Module 3
Interest-rate risk
You already know bond prices fall when rates rise. This lesson answers how much. There are three numbers that professionals live by:
- DV01 — the dollar change in your position for a 1 basis point (0.01%) move in rates. It's your risk in plain dollars.
- Duration — the % price change per 1% move in yield. A duration of 8 means a 1% rate rise costs you roughly 8%. Longer bonds have higher duration.
- Convexity — the curvature. Price vs yield isn't a straight line, so convexity corrects duration for big moves (and it works in your favour).
There's one more, and it's the punchline: key-rate DV01. Instead of bumping the whole curve, you bump one maturity at a timeto see where your risk actually lives. For a single bond, almost all of it sits at the bond's own maturity — bump the 2y point and a 10y bond barely notices. Try it.
🎛 Risk playground
Price
96.848
DV01 ($/bp)
$7,856
Mod. duration
8.11
Convexity
75.0
Key-rate DV01 — where the risk lives ($/bp per tenor)
Almost all the risk sits at the bond's own maturity (the tall amber bar) — that's why a single bond is mostly exposed to rates at its tenor, not the whole curve. DV01 is the dollar move per 1bp; duration is the % price move per 1% yield; convexity is the curvature that makes big moves asymmetric. Educational tool — not investment advice.
Things to try
- • Bump parallel +25 bp and read the P&L. Now raise the maturity — the same bump hurts more (higher duration).
- • Switch the bump to a single tenor away from the bond's maturity — barely any P&L. Bump the tenor at its maturity — that's where it all is.
- • Watch the amber bar in the key-rate chart: it's the bond's own maturity, holding nearly all the risk.
🎛 Zoom in on convexity: the curve vs the straight line
Duration assumes price moves in a straight line as yields change — but it doesn't, it curves. Slide a rate shock and watch the real price (amber dot) pull away from what duration predicts (grey dot). That gap is convexity.
Actual price
81.94
Duration says
79.48
+ Convexity says
82.18
Convexity
240
Duration draws a straight line (grey) through the price today. But the real price-vs-yield relationship curves (amber) — so for a 150 bp rise, duration alone is off by about +2.46 per 100. That gap is convexity — and notice the curve sits above the straight line on bothsides: you gain a little more when rates fall than you lose when they rise. That's why more convexity is better, and why it grows with longer maturities and bigger moves.
Base yield fixed at 4% to isolate the curvature. Educational tool — not investment advice.
But why does the price curve at all?
Two ways to see it — they're the same reason:
1. You're dividing by bigger and bigger numbers.A bond's price is every future payment divided by (1 + yield), compounded over time. As the yield rises, you're dividing by a larger and larger number — so each extra bit of yield strips away lessprice than the bit before it (you're shaving a slice off an already-smaller number). Going the other way, each drop in yield adds more. That lopsidedness — losses that shrink as rates rise, gains that grow as rates fall — is the curve bending. And since a price can never fall below zero, the line has to flatten toward the floor as yields climb, instead of plunging straight through it.
2. Duration itself isn't fixed. Duration is just the steepness of the line at one point — and it changes as yields move. When yields fall, a bond's far-off payments (the most rate-sensitive ones) balloon in value and take over the price, so the bond effectively gets longer and more sensitive → bigger gains. When yields rise, those distant payments shrink toward nothing, the bond gets shorter and lesssensitive → smaller losses. So a bond automatically becomes more sensitive right when rates are dropping, and less sensitive when they're climbing. Convexity is simply the measure of how fast duration changes — and because it always moves in your favour, more of it is better.
You can watch #2 happen above: push the yield shock far to the right and the amber curve flattens toward zero (never crossing it), while the grey straight line keeps plunging. That flattening — duration shrinking as yields rise — is convexity.
Things to try
- • Push the rate shock to ±400 bp — the straight line and the curve pull far apart. For small moves they're close; for big ones, duration alone is badly off.
- • Notice the amber curve sits above the grey line on both sides — you gain more when rates fall than you lose when they rise. Convexity is a free bonus.
- • Raise the maturity or drop the coupon — the curve bows more (higher convexity).