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# Making Sense of the Bond Data in the Newspaper

The difference between a yield and a discount rate, and why 20-year bond yields are so high.

Can you explain why the yield curve chart in

The Wall Street Journal

shows the yield of the three-month issue at about 5.85% and the 20-year issue at about 6.25%, while the Markets Diary has the three-month bill at 5.66%, and the Treasury price table says a 20-year bond due in 2020 yields 6.44%? -- Jack Schannep

Jack,

Indeed I can.

OK, everybody. Get out the Money & Investing section of Friday's

Journal

and get set for a short lesson.

You can find the yield curve chart Jack's talking about on page C18. Alternatively, the

Bloomberg

Web site has a graph of the yield curve.

Indeed, as Jack observes, it would appear from the charts that a three-month Treasury security yields about 5.85% while a 20-year issue yields about 6.25%.

Now, check out the Markets Diary on the front page of the Money & Investing section. Under the Interest heading, the three-month Treasury bill is quoted at 5.66%.

Finally, look at the Treasury Bonds, Notes & Bills price table on page C15. Indeed, the bonds due in 2020 are quoted at a yield of 6.44%.

What gives? Two things.

First, there's an important difference between the value plotted in the yield curve chart for the three-month Treasury bill on page C18 and the value that appears in the Markets Diary. The yield curve chart plots the bill's yield; the Markets Diary plots its price.

For any Treasury bill, a yield can be calculated that allows for an apples-to-apples comparison with other Treasury instruments. But traders don't talk about Treasury issues of any kind in terms of yield. They talk in terms of price.

For Treasury bonds and notes, prices are in terms of cents on the dollar. If a bond is quoted at 99 16/32, that means it costs \$995 per \$1,000 of face value (plus any accrued interest due to the seller, the topic of a previous

Fixed-Income Forum.)

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Treasury bills are different. Their prices are quoted by their

discount rate

.

Don't confuse this with

the

discount rate

, which is an interest rate set by the

Fed

.

The easiest way to understand bill discount rates is first to understand the concept of yield. The price of any debt instrument is equal to the sum of the present values of all future cash flows from the instrument. And the yield of any debt instrument is the interest rate used to discount its future cash flows to calculate their present values.

A Treasury bill's discount rate is different from its yield in this simple respect. The yield calculation assumes a 365-day year. The discount rate calculation assumes a 360-day year. Why? Because once upon a time there were no computers, and it was much easier to do manual calculations assuming a 360-day than a 365-day year.

A three-month bill with a face value of \$1,000 at a price of 5.66% costs \$985.69, according to this formula:

\$1,000 face value * (1 - (91 days to maturity/360 days) * 0.0566) = \$985.69

Why quote bills by their discount rates at all? Why not quote them like bonds and notes are quoted, by dollar prices? Because bills, like zero-coupon bonds, are discount instruments. Instead of making interest payments every six months until they mature (impossible since most Treasury bills are of the three- or six-month variety), they are issued at a discount to face value. Their dollar values go up pretty much every day on that basis alone. By quoting their discount rates, you factor out that effect, allowing for day-to-day comparisons.

Onto why the 20-year points in the yield curve charts don't match up with the figure in the price table. This is easier to understand. The yield curve charts (both of them) don't actually plot the yield of a 20-year Treasury. They merely plot the yields of the 10-year Treasury note and the 30-year Treasury bond, and then connect them with a line.

They do this because yield curve graphs are based only on actively traded issues. And the only actively traded issues are the ones the Treasury auctions on a regular basis. These include three- and six-month bills, a one-year bill, two-, five- and 10-year notes and a 30-year bond.

The 20-year bond in the Treasury price table has a higher yield than some of the active issues for a related reason. It is not actively traded, so it is not liquid. When you're a trader, liquidity is something you are willing to pay for. And so the actively traded issues trade at higher prices than 20-year bonds, which change hands much less frequently. The higher prices (all together now!) mean lower yields.