Yield is the expected rate of return on an investment given characteristics of the security. Yields are quantified and measured using various calculations, most notably yield spreads. Yield spreads measure the additional yield of one issue over another one with the same maturity.
A simple yield spread is calculated as:
Yield spread = Yield on bond ? yield on reference bond
Yield spreads can be measured on a relative basis, comparing one bond?s yield spread to a reference bond.
The relative yield spread is calculated as:
Relative yield spread = (Yield on bond - yield on ref bond) / yield on ref bond
Bonds can also be evaluated using a yield ratio, calculated as:
Yield ratio = Yield on bond / yield on ref bond
The excess return of one bond over another can be found using the absolute yield spread, calculated as:
Absolute yield spread = yield on bond ? yield on reference bond
Most securities issued in the U.S. are subject to federal, state, and local taxes. Yields on municipal securities are generally lower than Treasuries with equivalent maturities because they are subject to specific tax exemptions.
In general, higher marginal tax rates make tax-exempt securities more attractive and lower yield ratios. Yields on bond issues after federal income taxes are paid are known as after-tax yields.
After-tax yields are calculated as:
After-tax yield = Pre-tax yield (1 ? marginal tax rate)
The yield that is equal to the same after-tax yield as tax-exempt securities is known as the taxable-equivalent yield. The higher the marginal tax rate, the higher the tax-equivalent yield and vice versa.
The taxable-equivalent yield is calculated as:
Taxable Equivalent Yield = Tax Exempt Yield / (1 ? marginal tax rate)
A bond?s option adjusted spread measures the surplus or deficit return of a bond due to embedded options. A higher OAS signifies increased return in exchange for higher risk. The Z-spread, or zero volatility spread, measures the spread over a spot rate curve of a riskless asset. It is the return over a Treasury curve if held to maturity.
The Z-spread is calculated as:
Z-spread = Option cost + OAS
