United States
Hong KongBonds: price, yield, and what duration is telling you
A bond's price and its yield move inversely. Duration measures price sensitivity to a change in yield, rising with maturity and falling with coupon. Convexity corrects duration's straight-line approximation for larger moves.
Start with the relationship everything else follows from: price and yield move in opposite directions.
Rates rise, existing bonds paying lower coupons become less attractive, and their prices fall until the yield matches the market. That is the whole mechanism.
The yield measures
| Measure | What it is |
|---|---|
| Coupon rate | The stated rate on par value - fixed, and not a yield |
| Current yield | Annual coupon divided by current price |
| Yield to maturity | Total return if held to maturity, assuming coupons reinvested at the same rate |
| Yield to call | The same, assuming the bond is called at the first call date |
| Taxable equivalent yield | What a taxable bond must yield to match a municipal, given the tax bracket |
For a bond trading at a discount, coupon rate is below current yield, which is below yield to maturity. At a premium, the order reverses. Questions ask you to rank them.
Duration
A measure of price sensitivity to interest rate changes, expressed in years. A duration of seven implies roughly a seven per cent price move for a one percentage point change in yield, in the opposite direction.
- Longer maturity means higher duration.
- Lower coupon means higher duration.
- A zero-coupon bond has duration equal to its maturity - the only case where they are the same.
- Higher yield means slightly lower duration.
The zero-coupon point is the one to hold. Everything else pays cash along the way, which pulls the weighted average time of cash flows forward.
Matching a bond portfolio's duration to the time horizon of a liability immunizes against interest rate risk, because price risk and reinvestment risk offset. That is the practical use, and it is examined.
Convexity
Duration assumes a straight-line relationship. The real one is curved, so duration under-predicts price rises and over-predicts price falls.
Convexity is the correction. Positive convexity is desirable - it means gains are larger and losses smaller than duration alone suggests. Callable bonds can display negative convexity, because the call caps the upside.
Credit and structure
Investment grade above the threshold, high yield below. Callable bonds favor the issuer and therefore pay more. Putable bonds favor the holder and pay less. Convertibles carry equity upside and pay less again.
Municipal bonds pay interest that is generally exempt from federal income tax, and from state tax for residents of the issuing state. The taxable equivalent yield calculation is how you compare them, and it appears reliably.
Dollar limits and rate thresholds here are indexed annually. Confirm the current figure before relying on it, and expect the exam to test the rule rather than the number.
Common questions
Why do bond prices fall when rates rise?
Existing bonds paying lower coupons become less attractive, so their prices fall until the yield they offer matches the market. Price and yield move inversely.
What does duration measure?
Price sensitivity to a change in interest rates, expressed in years. A duration of seven implies roughly a seven per cent price move for a one percentage point yield change.
What increases duration?
Longer maturity and lower coupon. A zero-coupon bond has duration equal to its maturity, which is the only case where the two are the same.
What is convexity?
The correction to duration's straight-line assumption. Positive convexity means gains are larger and losses smaller than duration predicts; callable bonds can show negative convexity.
How do you compare a municipal bond to a taxable one?
Using the taxable equivalent yield - what a taxable bond must yield to match the municipal after tax at the client's bracket.