Fixed Interest: Pricing, Yield and Duration
What the exam tests
This domain tests bond valuation and interest-rate risk: clean versus dirty price, accrued interest, yield to maturity, duration and convexity, and the conventions of the South African bond market.
Core rules
- A bond's price is the present value of its coupons and redemption amount, discounted at the yield to maturity. SA government and corporate bonds typically pay semi-annual coupons, so the yield is quoted nominally annual but compounded half-yearly.
- The clean price is the quoted price. The dirty (all-in) price is the clean price plus accrued interest since the last coupon date. Settlement is at the dirty price.
- Price and yield move inversely. Modified duration estimates the percentage price change for a small yield change: percentage change = -modified duration x change in yield.
- Macaulay duration is a weighted average time in years; modified duration is Macaulay divided by (1 + yield/compounding frequency). Convexity corrects the duration estimate for larger yield moves and is always positive.
- Longer maturity and lower coupons mean higher duration and greater price sensitivity.
Worked example: pricing a semi-annual bond
Three-year bond, 10% coupon, face value R100, yield to maturity 12%.
- Half-yearly coupon = R5; periodic yield = 6%; periods = 6
- Annuity factor = (1 - 1.06 to the power -6) / 0.06 = 4.91732
- PV of coupons = 5 x 4.91732 = 24.5866
- PV of redemption = 100 x 0.704961 = 70.4961
- Price = 24.5866 + 70.4961 = R95.08 per R100 nominal
The bond trades at a discount because the 10% coupon is below the 12% yield.
Traps that cost marks
- Quoting the clean price as the settlement amount and omitting accrued interest.
- Discounting annual coupons when the bond pays semi-annually.
- Applying modified duration without the sign, or using it for a large yield move without convexity.
- Confusing duration in years with the percentage price sensitivity measure.