# Bond Futures: What Do The Quote Prices Really Mean?

I’m sitting at my computer looking through some commodity charts when I came across a bond chart. I was curious about the contract so I went to look up the specifics. Quickly I realized that I had forgotten almost everything I ever learned on the subject. Why were the quote prices so strange? I was seeing quotes like “98.54,” or “105’035,” but what did they mean? Why wasn’t it as simple as quoting the interest rate? Why don’t they line up with the market interest rate? How was the tick size determined? All these questions flooded into my head as I realized I had a good block of hours I needed to schedule in for some exciting, sitting-on-the-edge-of-my seat reading about bond future quote prices and contract specifications. Here is what I found:

In general, commodity futures were always pretty easy to understand. The price was quoted per amount of something (bushels, pounds, etc), the contract was for a fixed amount (bushels, pounds, etc) and you could derive the tick size by taking a quick look at the contract. I’ll use a corn contract as an example…

It usually goes something like this…

• The price of corn in quoted in cents/bushel
• The contract is for 5000 bushels
• The minimum price movement is .25/cent
• Because the minimum price movement is .0025/bushel and the contract is for 5000 bushels, one tick (minimum price move) will be ($0.0025*5000) which is$12.50/contract

Definitions:

Treasury Bills are short term U.S. government liabilities with a term of one year or less. Interest is paid in a lump sum at maturity. The bonds are sold at a discount to face value, and then the interest accrues and you collect a flat amount at maturity. (It might be sold to you for $995 and you would collect the face value of$1,000 at maturity.)

Treasury Notes are longer term U.S. government liabilities with a term of 1-10 years. Interest is paid semi-annually until maturity. (The principal is paid in a flat amount, like $200,000 and interest payments are made throughout the life of the bond. The principal of$200,000 would then be collected at the end.)

Treasury Bonds are even longer term U.S. government liabilities with a term of 10+ years. Interest is paid semi-annually until maturity. (These are treated the same way that Treasury Notes are.)

Treasury Bills

This type of contract is the easiest to understand. Take a look at the contract specifications. If you were to buy regular 13 week T-bills, NOT a futures contract, it would have a face value at maturity of $1,000,000. This means that if you purchased the bill you would let the government borrow a smaller amount of money now, and they would pay you that amount plus some interest to equal$1,000,000 in 13 weeks time.

The futures contract, however, is not for the outright purchase of a T-bill; it is for right to purchase one in the future at today’s interest rate. This contract is always settled in cash at the highest discount rate accepted by the treasury on the week of delivery. This means that the futures contract price will converge with the spot price of 13 week T-bills and the change in price will be settled in cash instead of actually buying the bills.

Why would anyone trade this contract? Maybe you plan on buying some T-bills in the future, but you suspect that the interest rate may fall before you have a chance to buy the bills at the future date. In this case, you could buy the long side of the T-bill contract to eliminate any risk of the interest rate going down. If the interest rate were to fall (inversely, the quote price of the T-bill contract would go up.) your position would pay the difference in cash by the end of the contract. You could then buy some T-bills at the market price with the lower interest rate and you still would have received the same amount of cash that the higher interest rate would have yielded. This strategy would be hedging against interest rate risk. Of course, you could always speculate on the movement of interest rates as well.

Why are the prices inverted? Why would I have to go long on the T-bill contract to protect against falling interest rates? It has to do with how the quote prices are figured…

