What have you actually learned about yield and duration?

You arrived able to say "rates up, bond prices down". You leave able to say how much, why the estimate is wrong, what it is worth in euros, and what the curve does that a single number can't capture.

The four movements

• Measuring yield. The coupon rate is about face value, current yield is about your price, and yield to maturity is the discount rate that equates the bond's cash flows to that price. YTM is a conditional promise: hold to maturity, get paid in full, and reinvest every coupon at the same rate — and that third condition is the one nobody controls. On a 30-year 5% bond, more than half the promised return is interest on interest. Where the issuer holds a call option, the honest number is yield to worst.
• Duration. Maturity is the wrong risk measure because it ignores when the bulk of the money arrives. Macaulay duration is the PV-weighted average time to the cash flows — 4.55 years for our 5-year 5% par bond. Divide by (1 + y ÷ k) to get modified duration, 4.33, which reads directly as a percentage price move per percentage point of yield. Duration is value-weighted additive across a portfolio. It equals maturity for one instrument only — the zero.
• Convexity and sensitivity. The price-yield relationship is a curve; duration is its tangent. So duration overstates losses and understates gains, and the error grows with the square of the move. Adding ½ × Convexity × (Δy)² fixes it — the house bond's 23.9 convexity turns a €1.17 error into two cents. That gift reverses for callables and mortgages, which show negative convexity and are measured with effective duration instead. In money terms, DV01 = modified duration × price × 0.0001 — €0.43 per €1,000 face, €4,329 on a €10m position. And immunisation, the reason duration was invented, matches asset duration to a liability's so that price risk and reinvestment risk cancel — with cash-flow matching as the honest baseline and rebalancing as the ongoing cost.
• The yield curve. Par, spot and forward curves are three views of one thing; forward rates are break-evens, not forecasts. Shapes — normal, flat, inverted, humped — encode expected short rates and the term premium, mixed inseparably. Curve moves are named by direction and by which end moves more (bull/bear × steepener/flattener), and a single duration number cannot see them, which is why desks report key rate durations. The term premium is the price of bearing duration risk — and it is a model estimate, not an observation, and it can be negative.

The formulas worth keeping on one card

• Current yield = annual coupon ÷ price
• YTM = the rate that makes PV of all cash flows equal the price
• Macaulay duration = Σ (PV-weight × time)
• Modified duration = Macaulay ÷ (1 + y ÷ k)
• Convexity = [ Σ t(t+1) × PV(CF_t) ] ÷ [ Price × (1 + y ÷ k)² × k² ] — computed in periods, annualised by that ÷ k²
• %ΔP ≈ − Modified duration × Δy + ½ × Convexity × (Δy)²
• DV01 = Modified duration × Price × 0.0001

The one sentence to keep

A yield tells you what a bond promises under conditions that may not hold; duration and convexity tell you what happens to its price when the world changes its mind about rates.

The non-negotiable framing

Everything here is education, not advice. This course teaches measurement — how each number is built, what it assumes, and where it misleads. It contains no forecast of interest rates, no view on any curve, and no suggestion about how anyone should be positioned. A steep curve is not an opportunity, an inverted one is not an alarm you should act on, and a high term premium is not an instruction. Bonds and figures were illustrations, rounded so the arithmetic stays visible.

Before you sit it

Each of these is a minute at your desk. Any one that is not names the lesson to reopen first.

• Say what yield to maturity counts that current yield ignores — What is yield to maturity really measuring?
• Estimate the price move on a duration-6 bond when yields rise 50 basis points — How much does a bond move when rates move 1%?
• Say what one basis point is worth in money on €1m of that bond — What is one basis point worth, in money?
• Say which end of the curve moves in a bull steepener — What do traders mean by a steepener or a flattener?

Try it now

1. From memory, take a 5-year, 5% annual coupon bond trading at par and produce its Macaulay duration, modified duration, DV01 per €1,000 face, and its estimated price after a 100bp rise using both the one-term and two-term formulas. Then reprice it properly and see how close you got.
2. The newest full Treasury curve is below. Name its shape, compute the implied 1-year rate one year forward from the 1-year and 2-year yields, and estimate what a 50bp parallel rise would do to a duration-7 portfolio.

3. Say the closing line out loud: "yield is a conditional promise, duration is a first-order answer, convexity is the correction, DV01 is the money — and none of it predicts where rates go." Then take the checkpoint quiz.

A note on what we do here. EODHD Academy teaches how markets work, using real market data as a laboratory. Nothing here is a recommendation to buy or sell anything, and nothing here forecasts interest rates. The point of this course is to make bond arithmetic legible — so you can see exactly which assumption every "yield" is resting on.