YTM, current yield and duration explained
Three numbers that describe a bond's return and risk: the full-roundtrip YTM, the snapshot current yield, and duration as the measure of interest-rate risk.
Quoting a bond only by its coupon is like judging a film by its poster. Three deeper measures — yield to maturity, current yield and duration — tell you what you actually earn and how much you can lose when rates move. The bond worksheet computes all three in one pass.
YTM: the single rate behind the price
Yield to maturity is the discount rate that makes the present value of all remaining cash flows equal today's clean price. It answers one question: if I hold this bond to maturity and reinvest coupons at the same rate, what annualized return do I earn? Because it is defined implicitly, it is computed by solving — which is why every bond worksheet has a price→YTM mode.
Current yield: the honest snapshot
Current yield is simply the annual coupon divided by the price: CY = coupon ÷ price. For the discount bond — coupon 8%, price 95.0263 — the current yield is 8.4187%. Notice the ordering: CY sits between the coupon (8%) and the YTM (10%). It ignores the capital gain from buying below par, which is exactly the piece YTM adds. For premium bonds the ordering flips, because the capital loss drags the YTM below the current yield.
| Measure | Formula | Value (8% coupon @ 95.0263) |
|---|---|---|
| Coupon rate | coupon / face | 8.0000% |
| Current yield | coupon / clean price | 8.4187% |
| YTM | solved from price | 10.0000% |
| Macaulay duration | time-weighted cash flows | 2.7773 years |
| Modified duration | Mac. dur / (1 + y/k) | 2.5249 |
Macaulay duration: the bond's center of gravity
Macaulay duration is the weighted-average time until the bond's cash flows arrive, where each cash flow is weighted by its own present value. A zero-coupon bond has duration exactly equal to its maturity; a coupon bond's duration is always shorter because coupons arrive earlier. Our verified 3-year bond has a Macaulay duration of 2.7773 years — less than 3, because the coupons pull the center of gravity forward.
Modified duration: the risk dial
Divide the Macaulay duration by one plus the periodic yield and you get modified duration — the first derivative of price with respect to yield. It converts rate moves into price moves directly: ΔP/P ≈ −ModDur × Δy. With 2.5249, a yield rise of one full percentage point costs roughly 2.52% of price — about 2.40 points on a 95.0263 bond, i.e. down to roughly 92.6. For the second-order correction you need convexity.
What raises interest-rate risk?
- Longer maturity → duration rises (more of the value sits far in the future).
- Lower coupon → duration rises (cash arrives later as a proportion of total).
- Lower yield level → duration rises slightly (discounting is gentler at low rates).
- Zero-coupon bonds are the extreme case: duration = maturity, maximum rate sensitivity.
Frequently asked questions
What is the difference between YTM and current yield?
Current yield is a snapshot: annual coupon ÷ price, ignoring any capital gain or loss. YTM is the full-horizon internal rate of return that also includes the pull toward par. For a bond bought at 95.0263 with an 8% coupon, current yield is 8.4187% while YTM is 10% — the gap is the annualized capital gain to maturity.
Why do we need modified duration if we have Macaulay duration?
Macaulay duration measures time; modified duration measures price sensitivity. Modified duration equals Macaulay duration divided by (1 + yield per period), and it plugs straight into the linear approximation ΔP/P ≈ −ModDur × Δy. For the verified 3-year bond, 2.7773 years converts to 2.5249, meaning a +1% yield move costs about 2.52% of price.
What does convexity add?
Duration is only the tangent to the curved price–yield line. Convexity measures that curvature and corrects the linear estimate for larger rate moves. Higher convexity is always good for the holder: prices fall less than duration predicts when yields rise, and rise more than predicted when yields fall.
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