What Is the Yield to Maturity Equation?

The so-called maturity income refers to the income obtained from holding the bond to the repayment period, including all interest due at maturity. Yield to maturity (YTM), also known as final yield, is the internal rate of return on investment and purchase of bonds, which means that the present value of future cash flows obtained by investing in bonds can be equal to the discount rate of the current market price of bonds. It is equivalent to the average annual rate of return that investors can buy at the current market price and hold it until maturity, which implies that the cash flow of investment income in each period can be reinvested at the yield to maturity.

Yield to maturity

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PV: present value of annuity;

C: cash flow per period;

y: the rate of return for each period;

The Commercial Press's "English-Chinese Dictionary of Securities Investment" explains: yield to maturity. Abbreviation: YTM. hold

Yield to maturity = (recovery amount-purchase price + total interest) / (purchase price × maturity time) × 100%

Like the holding period yield, the yield to maturity also takes into account interest income and capital gains and losses, and because the recovery amount is the nominal amount, it is fixed and unchanged, so it can be accurately determined when making decisions in advance, It can be used as a reference for decision-making. But the yield to maturity applies to holdings of maturity bonds.

Example

A bond has a face value of 100 yuan, a 10-year repayment, an annual interest of 8 yuan, and a nominal yield of 8%. If the market price of the bond is 95 yuan on a certain day, the current yield is 8/95. At the beginning of the year, a 10-year bond with a face value of 100 yuan was purchased at a market price of 95 yuan, and when it was held to maturity, in addition to the annual interest of 8 yuan in 9 years, it also received a principal profit of 5 yuan, with a yield to maturity of (8 × 10 +5) / (95 × 10). ^[1]

The maturity of interest-bearing bonds, discounted bonds and remaining circulation periods within one year (including one year) in the final interest payment period

The calculation method of the return rate of investment products such as stocks and funds. A fund with a net value of 1 yuan will be thrown out with a net value of 2 yuan after 2 years, and the annualized rate of return will be 2 to 2 powers and then reduced by 1, which is about 41.4%. But insurance products are complicated. Dividend insurance or annuity insurance, etc., many require investors to pay a fixed fee every year for the first 10 years, and then return a fund every year or every few years from a certain year. To be more complicated, invest in In the past few years, investors have repaid a sum of money from time to time. Because of the expenditure and income from time to time, many investors look confused and do not know how to calculate the rate of return.

Dividend insurance is a complex income method, but it is very similar to bonds. When calculating its rate of return, the internal rate of return (IRR, InternalRateofReturn) can also be used to calculate the rate of return to maturity. The internal rate of return is a rate of return calculated using the concept of discounting. Its specific meaning and differences from annualized rates of return, etc. Ordinary investors do not need to pay attention, they only need to know that this is a series of income that can measure dividend insurance, bonds, etc. An indicator of the level of return on the investment product you spend can be.