Bond Prices and Yields: The See-Saw

You bought a bond. It promises to pay you the same fixed dollars every year — that part never changes. So why does its price on the screen wobble up and down every single day? Because a bond isn’t frozen in the drawer where you left it: it trades in a market, and the market keeps repricing it against whatever shiny new bonds are being issued today. Here’s the twist that trips up everyone: when interest rates go up, the price of your bond goes down. They move on a see-saw — push one end up, the other drops. This lesson is about why that see-saw exists, and the vocabulary (par, premium, discount, current yield, yield to maturity) you need to read it.

A bond trades in a market — the coupon is fixed, the price moves

Recall from the investing basics what a bond is: a loan you make to a government or company. In return they promise you a coupon — a fixed dollar interest payment, usually paid once or twice a year — plus your money back (the face value, also called par, typically $1,000) on a set maturity date. That promise is written in stone. A “5% coupon, $1,000 face” bond pays $50 a year, every year, no matter what.

The analogy: think of a bond like a rental contract on a fixed monthly rent. The rent is locked in. But the building itself still gets bought and sold, and what someone will pay for it changes as the rental market around it shifts. The coupon is the locked rent; the price is what the building sells for today.

So a bond has two numbers that behave completely differently:

• The coupon rate — fixed forever, set the day the bond was born. It’s a percentage of face value.
• The market price — floats every day as the bond trades, quoted as a percentage of par (so “98” means 98% of $1,000 = $980).

The coupon can’t move to keep up with the market. So the only thing that can move — the price — does all the adjusting.

When it matters

Any day you might sell a bond before maturity, or mark a portfolio to its current value, the market price is the number that matters, not the coupon. Buy a bond and hold it to maturity and you’ll get your face value back regardless — but in between, its price lives and breathes with interest rates.

Why price and yield move inversely

Here’s the heart of it. A bond’s yield is the return a buyer actually earns at today’s price. When new bonds offer a higher return, your old bond can only compete one way: by getting cheaper, so the buyer earns more on a smaller outlay. Cheaper price → bigger return per dollar → higher yield. Price down, yield up. They’re two ends of the same see-saw.

The cleanest way to see this uses a perpetual bond (a “consol”) — a bond with no maturity that just pays its coupon forever. Its price is gorgeously simple:

$\text{Price} = \frac{\text{annual coupon}}{\text{required yield}}$

Worked example — the $50-forever bond

Take a consol paying $50 a year forever. Investors currently require a 5% yield to hold something of this risk. Its price:

$\text{Price} = \frac{50}{0.05} = \$1{,}000$

At a 5% required yield, the bond is worth exactly $1,000. Now suppose rates rise and investors demand 6.25% instead. The coupon is still $50 — it can’t change. So the price must move:

$\text{Price} = \frac{50}{0.0625} = \$800$

The required yield rose from 5% to 6.25% (up about a quarter), and the price fell from $1,000 to $800 — a 20% drop. Notice the denominator did all the work: a bigger required yield divides the same fixed coupon into a smaller price. That’s the inverse link in one tidy fraction.

Read the table top to bottom: as the yield buyers demand climbs, the price of the fixed-$50 stream falls, every time.

When it matters

The inverse relationship is the fact of bond investing. It’s why a portfolio of “safe” bonds can lose value in a year when central banks hike rates — the coupons kept paying, but the prices sank. Long-dated bonds swing the most (more on that in a later lesson), but every fixed-coupon bond rides this see-saw.

Par, premium, and discount

Once you accept the see-saw, three words describe where on it a bond sits. They all compare the bond’s price to its face value (par, = 100):

• Par — price equals face value (quoted 100). This happens when the bond’s coupon rate matches what the market currently demands. Here the yield equals the coupon.
• Premium — price is above par (e.g. 105). The bond’s coupon is higher than what new bonds offer, so it’s extra desirable and buyers pay up. Because you pay more than you’ll get back at maturity, your yield is below the coupon.
• Discount — price is below par (e.g. 95). The bond’s coupon is lower than current rates, so it’s on sale. You pay less than face but collect full face at maturity, so your yield is above the coupon.

The analogy: par is paying sticker price, premium is paying over sticker for the hot item, discount is grabbing it from the clearance rack. The rack price always nudges your effective return back in line with everyone else’s.

