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Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the annualized return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i) 10 = (25.84/5.73), giving 0.1625.
The Z-spread of a bond is the number of basis points (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury forward rates) so that the Net present value of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including accrued interest).
Analytic Example: Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
The vertical or y-axis depicts the annualized yield to maturity. [3] Those who issue and trade in forms of debt, such as loans and bonds, use yield curves to determine their value. [4] Shifts in the shape and slope of the yield curve are thought to be related to investor expectations for the economy and interest rates.
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The YTM article should have additional formula for reinvestment risk where the rate at which coupons are reinvested is different than the yield of the bond. A 30 year bond for example with a YTM of 5% would have a much much lower YTM if the coupons are reinvested at 1%.