— Glossary

Bonds, priced.

A bond is a loan with a stamped coupon and a stamped maturity, repackaged as a contract that trades every second. The coupon never moves. The price does all the moving, and that is the entire reason your bond fund went down 25% the year the Fed hiked.

— The formula, written out

price = Σ coupon / (1 + r)^t + face / (1 + r)^N

  • coupon: the annual dollar payment, equal to coupon rate times face value.
  • r: the market rate, i.e. what comparable bonds yield right now.
  • N: years until you get the face value back.

— Inputs

Price the bond

A standard ten-year Treasury today is roughly 1000 face, a 4 to 5 handle on the coupon, and the market rate wherever the bond market decides this morning.

— What the bond is worth

Price today

$1,060.08

+$60.08 versus a $1,000.00 face value

PremiumYTM 4.25%

The coupon beats prevailing rates, so the market pays more than face for the privilege.

Face value

$1,000.00

what the issuer pays back at maturity

Coupon rate

5.00%

$50.00 per year

Market rate

4.25%

the discount rate for everything in this calculation

Years to maturity

10 yr

how long until you get the face value back

— What this means

Your coupon is bigger than what the market is offering on new bonds, so people will pay you more than face for it.

The mechanic is the same in both directions. A bond is a stream of fixed dollar payments, and the market is constantly repricing how much it will pay today for that fixed stream. When rates move, the coupon does not. The only thing that can move is the price.

— Why bond prices move opposite to rates

Your coupon is locked in. The market is not.

The day a bond is issued, the coupon is stamped on it forever. A 4% coupon on a $1,000 bond pays you $40 a year, no matter what the Fed does next Tuesday or what the 10-year Treasury auction prints next month. The coupon is a contract. The market price of the bond is not.

When new bonds start coming out at 5%, your 4% bond becomes the inferior product on the shelf. The only way to sell it is to mark it down, until the discount on the price plus the coupons you still collect adds up to the same total return as the new 5% bond. That markdown is what we call the price falling. It is the math doing its job, not anyone panicking.

The reverse is just as mechanical. Cut rates, and brand-new bonds pay 3% while yours still pays 4%. Now your bond is the scarce thing, and the market bids the price up until the math matches again. This is why a 30-year Treasury can move 10% in a week without a single coupon being missed. The coupon does the paying. The price does the adjusting.

The longer the bond, the more coupons are riding on the new discount rate, and the more the price has to swing to compensate. A 2-year note barely flinches when rates move. A 30-year long bond moves like a tech stock. That sensitivity has a name, duration, and it is the single most important word in fixed income.

— FAQ

Bonds, answered.

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