Now drag the market-yield slider below. Start it at the coupon (5%) and the bond sits at par (100); push the yield above 5% and watch the price drop into discount territory; pull it below 5% and the price climbs to a premium. The curve is the see-saw, drawn:

When it matters

Whether a bond trades at a premium or discount tells you instantly which way rates have moved since it was issued. A portfolio full of premium bonds was bought when rates were higher; a sea of discounts means rates have risen since. It also matters for taxes and cash flow — but the core read is: premium = above-market coupon, discount = below-market coupon.

Current yield — the quick-and-dirty number

The simplest yield measure asks: what return do the coupons alone give me on what I paid? That’s the current yield:

$\text{Current yield} = \frac{\text{annual coupon}}{\text{market price}}$

It’s the dividend-style snapshot — annual cash in, divided by price out. Easy to compute, and it moves the right way (price down → current yield up), so it captures the see-saw’s direction.

Worked example

A bond with a $60 annual coupon (6% coupon on $1,000 face) is trading at a discount price of $900:

$\text{Current yield} = \frac{60}{900} = 0.0667 = 6.67\%$

You paid $900 and collect $60 a year, so your coupon-only return is 6.67% — higher than the 6% coupon rate, exactly because you bought below par. If instead the bond traded at a premium of $1,200:

$\text{Current yield} = \frac{60}{1{,}200} = 0.05 = 5.00\%$

Now your coupon-only return is just 5% — below the 6% coupon, because you overpaid. Same coupon, different price, different yield. The see-saw again.

When it matters

Current yield is fine for a fast, back-of-the-envelope comparison of coupon income, or for perpetual bonds (where there’s no maturity payment to ignore — for a consol, current yield is the yield). For any normal bond with a maturity date, it’s only a first approximation. The number professionals actually quote is next.

Yield to maturity (YTM) — the real total return

The analogy: current yield is like rating a road trip by your gas mileage alone. Yield to maturity rates the whole trip — every coupon, plus the gain or loss when you cash out at the end, all rolled into one annualized rate.

Formally, YTM is the single discount rate that makes the present value of all the bond’s future cash flows equal its current price. It’s the bond’s internal rate of return (IRR) — the one interest rate that, applied to every coupon and the final face value, prices the bond exactly where it trades. For a bond paying coupon $C$ each period for $n$ periods, redeeming face $F$, at price $P$, the YTM $y$ solves:

$P = \sum_{t=1}^{n} \frac{C}{(1+y)^{t}} + \frac{F}{(1+y)^{n}}$

Each future dollar is discounted back to today (worth less the further out it is — that’s the present-value idea from earlier topics), and YTM is the rate that makes those discounted dollars sum to exactly the price you’d pay.

Worked example — a short bond priced two ways

Take a 2-year bond, $1,000 face, paying a $50 coupon once a year (5% coupon). Let’s price it as the present value of its cash flows — $50 next year, then $50 + $1,000 = $1,050 the year after — at two different market yields.

At a 5% yield (equal to the coupon):

$P = \frac{50}{1.05} + \frac{1{,}050}{1.05^{2}} = 47.62 + 952.38 = \$1{,}000.00$

Yield equals coupon → price is exactly par. Now bump the market yield to 7%:

$P = \frac{50}{1.07} + \frac{1{,}050}{1.07^{2}} = 46.73 + 917.16 = \$963.84$

The market yield rose from 5% to 7%, and the price fell from $1,000 to $963.84 — a discount. Run it the other way at a 3% yield and you’d get a price above $1,000, a premium. The PV machinery is the see-saw: higher discount rate, lower price.

There’s a neat ordering between the two yield measures, depending on where the bond trades:

Why? For a discount bond, YTM adds the coupon income plus the capital gain pulling the price up to face at maturity — so YTM beats current yield (which counted only the coupons). For a premium bond, YTM subtracts the capital loss as the price slides down to face — so YTM lands below current yield. At par, all three coincide.

When it matters

YTM is the standard yardstick for comparing bonds — it’s what gets quoted, screened, and plotted on the yield curve. Any time you’re choosing between bonds, or asking “what will I actually earn if I hold this to maturity?”, YTM is the answer (assuming you reinvest coupons at that rate and the issuer doesn’t default). Current yield is the appetizer; YTM is the meal.

Putting it together

One fixed coupon, one floating price, joined by an inverse see-saw — and three yield words to read where a bond sits. Chunk the whole idea into one picture:

A mixed recap — it pulls from every section above:

Key Takeaways