Bond prices and yields

When rates rise, the price of an old bond falls

Why does a bond's price fall when rates rise? A bond is a loan you make to a company or a government, and you can sell it. The coupon is the yearly interest the bond pays, and it never changes. Par is the 1,000 dollars you get back at maturity, the end date.

Say Maria buys a new bond with a 5 percent coupon. It pays her 50 dollars a year. A year later, rates rise. New bonds pay 6 percent, or 60 dollars a year.

No buyer pays Maria 1,000 dollars for 50 a year when new bonds pay 60. So she cuts her price. If rates fall instead, her 50 dollars looks good, and buyers pay more than 1,000.

Rates and bond prices move opposite, like a seesaw. Maria's coupon never changed. Only the price did. The longer until maturity, the bigger the swing. A lower coupon swings more too.

The common mistake is thinking higher rates help the bond you own. They help new bonds and push old ones down. Rates and bond prices move opposite. When rates go up, the price of the bond you own goes down.

A premium is a price above par, a discount is below

When does a bond sell at a premium, and when at a discount? Start with par. Par is the 1,000 dollars you get back at maturity, the end date. A premium is a price above par. A discount is a price below par.

Take Maria's bond. Its coupon, the yearly interest it pays, is 5 percent. That's 50 dollars a year. If new bonds pay 6 percent, her coupon is lower than today's rate. Buyers pay less than par, so it's a discount bond.

If new bonds pay 4 percent, her coupon beats today's rate. Buyers pay more than par, so it's a premium bond. Compare the coupon with today's rates. If the coupon is higher, the bond sells at a premium. If it's lower, a discount. If they're equal, the bond sells at par.

People flip this one. A high coupon is a good deal, so buyers pay extra for it. A high coupon means a premium, not a discount. A premium is a price above par. A discount is a price below par. The coupon against today's rates decides which one you get.

A bond has four yields: nominal, current, to maturity, to call

How do you measure what a bond pays you? The exam uses four yields. A yield is your return, written as a percent. First, nominal yield. It's the coupon rate, the yearly interest printed on the bond.

Second, current yield. It's the yearly interest divided by the price you pay today. Pay 950 dollars for a bond paying 50 a year, and your current yield is 50 over 950, or 5.26 percent.

Third, yield to maturity, or YTM. It's your yearly return if you hold the bond to maturity, counting the gain or loss as the price moves to par. Pay 950, and you also gain 50 dollars back at maturity. That gain lifts YTM above current yield.

Fourth, yield to call, or YTC. A callable bond can be paid back early by the issuer. YTC is the same math as YTM, but it stops at the call date. The common mistake is treating the four as one number. They only match when the price is exactly par.

Nominal uses the coupon. Current uses the price you pay. YTM and YTC also count the gain or loss back to par.

Premium or discount decides which yield is highest

Which yield is highest when a bond isn't at par? A discount is a price below par, the 1,000 dollars you get back. A premium is above par. Line up the four yields: nominal, which is the coupon, then current, then yield to maturity, then yield to call.

Say you pay 900 dollars for a bond. When it pays back par, you gain 100 dollars. If the issuer calls it early at par, you get that gain sooner. The sooner the gain, the bigger the yield.

So at a discount, the yields climb from left to right. The coupon is lowest, and yield to call is on top. At a premium it flips. You lose the extra you paid by maturity, and losing it sooner, on a call, hurts most. So the coupon is on top and YTC is lowest.

At par, there's no gain or loss, so all four yields are the same. The common mistake is using one order for every bond. Check the price first, because it flips the whole line.

Below par, at a discount, yield to call is on top. Above par, at a premium, the coupon is on top.

Worked example: rank the yields on a 6% bond at 104

1. A 6 percent bond is quoted at 104. Rank its nominal yield, current yield and yield to maturity.
2. Step one, the price. Bond prices are quoted as a percent of par, so 104 means 1,040 dollars.
3. Step two. 1,040 is above par, the 1,000 dollars paid back at maturity. So this is a premium bond, and that sets the order.
4. Step three, nominal yield. That's the coupon rate: 6 percent, or 60 dollars a year.
5. Step four, current yield. Divide the 60 dollars of interest by the 1,040 dollar price. That gives 5.77 percent.
6. Step five, yield to maturity. You paid 40 dollars over par, and you lose it by maturity. That pulls YTM below 5.77 percent.
7. The order is nominal, then current, then yield to maturity. At a premium, the coupon is on top.

Common mistakes

check premium or discount before you rank

You used the wrong order for this bond's price. Check the price first. Above par is a premium. The coupon is on top, and yield to call is lowest. Below par is a discount. The order flips, and yield to call is on top. Price first, then rank.