The quote price

The quote price is (100 – treasury bill discount rate). This inverts the relationship of the discount rate to the quote price. If the discount rate goes up then the quote price will go down, and if the discount rate goes down the quote price will go up. Because of this, you would have to be long on the contract if you wanted to hedge or speculate on interest rates falling. This type of price quote is common for interest rate products that have a 1 year or less maturity date. The discount rate, in this case, is the rate at which $1,000,000 is discounted to get a present value of the bill. It is also the annual interest rate you will be paid for letting the government borrow your money. If the quote price was 99.98 then you would be entering into a contract to be paid an annual rate of 0.02% for 13 weeks (or 3/12 of a year) on the hypothetical future purchase of the bill at a different market interest rate. You can easily figure out what the current discounted present value is by doing some simple math… $X*1.0002*\frac{3}{12}=1,000,000$ So if you were to go to the treasury and buy this bill, you would give the government$999,950.00, and they would give you $100,000 in 13 weeks time if the market interest rate was 0.02%. The price movement The smallest allowable price movement for this contract is one half of one basis point (0.005%), which is$12.50/contract. This is figured by taking the smallest movement in the annual interest rate, multiplying that by the fraction of the year that the bill will be held, and multiplying it by the face value at maturity (0.00005 * 3/12 * $1,000,000 =$12.50).

In the real world, if you were planning on purchasing a 13-week T-bill from the treasury, every interest rate fluctuation up or down of 0.005% would mean you would pay $12.50 more or less to receive$1,000,000 in 13 weeks.

As of this writing, 13 week T-bills (symbol: /GTB) are not actively traded. Other short term interest rate products such as the Eurodollar and 30-Day Fed Funds operate the same way though.

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Treasury Notes and Bonds

Before I continue, it’s important to understand what is being traded. Futures prices on bonds aren’t directly reflecting of market interest rates. When you enter a futures contract, you have the ability to eventually take delivery of the underlying asset. In the case of notes and bonds this means you could potentially take delivery of a bunch of bonds if the contract is not cash settled. The bonds which the seller can deliver vary depending on the futures contract. The seller can choose to deliver a variety of bonds to the buyer that fit the definitions laid out in the contract. The futures contract price takes this into account so prices have less to do with current rates, and more to do with what existing bonds in the market are cheapest to deliver to the buyer.

Market prices of pre-existing bonds will fluctuate in step with the market interest rates, of course, but the purchase price of those bonds may vary depending on when the payouts are, how far in the payout cycle they are, and the amount of time to maturity, inflation, and U.S. credit ratings.

The U.S. Treasury Notes and Bond futures contracts differ T-bills and become harder to understand. Here is the CME contract specifications for 2 year U.S. Treasury Note futures.

If you were to go to the U.S. Treasury and buy a two year note with a face value of $200,000, you would give the government$200,000 now. They would then pay you interest payments every so often, and return the principal after 2 years. The total amount you would receive back from them is $200,000 + the interest payments. The futures contract is meant to simulate the buyer purchasing one U.S. Treasury note at a future date, at current interest rates, that has a face value at maturity of$200,000. Again, like the previous example with T-bills, this could be used to hedge or speculate against interest rate movements. Unlike the T-bills, these contracts will actually result in bonds being delivered if the position is not closed.

The quote price

The quote price becomes more complicated on these notes. First, you should know how to read it. For the 2 year U.S. Treasury Note futures, a quote price of 100’000 is made to equal $200,000 (present value) lent to the government at 6% interest for two years to equal$200,000 (+ interest received) at maturity (future value).  Treasury notes do not compound interest so the total amount you would receive would be $224,000… $\200,000&space;+&space;(\200,000*.06*2)$ You can calculate that at a quote price of 100’000, the total of future interest payments would be$24,000. So at a futures quote price of 100’000 you would hypothetically pay $200,000 at a delivery date in the future and receive bonds which would make interest payments over the next two years totaling$24,000 plus the return of the principle after two years.

You probably noticed that the quote price has an apostrophe in it. Numbers before the apostrophe are points, and numbers after the apostrophe are fractions of a point. The numbers after the apostrophe do not move in the same way that decimals do. The first two digits represent 1/32, so 100’020 would be 100 points and 2/32. 100’230 would mean 100 points and 23/32. The very last digit represents 1/4 of 1/32. 100’012 is the same as 100’0125 which is to say 100 points (100′) plus 1/32 (’01) and 1/4 of 1/32 (‘002). The ‘002 is meant to represent the decimal of .025. Below are some more examples and their equivalents:

