# Are a bond's yield and interest rate the same thing?

Are they the same thing?

Is yield the annualized return rate?

Why when yield rise, yearly return increases, but price falls?

Let's say you paid \$10,000 for a ten-year bond with a coupon rate of 5%. That's a promise from the bond issuer that they'll pay you \$500 per year for ten years, and at the end of those ten years they'll pay you back your \$10,000. The \$10,000 is the bond's face value; the 5% is its coupon rate.

Now suppose interest rates go up, so new bond issues are paying 10%. What can you sell your bond for? Clearly, nobody's going to pay you \$10,000 for a \$500 annual income when they can get \$1000 annual income for the same \$10,000. So the market value of your bond is less than the \$10,000 that you paid for it. If it's a really long way from maturity (think, temporarily, of 100-year railroad bonds), it's worth \$5,000, because that's what someone would pay for \$500 per year now that interest rates are 10%.

On the other hand, if you've held your ten-year bond for nine years, it will mature in one year, and whoever you sell it to will get \$10,000 when that happens. That means you can sell it for nearly \$10,000, since that's what the issuer will pay to whoever holds the bond. So the closer the bond is to maturity, the closer its market value is to its face value.

If someone bought your \$10,000 bond for \$7,000 with, say, nine years to go to maturity, they'd expect to be paid \$500 per year in interest. They'd also expect to get \$10,000 in nine years, which is a \$3,000 gain. Caution: what follows is a gross oversimplification, offered only to provide some intuition for how this stuff works. They'd get roughly \$333 per year in appreciation, so the bond "pays" them \$500 + \$333, or \$833, per year. Based on the \$7,000 that they paid for it, that works out to about 12% each year. That 12% is the yield to maturity.

They are related but not completely the same. The yield of an instrument such as a bond is the ratio of its coupon (payment) to its Par value (price/face value). This is often expressed as an annual return per year, but not all APY/annual return rates are yields. The annual yield can also vary somewhat due to other factors, but let's ignore that for now.

The yield and the price of such an instrument are inversely related because the coupon payment is often fixed in the short term. So for example, when a commercial bond is issued, the issuer promises to pay \$X per period. This doesn't change over the life of the bond. If the company chooses to restructure, they might offer a tender to pay off the bond early and issue a new bond on different terms, but the coupon is fixed for the life of the bond. In this case, the yield is essentially a function that depends on the price.

As a result, if the price of the bond changes over the duration of the bond, this affects the ratio of the price to the coupon. So for example, let's say ACME company sells a \$100 bond that pays \$3 per year with one payment per year. The yield is 3% per year. Now, let's assume that the market decides that ACME company is in big trouble and may have trouble paying its debt service. At this point, investors will demand a higher yield in order to be interested in buying the bond on the open market, in order to reflect the increased risk of default. However, since the coupon payment is fixed, this will be expressed in a decrease in the bid price investors are willing to offer for the bond. So instead of offering \$100 for the bond, let's say they are now only willing to offer \$75. In this case, the yield has now risen to 4% per year (the \$3 fixed coupon divided by the new lower \$75 price). The price will continue to fall until the yield rises high enough to satisfy buyers.

In order to really evaluate an investment like this, you need to consider the level of risk implied by the yield, or a risk-adjusted yield. This is where markets and rating agencies come in, such that bonds, for example, are separated into various grades of investment-quality and "junk" bonds. The movement of assets between these classes is what people are referring to when they say that investors are "chasing" yields or there has been a "flight to safety". On the whole, higher yields tend to carry greater underlying risks, and the market is compensating investors for taking on those additional risks through the higher yields.

Conversely, if conditions improved, or under the same conditions ACME company issued bonds with a higher coupon/rate of return, the market might well bid the price of the bond up from its PAR/issuing value, resulting in a lower yield. The yield on US government bonds is often considered an example of what the global bond market considers to be a "risk-less" rate of return.

• If, as you claim, the yield of a bond is the ratio of the coupon amount to the face value, what is the interest rate and the coupon rate? – Dilip Sarwate May 23 '15 at 19:53
• See Pete B.'s answer on the Coupon rate. – JAGAnalyst May 26 '15 at 18:49
• Oh, I know what coupon rate means. I am just very interested in your opening statement that the yield of a bond is the ratio of the coupon payment to the face value of the bond. The coupon rate is also the ratio of the coupon payment to the face value (as clearly and correctly stated in Pete B.'s answer), and so according to you, the coupon rate and the yield are the same? – Dilip Sarwate May 26 '15 at 22:59

Are they the same thing?

Sometimes. When the bond is sold at par, then the 2 are the same thing. If a \$1000 bond with a \$50 coupon has its price drop to \$500, then the yield becomes 10% since 50/500 is 1/10 or 10%. However, the interest rate isn't necessarily the same thing as some bonds may have higher yields do to the potential for defaults like junk bonds for example.

Is yield the annualized return rate?

No. The yield is the interest the bond gives in a year based on its value which may or may not be the entire story on the return. In the US, there are TIPS which can have principal adjustments that make the annualized return different and if one is looking at bond funds, there can be capital appreciation from the bonds that are also part of the return.

Why when yield rise, yearly return increases but price falls?

Because the 2 are linked. The bond above was originally sold for \$1000 and paid \$50. If the price drops down to \$x then the new yield will be \$50/x which is likely to be more than the 5% initially thought. Similarly, to bring up the yield, the price has to go down.