What is the relationship between a bond's market price and its promised yield to maturity?

There is an inverse relationship between market price of the bond and its yield. The higher the market price, the lower the return and the lower the market price the higher the return in bond. The main reason that affect bond price is market rating of the issuing company, interest rate and inflationary expectations. People prefer bond holding to shares to protect their capital in times of inflation. In case of share holding the return may be high but sometimes the value of share holding may crash wiping out the entire capital. Bond prices manage interest rate risk to protect the capital of the investor in a better manner.

There are two kinds of yield 1) current yield 2) yield to maturity Current Yield- Suppose any bond(not the zero coupon obviously ) with the coupon bearing 8% with par value 100 and time to maturity 10 years is currently selling at 101. The current yield will be (8/101)*100% = 7.92% Yield to maturity - it will be sum of all the coupoun i.e. 8  and the par value i.e. 100 discounted at required yield. Please read time value of money to understand better. Now the price and yield are in reciprocal relationship. Increase of any variable will decrease the other one (see the price yield relationship curve). So any moment whenever the price changes the yield also shifts in opposite dierection.

Bond's market price is the price we get in case of sale at current market price, which may be higher or lower than the promised value on due date. The promised yield to maturity is the assured amount we get on the due date of the bond, which is fixed.