Yield to maturity (also called redemption yield or yield to redemption) is the internal rate of return of bond cash flows. It is the single/uniform discount rate at which the present value of bond cash flows equals its current market price.

Yield to maturity is based on three critical assumptions:

- the bond is held till maturity,
- the issuer does not default on the coupon or principal payment, and
- the investor can reinvest the bond cash flows at the same yield.

Yield to maturity can be determined by solving the equation for bond price as given below for y.

\[ P=\frac{c}{m}\times\frac{{1\ -\left(1+\frac{y}{m}\right)}^{-n\times m}}{\frac{y}{m}}+\frac{F}{\left(1+\frac{y}{m}\right)^n} \]## Relationship between bond price and bond characteristics.

There are four common relationships between bond price and its characteristics:

**Inverse effect**: there is an inverse relationship between the market discount rate and bond price.**Convexity effect**: for the same coupon and yield to maturity, (absolute) percentage price change is higher when market interest rates decline and vice versa.**Coupon effect**: for the same time to maturity, low coupon bonds have a greater percentage price change and vice versa.**Maturity effect**: generally, for the same coupon rate, a longer-term bond has a greater percentage change in response to the market discount rate.

Hence, a bond most exposed to a change in market price would be one with a low coupon rate and a longer time to maturity. This makes sense because a low coupon bond with a long maturity date would have a larger chunk of cash flows farther away from time 0 and would be more exposed to the swings induced by the time value of money.