Module 1
What is a bond, and how is it priced?
A bond is an IOU with a payment schedule. When you buy one, you're lending money. In return you get a stream of fixed coupon payments (interest), and your original face valueback on the maturity date. A “4% 5-year” bond pays 4% a year (usually split into two payments) for five years, then returns your principal.
So what should it cost today? Here's the one big idea: a bond's price is just the sum of its future payments, each discounted back to today. A dollar in five years is worth less than a dollar now, so we shrink each future payment by a discount factor before adding them up. The rate we discount at is the yield— the market's going rate for that bond's risk and maturity.
That single relationship explains the whole thing:
- Coupon = yield → the bond is worth exactly its face value. It trades at par (100).
- Coupon > yield → it pays more than the market demands, so it's worth more than face — a premium.
- Coupon < yield → it pays less than the market demands, so it's worth less than face — a discount.
And it's why bond prices fall when interest rates rise: a higher yield discounts those future payments harder, so the price drops. Enough talk — see it for yourself.
🎛 Try it yourself
Price per $100 face
100.00
PARModified duration 4.49
This bond trades at a par — coupon = yield, so it's worth exactly face. A ~1% rise in yield would move its price about 4.5%the other way (that's duration).
| Period | Years | Cashflow | Discount factor | Present value |
|---|---|---|---|---|
| 1 | 0.5 | $2.00 | 0.9804 | $1.96 |
| 2 | 1.0 | $2.00 | 0.9612 | $1.92 |
| 3 | 1.5 | $2.00 | 0.9423 | $1.88 |
| 4 | 2.0 | $2.00 | 0.9238 | $1.85 |
| 5 | 2.5 | $2.00 | 0.9057 | $1.81 |
| 6 | 3.0 | $2.00 | 0.8880 | $1.78 |
| 7 | 3.5 | $2.00 | 0.8706 | $1.74 |
| 8 | 4.0 | $2.00 | 0.8535 | $1.71 |
| 9 | 4.5 | $2.00 | 0.8368 | $1.67 |
| 10 | 5.0 | $102.00 | 0.8203 | $83.68 |
| Total price (sum of present values) | $100.00 | |||
A bond's price is simply the sum of its future payments, each discounted to today. Educational tool — not investment advice.
What's that “modified duration” number?
The pricer also shows modified duration — a one-number measure of how sensitive the price is to interest rates. It estimates the percentage change in price for a 1% (100 bp) change in yield.
A modified duration of 4.5 means: if the yield rises 1%, the price falls about 4.5%; if the yield falls 1%, the price rises about 4.5%. It's roughly the number of years, weighted by when you get your money back — so longer maturities and lower coupons give higher duration (more rate risk), because more of your money is tied up further out. Drag the maturity slider up and watch it climb.
It's the single most important risk number for a bond — we go deeper (plus DV01 and convexity) in Module 3: Interest-rate risk.
Things to try
- • Set coupon = yield (both 4%). The price is exactly 100 — par.
- • Drag the yield above the coupon. Watch the price fall below 100 — that's a discount bond, and it's what happens to existing bonds when rates rise.
- • Increase the maturity. Notice the price reacts more to the same yield change — longer bonds are riskier to rate moves (higher duration).