In a number of major markets, the convention is to quote annualized yields with semi-annual compounding.
[4] The YTM calculation formulates certain stability conditions of the security, its owner, and the market going forward:[5][6] The YTM calculation accounts for the effect of the current market price on the yield going forward, but omits the possible effects of contingent events.
The total return realized at maturity is likely to differ from the YTM calculated at the time of purchase, perhaps considerably.
[7][8] In practice, the rates that will actually be earned on reinvested interest payments are a critical component of a bond's investment return.
If the bond is priced at an annual YTM of 10%, it will cost $5.73 today (the present value of this cash flow, 100/(1.1)30 = 5.73).
Suppose that over the first 10 years of the holding period, interest rates decline, and the yield-to-maturity on the bond falls to 7%.
Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10% per annum was earned, irrespective of any interest rate changes in between.
For bonds with multiple coupons, it is not generally possible to solve for yield in terms of price algebraically.
A numerical root-finding technique such as Newton's method must be used to approximate the yield, which renders the present value of future cash flows equal to the bond price.