Library/CFA (Chartered Financial Analyst)/JuiceNotes 2024 Fixed Income/Yield and Yield Spread Measures for Fixed-Rate Bonds

Yield and Yield Spread Measures for Fixed-Rate Bonds

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Yield to Maturity and Periodicity5 min

Yield to Maturity (YTM) represents the expected annual return if a bond is held to maturity and coupons are reinvested at the same rate. Periodicity refers to the assumed number of compounding periods per year (typically 2 for US/UK bonds). The chapter provides formulas to convert between Annual Effective Yields and Semiannual Bond Equivalent Yields, noting that for the same bond, a higher periodicity results in a lower stated annual rate due to compounding effects. Special attention is given to negative yields, where the conversion logic remains consistent.

Key Points

YTM assumes reinvestment of coupons at the YTM rate.
Semiannual bond basis has a periodicity of 2.
Effective Annual Rate (EAR) has a periodicity of 1.
Conversions involve equating (1 + Periodic Rate)^Periodicity.
Negative yields are handled using the standard time value of money equations.

Alternative Yield Measures5 min

Beyond YTM, investors use other metrics. Current Yield provides a snapshot of income relative to price but ignores principal repayment. Simple Yield adjusts current yield with straight-line amortization. The Government Equivalent Yield (GEY) restates corporate yields (often 30/360 day count) to the actual/actual day count used by government bonds to allow for accurate spread calculation. 'Street convention' yields neglect weekends/holidays, while 'True yields' account for them.

Key Points

Current Yield = Annual Coupon / Flat Price.
Simple Yield adds straight-line amortization to coupon income.
GEY converts 30/360 yields to an Actual/Actual basis.
True yield is never higher than street convention yield due to payment delays.

Yield to Call, Worst, and Option-Adjusted Yields5 min

For callable bonds, YTM may not be realized if the issuer calls the bond. Yield to Call (YTC) calculates the return assuming a specific call date and price. Yield to Worst (YTW) is the most conservative metric, being the minimum of the YTM and all YTCs. Option-adjusted yield uses a model to incorporate interest rate volatility and the value of the embedded option, providing a yield based on the option-adjusted price (Market Price +/- Option Value).

Key Points

YTC replaces maturity date/price with call date/price.
YTW is the lowest potential yield (excluding default).
Option Adjusted Price = Flat Price +/- Option Value.
Investors pay less for callable bonds due to the issuer's option.

Yield Spreads6 min

Yield spreads quantify the risk premium. The G-Spread compares a bond to a government benchmark (matched by maturity). The I-Spread uses swap rates as the benchmark. The Z-Spread (static spread) uses the entire spot rate curve rather than a single point YTM, adding a constant spread to each spot rate to price the bond. The Option-Adjusted Spread (OAS) strips out the portion of the spread attributable to option risk, leaving a pure measure of credit and liquidity risk.

Key Points

G-Spread = Bond Yield - Interpolated Govt Yield.
I-Spread uses swap rates; common for Euro-denominated bonds.
Z-Spread is added to the spot curve.
OAS = Z-Spread - Option Cost (in basis points).
OAS is used to compare bonds with different optionality.

Questions

Question 1

Which of the following assumptions is required for a bond investor to earn a rate of return exactly equal to the Yield to Maturity (YTM) at purchase?

Yield and Yield Spread Measures for Fixed-Rate Bonds

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