interest vehicle denominated in U.S. dollars but deposited in off-shore banks. In its simplest form it is a Certificate of Deposit located in a foreign bank. Accordingly, the interest rates offered to Eurodollar holders (in the cash market) are relatively low due to the perceived risk of default being minimal.

Together, the CME Eurodollar futures and options and lead the worldwide industry in open interest and based on daily trading volume, Eurodollars are considered the most liquid futures market in the world.

The contract size of a Eurodollar futures contract is $1,000,000, and similar to the other interest rate futures products, contract expirations are quarterly; March, June, September, December.

Eurodollar futures are quoted in handles and decimals and are simply an inverse of the corresponding yield. For example, a Eurodollar price of 97.50 implies a yield of 2.5%. This is figured by subtracting the contract price from 100 (100 – 97.50). Clearly, yields can’t go to zero, so we can infer that the Eurodollar will never trade at 100.00. Thus, as the futures price approaches 100.00, you should consider market fundamentals and technical analysis to construct a bearish strategy.

The point (handle) value of a Eurodollar is $2,500 and the tick value is $25; so a drop from 99.50 to 98.50 equates to a profit or loss of $2,500 per contract. The Eurodollar futures contract has a minimum price movement of a half of a tick, or $12.50 for most months but is a quarter of a tick, $6.25 for the nearest expiring month. This is likely because the near month Eurodollar futures contract doesn’t typically see much in the way of price change. The daily price change in the front month is typically less than 5 ticks, making it a great place for beginning speculators to get their feet wet. However, considered yourself warned, the deferred Eurodollar futures contracts will react more violently to changes in interest rates or climate. If your risk tolerance is low to moderate, stay with the near month.

Calculating the profit, loss and risk of any given Eurodollar position is different that that of the Treasury complex but is also less cumbersome. Before you begin your calculation, you can simply move the decimal point and multiply each (full) tick by $25. For instance, if a trader buys a December Eurodollar futures contract at 99.085 (99.08 ½) and later sells it at 99.290, the realized profit on the trade would have been 20.5 ticks or $512.50. The mechanics are the same as the other contracts; it is just the point value that differs (but don’t forget to move the decimal two places to the right).

9929 – 9908.5 = 20.5

20.5 x $25 = $512.50

The information included in this article certainly won’t make or break you as a trader, but without familiarity of the basic specifications of the contract that you are trading you aren’t giving yourself a fair shake. After all, awareness and experience may prevent you from becoming emotional or panicky while your hard earned dollars are on the line.