Bond Yield

A bond yield is the return on a bond expressed as an annual percentage rate. The complication worth clearing up first is that "the yield" is not one number. At least three figures are routinely called a yield and they answer different questions. The coupon rate is the interest rate written on the security at issue, applied to face value, and it never changes. Current yield is the annual interest divided by the price actually paid or the current market price, which the Municipal Securities Rulemaking Board defines as "the ratio of the annual dollar amount of interest paid on a security to the purchase price or market price of the security, stated as a percentage." Yield to maturity is the rate that accounts for the interest payments and for the gain or loss between the price paid and the amount repaid at maturity.

Someone quoting "the yield" on a bond is almost always quoting yield to maturity, because it is the figure that makes two bonds with different coupons, prices and maturity dates comparable. Someone describing "a 5 percent bond" is almost always naming the coupon rate. The two coincide only when a bond trades at exactly its face value, which is the case at issue and rarely afterwards.

The organizing fact, from which the rest follows. A bond's interest payments are fixed by contract and its price is not. When conditions change, the payments cannot move, so the price moves instead, and the yield is simply the arithmetic relationship between the two. That is why the market quotes bonds by yield rather than by price: the yield is the variable carrying the information. A bond's coupon tells you what its issuer promised on the day it was sold. Its yield tells you what the market thinks that promise is worth today.

Current yield, and the direction of the effect. Take a bond with a $1,000 face value paying 5 percent, so $50 a year. Bought at face value, the current yield is 5 percent, the same as the coupon. Bought for less than face value, the same $50 is divided by a smaller number, so the current yield rises above 5 percent. Bought for more than face value, it falls below. Current yield is useful for one question only, which is how much income the money is generating right now relative to what it cost. It ignores the maturity date entirely, so it says nothing about the gain or loss waiting at the end.

Yield to maturity, and the assumption that makes it a projection. Yield to maturity fills in what current yield leaves out by including that final gain or loss, spread over the remaining life of the bond. The MSRB defines it as the rate of return earned from payments of principal and interest "with interest compounded semi-annually at the stated yield, presuming that the security remains outstanding until the maturity date." Both halves of that sentence are conditions. The bond has to survive to maturity, and every interest payment has to be reinvested at the same yield along the way. A holder who spends the interest, or reinvests it at a different rate, will not earn the quoted figure. Yield to maturity is therefore the best available single number for comparing bonds and a poor description of what any particular holder will actually receive.

Where the family extends. A bond the issuer can repay early has a yield to call, computed to the earliest date the issuer may act rather than to maturity, and a yield to worst, which is the lowest of the possible outcomes. Those matter on callable bonds because the issuer chooses the date, and it will choose the one that suits the issuer. The formal computation of each, and the mechanics of amortizing a premium or accreting a discount toward maturity, belong with yield to maturity and the coupon rate rather than here.

Why two bonds maturing on the same day yield differently. The yield is the market's price for the whole package, so any difference in the package shows up in it. A weaker issuer must offer more to be bought at all. A bond the issuer can call away is worth less to a buyer than one it cannot, so it yields more. Interest exempt from federal income tax is worth more per dollar received, so a tax-exempt bond can yield less than a taxable bond and still leave the same amount in the buyer's pocket. Reading a higher yield as a better deal, without asking what is being compensated, is the most common way to misuse the number.

Start from the two fixed quantities: the face value repaid at maturity, and the coupon rate that sets the interest payments. Then compare them with a third quantity that is not fixed, the price. Every yield measure is some version of that comparison, and they differ in what they include.

A hypothetical example, using round figures rather than any current market rate. A bond has a $1,000 face value, a 5 percent coupon, and pays $50 a year.

Bought at face value for $1,000, the current yield is $50 ÷ $1,000 = 5.0 percent, identical to the coupon.

Bought in the secondary market for $800, the current yield is $50 ÷ $800 = 6.25 percent. The payments did not change. The price did.

Bought for $1,200, the current yield is $50 ÷ $1,200 = about 4.17 percent.

Now add the maturity date. On the $800 purchase, the holder also receives $1,000 at maturity, which is $200 more than was paid. Yield to maturity counts that $200 as part of the return and spreads it across the remaining years, so it comes out above the 6.25 percent current yield. On the $1,200 purchase the reverse happens: $200 of the purchase price is not repaid at maturity, so yield to maturity comes out below the 4.17 percent current yield. The exact figures require solving for the rate that makes all the future payments worth the price today, which is why yield to maturity is read off a quote or a calculator rather than worked out by hand.

Pros (what the yield tells you)

• It makes bonds with different coupons, prices and maturity dates directly comparable, which a coupon rate cannot do.
• It updates continuously, so it reflects what the market currently thinks the issuer's promise is worth rather than what was true at issue.
• Set beside a bond of the same maturity from a stronger issuer, the difference is a readable price for the extra risk being taken.
• Yield to maturity is close to what a buy-and-hold owner of a sound issuer's bond actually earns, provided the interest is reinvested.

Cons (what it does not tell you)

• Yield to maturity assumes every interest payment is reinvested at the same yield, which nobody can guarantee and most holders do not do.
• It assumes the bond survives to maturity, so it silently prices out both default and an early call by the issuer.
• Current yield ignores the maturity date, so it can flatter a bond bought above face value that will repay less than it cost.
• A yield quoted before tax can mislead badly across bonds whose interest is taxed differently.
• Comparing yields on bonds of different maturities is comparing different commitments, since the longer bond is being paid for locking money up longer and for carrying more price sensitivity.