Yield to Maturity

The yield to maturity is the annual return annual rate (discounted) earned over a bond kept until maturity. The yield to maturity is the discount rate estimated mathematically that equals the cash flow of payment of interest and principal received with the purchasing price of the bond.

This term is also referred to as internal rate of return or as the expected rate of return of the bond and it is the yield in which most bond investors are interested in.

Yield-to-Maturity Approximation Formula

Yield to Maturity =

Using the approximation formula, the yield understates the true yield-to-maturity that is calculated using a computer. The reason is that the approximation formula does not use the time value of money for compounding of the coupon payments.

The yield-to-maturity depends on two assumptions:

• The bonds are held to maturity
• The interest payments received are reinvested at the same rate as the yield-to-maturity

If the bond is not kept until maturity, you could estimate the internal return rate of the bond by substituting the sales price of the bond for that of its maturity value and the period kept until the selling date for its maturity date.

The yield-to-maturity rate assumes that bondholders reinvest the received interests from the same yield-to-maturity. If this does not happen the owners return rate will differ from that of the quoted yield-to-maturity rate. For example, if the interest received is spent and not reinvested, the interest does not earn interest; the investor earns much lesser (or greater) rates, the 8% is not achieved. In reality matching the yield-to-maturity rate from the interest received is difficult because interest rates are changing constantly. The interest received is usually reinvested at different rates from the stated yield-to-maturity rate.

However, the yield-to-maturity is useful to compare and evaluate different bonds with variable qualities with different coupon rates and prices. For example when comparing the yield-to-maturity of an A&A-rated bond with a BBB-rated bond you can easily notice in how much would the yield increase when choosing the longer-rated bond. Also you will observe the yield differential between bonds with different periods of maturity.

The concept of current yield is closely related to other bond concepts, including yield to maturity, and coupon yield. The relationship between yield to maturity and coupon rate is as follows:

• When a bond sells at a discount, YTM > current yield > coupon yield.
• When a bond sells at a premium, coupon yield > current yield > YTM.
• When a bond sells at par, YTM = current yield = coupon yield.