# The Relationship Between a Bond’s Price and a Bond’s Yield

In a 2012 survey only 28% of respondents were able to correctly answer this question: “If interest rates rise, what will typically happen to bond prices?” Here is an explanation of how bond prices and yields work, and the answer to the question.

The answer to the question:

As interest rates rise, bond prices decrease. As interest rates drop, bond prices rise.

Now let’s spend some time to look at how bonds work in depth.

In almost any news article you read about bonds there is always one statement in every article. “Bond prices move inversely to yields”:

Although this statement is everywhere, it is rarely explained in detail and based on financial literacy quizzes, is still not understood by the general investing public.

**Intro – A Quick Primer On Bonds**

Lets start our example by taking the most liquid bonds in the world, United States Treasuries.

When a treasury bond, note or bill (What’s The Difference? Find out here: https://www.begintoinvest.com/treasury-bills-notes-bonds-whats-difference/ ) is auctioned off investors place bids for the price of the bond of a certain fixed yield. Typically the only difference between a “note” and a “bond” for the U.S. Treasury is maturity, so for the sake of our discussion here the term note or bond is interchangeable.

A week before each every auction, the Treasury releases an offering announcement:

Now there is a lot of information on this announcement. For now just consider the 3 aspects of the announcement that are highlighted above.

**Interest Rate** – This is the interest rate that the bond will pay. For standard bonds this is fixed for the life of the bond, hence the term “fixed income”. This may also be called the **coupon rate**.

**Premium or Discount** – All bonds have a “Par” value ($100 for treasuries. Corporate bonds may differ). A bond that is purchased at par will yield exactly the Interest Rate.

**Real Yield** – This is the yield the bond will have factoring in the premium or discount the bond is purchased for. (Shown as just “Yield %” in the picture below)

So let’s consider the auction highlighted in the picture above and dissect what it means.

On October 15^{th} 2013, the U.S. Treasury auctioned off a 9 year 10 month treasury note. The note had a set interest rate of 2.5%.

Investors then bid on the note, telling the Treasury the price they are willing to pay for the note (or they could simply put in a non-competitive bid and accept whatever the average yield of the auction was).

For this auction, if an investor was happy with a 2.5% interest rate they would have purchased the note for its par value. If this investor purchased $100 in notes, (all amounts must be in increments of $100, with a $100 minimum) they would receive $2.50 every year (2.5% of $100) for the next 9 years and 10 months. Once the note matures, in other words after 9 years and 10 months, the investor gets their original $100 back.

Still unclear on the basics of bonds? Check out our Bonds Definition page here: https://www.begintoinvest.com/definitions/bonds/

But as evident in this auction, investors were not happy with just 2.5%, they wanted a higher interest rate. So investors put in bids under par (or at a discount – see above). The average investor put in a bid of 98.645362. What does this mean? Instead of having to pay $100 for the $2.50 interest payment, investors only paid $98.645362 on average.

The note still pays $2.50, even though investors did not pay full price for the note. This means that the yield on the bond is no longer 2.5%. The new current yield on the note is:

Meaning the note has a current yield of 2.53%, slightly higher than the 2.50% coupon rate. Here is our first look at how the price of a bond changed (down, from $100 to 98.645362) and how the affected the bond’s yield (which rose, from 2.50% to 2.53%).

But why does the table above show 2.657%?

2.657% is the bond’s Yield To Maturity, or your effective yield if you hold the bond to maturity. We will go in depth with yield to maturity and how to calculate it later.

The point to be able to understand today is;

**When a bond is trading at a discount to par, its current yield and yield to maturity is higher than the coupon rate.**

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**When a bond is trading at a premium to par, its current yield and yield to maturity is lower than the coupon rate.**

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That Treasury note will pay a fixed $2.50 until it matures. So if another investor buys this bond in the future for say, $96, they will have an even higher yield (about a 3% yield to maturity).

If an investor in the future buys the bond for $102, their yield will be much less (about 2.27%).

Want to play around with how bond prices and yields change? There are plenty of free bond/yield calculators available online. For example, here is a nice one from Fidelity: https://powertools.fidelity.com/fixedincome/startYield.do . Here are the results from some of our examples used above:

If a bond is purchased at **par**, its current yield and yield to maturity equal the bond’s coupon rate:

If the price of the bond is at a **discount than par**, the bond’s yield will be higher than the bond’s coupon rate. At time of the auction, the Treasury note was trading at 98.645362 giving the bond a yield to maturity of 2.66% (This calculator rounds to nearest hundredth of a percent, actually it is 2.657%):

If the price of the bond **continues to decline**, the bond’s yield will increase even more:

And if the price of the bond is at a **premium to par**, the bond’s yield will be less than the coupon rate:

Is the concept of yield still puzzling you? Check out our definitions page for yield: https://www.begintoinvest.com/definitions/yield/ where we discuss calculating yield for corporate bonds as well as stocks.