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 Annual equivalent Yield

Converting a bond equivalent yield (BEY) to an equivalent annual yield (EAY) or vice versa:

BEY of an annual pay bond


Annual equivalent Yield= (1+(BEY/2))2 -1


Yield Volatility


When the yield level is high, a change in interest rates does not produce a large change in price.

However, when yields are low, changes in interest rates produces a large change in price.


 Nominal Spread



Z-Spread: Solve for ZS where price =



OAS: Option Adjusted Spread
         =  Z-Spread – Option Cost

Forward Rates given  Spot Rates:

(1 + S2)2 = (1 + 1f0) (1+1f1)

For Callable Bonds, Z-Spread > OAS and Option Cost > 0

For Putable Bonds, Z-Spread < OAS and Option Cost < 0


Forward rate

Forward rate is a lending rate for a future loan (1+S2)2 = (1+S1)*(1+1f1)

Calculate the 1yr fwd rate two years from now, if S1 = 4% S2 = 5% & S3 = 6%

(1+S3)3 = (1+S2)2*(1+1f2) 1f2 = 8.03%


YTM is a IRR based on bond price & its future cash flow.

Current yield

Current yield = Annual coupon payment / Bond price

If a bond has a 5.5% annual pay coupon and the current market price of the bond is $1,050, the current yield is?

55/1050 = 5.24%

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