$100'052&space;=&space;100+\frac{5}{32}+\frac{\frac{1}{4}}{32}$

$100'105&space;=&space;100+\frac{10}{32}+\frac{\frac{2}{4}}{32}$

$100'157&space;=&space;100+\frac{15}{32}+\frac{\frac{3}{4}}{32}$

$107'310&space;=&space;107+\frac{31}{32}+\frac{\frac{0}{4}}{32}$

This seems absolutely bizarre at first, but becomes easier to read with time. There is also a fundamental difference in what the quote price means. In the earlier example of T-bills, the quote price is the inverse of the interest rate (1-rate), but in the T-notes, an arbitrary interest rate is already stated in the contract. (“a quote price of 100’000 is $200,000 lent at 6% for two years time.”) The consequences of this will become more apparent in the next section. The price movement? The directionality of the price movement works in the same way as T-bills in that a rise in the quote price means the value of the “6%” note has become more expensive and the yield has gone down. With a quote price of 100’000 (6% interest) as a baseline, if the price is below 100’000 then the interest rate must be above 6% and if the price is above 100’000 then the interest rate must be below 6%. The smallest allowable movement in price is 1/4 of 1/32 of a point or$15.625 per contract. You can arrive at this number by dividing $200,000 by the arbitrary base quote price at 6% which is 100’000…. $\200,000/100'000&space;=\2,000\&space;per\&space;point$ $\2,000/32=\62.5\&space;per\&space;\frac{1}{32}$ $\62.5/4&space;=\15.625\&space;per\&space;\frac{\frac{1}{4}}{32}$ The current price quote at the time of writing is 110’030. So if you followed the information above, you would hypothetically pay 10 points, and 3/32 ($20,187) above the face value of the “$200,000 @ 6%” bond which is$220,187.5. So the effective interest rate (yield) is much lower than 6%. If you wanted to figure out what it would be, you have to do some simple math…

$\220,187.5&space;+&space;(\220,187.5&space;*&space;R&space;*2)&space;=&space;\224,000$

At this quote price, if you were to take delivery, you would pay about $220,187.5 to receive 0.865% annual interest payments to total$3,812.5. Almost no one would opts to take delivery though. Delivery becomes even more complicated as you will see below.

The strange case of delivery

Of course, in the real world there is not just one standard bond to be delivered. The holder of the contract will be delivered pre-existing bonds that have already been issued from the treasury. There are tons of them, all different, floating around in the market. So in order to be able to actually take delivery of these (if you wanted to, which 99% of people don’t.), you must be willing to accept a variety of different bonds at different stages of their life cycle that will have the same net effect to you as if you bought them from the treasury.

For the 2 year U.S. Treasury note futures contracts, you can be delivered:

Any bond that has been issued with an initial term of no more than 5 years and 3 months. A remaining term of no less than 1 year and nine months from the first day of the delivery month and no more than 2 years from the last day of the delivery month. (many, many different bonds can be delivered to you)

So the invoice price to the trader who shall be delivered the bonds is:

(Invoice price = Futures settlement price * Conversion factor * Accrued interest)

Invoice price

The price that the buyer of the bonds must pay for the bonds at delivery.

Future settlement price

The price at which the futures contract was settled (in the hypothetical case of this article, it is $220,187.5) Conversion Factor The conversion factor is supposed to even out all the deliverable bonds by pricing them at the coupon rate stated in the contract, (in this case 6%). You may be delivered a bond that is higher or lower in value, and the conversion factor evens this out so it has the same net effect to you. Accrued interest The buyer should also pay interest that has accrued since the last coupon payment. If the coupon pays every six months, and three months has passed, then the buyer of the bonds should pay for that interest that has already accrued. If he didn’t, he would be getting it for free which is crazy talk. So although the quote prices are strange, they do make logical sense when you derive them yourself. The tick value is determined by dividing the face value by the minimum movement of price (interest rate). This shows how much more or less one would have to pay up front to receive principal + interest payments totaling$224,000 in two years time. But the most important factor for me was learning that the futures prices don’t mimic the current market interest rates because often what you are entering into a contract to buy or sell in the future is a derivative of the market interest rate and has many other factors in it as well.

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