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# Yield to maturity and factors affecting bond price

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.