Module 7 · Fixed Income

Yield and Yield Spread Measures for Fixed-Rate Bonds

EN: YTM, current yield, BEY, EAY, and the spread family (G, I, Z, OAS).
VN: Các loại yield và spread.

\[ P_0 = \sum_{t=1}^{N} \frac{C}{(1 + YTM)^{t}} + \frac{F}{(1 + YTM)^{N}} \]

YTM assumptions: bond held to maturity, no default, all coupons reinvested at the YTM.

Practice problem

1-year zero, face $1,000, price $940. Compute YTM.

Show solution

1+YTM = 1000/940 = 1.0638

YTM ≈ 6.38%

\[ \text{Current yield} = \frac{\text{Annual coupon}}{P_0} \]

Practice problem

Annual coupon $60, price $950. Compute current yield.

Show solution

= 60/950

≈ 6.32%

\[ BEY = 2 \times \text{Semi-annual YTM} \]

Practice problem

Semi-annual YTM 2.5%. Compute BEY.

Show solution

BEY = 2 × 2.5%

BEY = 5.00%

\[ EAY = (1 + YTM_{\text{periodic}})^{m} - 1 \]

Practice problem

Semi-annual YTM 2.5%. Compute EAY.

Show solution

$EAY = (1.025)^{2} - 1 = 1.050625 - 1$

EAY ≈ 5.06%

G-spread Yield − interpolated yield on benchmark government bond of same maturity.
I-spread Yield − corresponding swap rate.
Z-spread Constant spread added to each spot rate to make PV(CF) = price (for option-free bonds).
OAS Option-adjusted spread = Z-spread − value of embedded option (callable).

For a callable: OAS < Z-spread (compensation for option risk removed).

Practice problem

A bond's semi-annual YTM is 3%. Compute the BEY and EAY.

Show solution

BEY = 2 × 3% = 6%

EAY = (1.03)$^{2}$ − 1 = 1.0609 − 1

BEY = 6.00%; EAY = 6.09%