Fixed Income
Fixed Income tests the pricing of bonds from their cash flows, the yield measures used to quote them, the interest-rate risk measures used to manage them, and the credit and structural features that change their behaviour. Expect pricing, duration and yield-curve items.
Pricing and yields
- A bond's price is the present value of its coupons and principal discounted at the market yield for each period.
- Price and yield move inversely. If the coupon exceeds the yield, the bond trades at a premium; if below, at a discount; at par when they are equal.
- Yield to maturity assumes coupons are reinvested at the YTM, which is the reinvestment assumption candidates forget. Spot rates price each cash flow separately; forward rates are implied by the spot curve.
Duration and convexity
- Macaulay duration is the weighted average time to the cash flows; modified duration = Macaulay / (1 + yield per period).
- Approximate percentage price change = -modified duration x change in yield, with convexity adding a small positive correction for large moves.
- A zero-coupon bond has duration equal to its maturity.
Worked example
Value a three-year bond with a 5% annual coupon and a face value of 100 at a yield to maturity of 6%. Cash flows: 5, 5, 105. 5/1.06 = 4.72; 5/1.06^2 = 4.45; 105/1.06^3 = 88.16. Total price = 97.33. The bond trades at a discount because the 5% coupon is below the 6% yield. If the yield fell to 5%, the price would be exactly 100.
Traps that cost marks
- Confusing clean price with the dirty (full) price that includes accrued interest.
- Assuming a callable bond's yield to maturity is the best measure; yield to worst is the conservative figure.
- Ignoring reinvestment risk, which rises with the coupon and the holding period.
- Using modified duration for a large yield move without convexity, which systematically understates the price gain and overstates the loss.