The calculation methods, formulas, and steps of bond yields are described in detail below, and illustrated with examples.
Bond yield is the rate of return that investors can expect from buying and holding bonds, and is often used to measure the investment value of a bond. Bond yields can be yields to maturity, current yields, or holding period yields, among which yield to maturity is the most commonly used one.
1.Definition of yield to maturity
Yield to maturity (YTM) refers to the annualized average rate of return that investors can obtain by buying and holding bonds to maturity. This rate of return takes into account the interest income on the bond and the capital appreciation or impairment between the purchase** and the principal at maturity.
2.Calculation formula
text = \sqrt[n] +text \times \frac} }1
Where: face value is the face value or maturity principal of the bond;
A coupon is an annual interest payment;
price is the current market for bonds**;
ytm is the yield to maturity (which we need to solve);
n is the remaining maturity period.
This is a nonlinear equation that is usually solved using numerical methods such as the Newton-Raphson method.
3.Calculation steps
1) Gather the necessary information: including the face value of the bond, annual interest payments, current market**, and remaining maturity years.
2) Set an initial yield to maturity estimate.
3) Substitute the above information into the formula and use numerical methods to solve the yield to maturity.
4) Check the reasonableness of the yield to maturity to ensure that it meets market expectations and investors' risk appetite.
Suppose an investor buys a bond with a face value of $1,000, an annual interest rate of 5%, and a remaining maturity of 10 years, and its current market** is $950. We need to calculate the yield to maturity of the bond.
Following the above calculation steps, we can get the annualized average return of the bond of 531%。This means that if an investor buys and holds the bond to maturity at $950**, the expected annualized average return is about 531%。
1.Bonds** and yields have an inverse relationship: when market interest rates rise, bonds** fall and vice versa. This is because the relative value of a bond with a fixed interest payment changes when the market interest rate changes.
2.Yield to maturity is the rate of return that an investor assumes to hold a bond to maturity, regardless of the mid-bid-ask spread. For investors who plan to bond before maturity, other types of yields, such as holding period yields, should also be considered.
3.When calculating yield to maturity, you need to ensure the accuracy and consistency of all input data, especially the market** and remaining maturity years of the bond. Changes in these data can directly affect the accuracy of the calculations.
4.The yield to maturity calculation assumes that all interest payments and principal repayments are made on time. In practice, investors also need to consider the impact of factors such as credit risk and liquidity risk on yield.
5.For complex bonds (such as weighted bonds, convertible bonds, etc.), the calculation of their yields may involve more factors and complex models, which need to be analyzed and calculated on a case-by-case basis.
6.When comparing the yields of different bonds, you should pay attention to the impact of factors such as maturity, credit rating, and taxation on the yield in order to make more accurate investment decisions.