Why a bond trades away from face value
A bond pays a fixed coupon set at issue. If market rates move afterwards, the only thing that can adjust is the price — until the yield a buyer receives matches what new issues offer.
The formula
Every future payment discounted at the current market rate, added up. That sum is what the bond is worth today.
Worked example: $1,000 face, 5% coupon, 6% market rate, 10 years
- Coupon payment: $25 every six months
- Total coupons over the term: $500
- Price: $925.61
- Current yield: 5.40%
The bond trades at a discount because 5% is below the 6% available elsewhere. The $74.39 shortfall against face value is exactly what compensates a buyer for the below-market coupon.
Price and rate move in opposite directions
| Market rate | Price | Trades at |
|---|---|---|
| 3% | $1,170.60 | Premium |
| 4% | $1,081.76 | Premium |
| 5% | $1,000.00 | Par |
| 6% | $925.61 | Discount |
| 8% | $796.15 | Discount |
At par the coupon equals the market rate and no adjustment is needed. Away from it the price does all the work.
Duration: why long bonds move more
The same one-point rate rise costs a two-year bond about 2% of its price and a thirty-year bond about 15%. The longer the remaining term, the more payments are affected and the further the price must fall.
This is why "safe" long-dated government bonds lost 20 to 30% in 2022 without any default risk materialising. The credit was never in question; the discount rate was.
Clean price and dirty price
Quoted prices exclude interest accrued since the last coupon. The amount you actually pay — the dirty price — adds it.
Buying three months after a coupon on this bond means paying $925.61 plus roughly $12.50 of accrued interest. The seller earned it and you receive it back at the next payment date.
What this calculator leaves out
Default risk, call provisions that let the issuer redeem early when rates fall, and dealer spread. Corporate bonds also carry a credit spread over the government rate, which is the market's price for the possibility of not being repaid.
Reading a quoted bond
Bonds are quoted as a percentage of face value, not in currency. A price of 92.56 means 92.56% of $1,000 — the $925.61 above, allowing for rounding.
That convention exists because face values differ while the comparison should not. A bond at 92.56 and another at 104.20 are immediately comparable regardless of whether they were issued in $1,000 or $100,000 denominations, and it is why market commentary talks about prices in the nineties rather than in pounds.
Why individual investors usually buy funds
A single bond ties the outcome to one issuer and one maturity date. A bond fund holds hundreds and rolls them continuously, which removes issuer risk and the need to reinvest each maturity yourself.
The trade is that a fund never matures, so there is no date on which you are guaranteed to get face value back. Holding an individual bond to maturity removes price risk entirely; holding a fund does not, which is why the two behave very differently when rates move.
Related calculators
- Yield to maturity calculator — the same relationship solved for yield
- Current yield calculator — income against price, ignoring maturity
- Duration calculator — how far the price moves per point of rate