Why does a bond trade above 100?Needs one idea

Because its coupon is better than what is on offer today, and the market charges for that difference up front.

3 min read · 502 words

Because it pays more than a new bond would. A bond issued years ago with a 5% coupon still pays 5% of face value every year. If a similar borrower can raise money at 3% today, the old bond's payments are worth more than face value, and its price says so.

The arithmetic

Take a bond paying 5 a year on a face value of 100, with three years left, when the market rate for that borrower is 3%. Its price is the present value of what it pays:

• Year 1: 5 ÷ 1.03 = 4.85
• Year 2: 5 ÷ 1.03² = 4.71
• Year 3: 105 ÷ 1.03³ = 96.09

Total: about 105.65. That is the premium — roughly 5.65 above face value — and it is not a mystery or an overpayment. It is the value of receiving 2 extra per year for three years, discounted.

And then it disappears

At maturity the bond repays 100, not 105.65. So a holder who paid 105.65 receives coupons above the market rate and a capital loss of 5.65 spread over three years. The two cancel down to the market rate of 3%, which is exactly what the yield to maturity says.

This is why a bond above par always has a yield to maturity below its coupon, and why quoting the coupon as the return is wrong in a specific, calculable way. What yield actually means takes the four measures apart.

The mirror image

Below 100, everything reverses. A bond with a 2% coupon in a 4% market is worth less than face value, and the buyer receives a below-market coupon plus a capital gain at maturity. The discount is the compensation, paid at the end rather than along the way.

A bond issued at a discount and paying no coupon at all — a zero-coupon bond — is the pure case: the entire return is the pull towards 100.

Two things that are not the reason

• Credit improving. It can push the price up, but the ordinary reason for a premium is simply that the coupon was set when rates were higher. Most bonds above par are there because of rates, not because the borrower got safer.
• Demand. True in a loose sense and unhelpful. The price is a discounted stream of contractual payments; "demand" is what moves the discount rate, and the discount rate is the thing to look at.

One complication worth knowing

A callable bond can be repaid early by the borrower — and a borrower calls precisely when the bond is expensive, because it can refinance more cheaply. That caps how far above par such a bond goes, and it means the yield to maturity is the wrong measure for it. The convention there is yield to worst: the lowest yield across every date the borrower might choose.

The quoted price also usually excludes interest accrued since the last coupon, which is added separately at settlement. Reading a bond quote is about telling clean prices from dirty ones.