Most bonds pay interest every year or every six months. A zero-coupon bond pays nothing until the last day. You buy it below its face value. On the maturity date the issuer pays you the full face value. The gap between the two amounts is your return.
This guide explains how a zero-coupon bond works and how to calculate its price and its yield. It lists the risks to check. It also compares the bond with a coupon bond and shows where to find zero-coupon bonds in Europe.
1. What is a zero-coupon bond?
A zero-coupon bond has a coupon of 0%. It makes one payment: the face value, on the maturity date. Bond prices are quoted per 100 of face value, so the bond repays 100.
Nobody pays 100 today for a bond that gives back 100 in a few years and nothing in between. So the issuer sells it at a discount, for example at 86. That discount is your interest. People also call these bonds discount bonds or zeros.
- Face value: the amount the issuer repays at maturity. Prices are quoted per 100, so this is 100.
- Issue price: the price on the first day. It is below 100.
- Maturity date: the day you get paid.
- Yield: the yearly return you earn from the discount if you keep the bond to maturity.
2. How a zero-coupon bond works
Take a 5-year zero-coupon bond with a yield of 3% a year. You pay 86.26 today. For five years you get nothing. On the maturity date you get 100. Your gain is 13.74 per 100 of face value.
If the yield stays the same, the value of the bond rises every year, because the maturity date gets closer. Traders call this the pull to par.
The table shows the cash flows of this bond next to a 5-year bond with a 3% yearly coupon. You buy both today.
| When | Zero coupon | 3% coupon |
|---|---|---|
| You buy | −86.26 | −100.00 |
| Year 1 | 0.00 | 3.00 |
| Year 2 | 0.00 | 3.00 |
| Year 3 | 0.00 | 3.00 |
| Year 4 | 0.00 | 3.00 |
| Year 5 | 100.00 | 103.00 |
| Gain | 13.74 | 15.00 |
Both bonds yield 3% a year. The coupon bond gives a bigger total gain, because you put in more money at the start. The zero-coupon bond pays its whole gain on one day.
3. How to calculate the price and the yield
The price of a zero-coupon bond is the face value, discounted at the yield for the years that are left:
price = 100 / (1 + y) ^ t y yearly yield, as a decimal (3% = 0.03) t years to maturity
To get the yield from the price, turn the formula around:
y = (100 / price) ^ (1 / t) − 1
You buy a BOT that matures in one year at a price of 97.80. At maturity you get 100. The yield is 100 / 97.80 − 1 = 2.25%.
The Italian Treasury quotes BOT yields as a simple rate on a 360-day year (ACT/360). So the yield you see at the auction differs a little from this result.
You can check any zero-coupon bond with the yield to maturity calculator. Enter 0 as the coupon, then the price and the maturity date.
4. Zero-coupon bonds and coupon bonds compared
| Zero-coupon bond | Coupon bond | |
|---|---|---|
| Payments | One, at maturity | A coupon each period, plus 100 at maturity |
| Price at issue | Below 100 | Close to 100 |
| Income before maturity | None | Regular coupons |
| Reinvestment risk | None | You reinvest each coupon at the rate of that day |
| Price move when rates change | Larger | Smaller, for the same maturity |
| Duration | Equal to the maturity | Shorter than the maturity |
5. The risks of zero-coupon bonds
Interest rate risk
When market yields go up, bond prices go down. A zero-coupon bond falls more than a coupon bond of the same maturity, because all of its money comes at the end. Its duration is equal to its maturity. A coupon bond pays part of its money earlier, so its duration is shorter.
A 10-year zero-coupon bond falls from 74.41 to 67.56. That is a change of -9.2%. The price of a 10-year bond with a 3% coupon goes from 100.00 to 91.89, a change of -8.1%.
This risk matters only if you sell before maturity. Keep the bond to the end and you get 100, whatever the market does in between. When yields go down, the same effect works for you. The price of a zero then rises more.
Credit risk
You get all your money on one day. If the issuer defaults before that day, you have received nothing. A coupon bond would have paid you some coupons first. Check who the issuer is and how long you have to wait.
Inflation risk
The 100 you get at maturity is a fixed amount. Inflation makes that amount buy less. The longer the bond, the larger this effect.
Liquidity
Government bills trade every day in large amounts. Some corporate and bank zero-coupon bonds trade rarely. On a bond page, look at the venues and the date of the last trade before you buy.
6. Where to find zero-coupon bonds in Europe
- Treasury bills. Governments sell short zero-coupon bills: BOT in Italy, Bubills in Germany, BTF in France and Letras del Tesoro in Spain. They mature in 12 months or less.
- Longer government zeros and strips. Some Treasuries let banks split a coupon bond into its separate payments. Each payment then trades as a zero-coupon bond of its own.
- Corporate and bank bonds. Some companies and banks issue zero-coupon notes with maturities of several years. Read the final terms to see what the note pays.
Find zero-coupon bonds
The screener lists the zero-coupon bonds traded on European venues, with the price, the yield and the maturity of each one.
7. Who are zero-coupon bonds for?
A zero-coupon bond suits you if you need a set amount of money on a set date. Examples are a house deposit or school fees that fall due in a few years. You buy a zero that matures just before that date. You know today the amount you will get.
If you need regular income, a coupon bond is a better fit. The same is true if you may have to sell early. Yields could then be higher than on the day you bought, and the price lower.
Summary
- A zero-coupon bond pays no coupons. You buy it below 100 and get 100 at maturity.
- The gap between the price and 100 is your interest. You get all of it on the maturity date.
- The price is 100 / (1 + y)t. If the yield does not change, the price rises to 100 over time.
- When rates change, its price moves more than the price of a coupon bond with the same maturity. Its duration is equal to its maturity.
- It has no reinvestment risk. If you keep it to maturity, you know your return on the day you buy.
- In Europe, the best known zero-coupon bonds are Treasury bills such as the Italian BOT.
Questions
Does a zero-coupon bond pay any interest?
It pays no coupons. Your interest is the gap between the price you pay and the 100 you get at maturity. You receive all of it on the last day.
Can I sell a zero-coupon bond before maturity?
Yes. Many zero-coupon bonds are listed on an exchange, for example Borsa Italiana MOT or EuroTLX. You get the market price of that day. If yields went up after you bought, that price can be below the price you paid.
Why does the price of a zero-coupon bond go up over time?
The bond moves closer to the day it repays 100. With less time to wait, the discount gets smaller. If the yield stays the same, the price rises a little each day until it reaches 100 at maturity.
Is a zero-coupon bond safer than a coupon bond?
For the same issuer, the credit risk is the same. The price risk is higher, because all the money comes at the end. There is no reinvestment risk, because there are no coupons to reinvest.
What happens if I hold the bond until maturity?
If the issuer does not default, you get 100 for each 100 of face value. The price moves in between do not change that amount. Your yearly return is the yield on the day you bought, before costs.
Are Italian BOT zero-coupon bonds?
Yes. BOT (Buoni Ordinari del Tesoro) are Italian Treasury bills with a maturity of 12 months or less. They pay no coupon. The Treasury sells them below 100 and repays 100 at maturity.