# Relationship between price and yield to maturity in bonds

### Bond Pricing - Formula, How to Calculate a Bond's Price

A bond's yield to maturity is a measure of total return. The lower the price of a bond, all other things being equal, the higher the yield to maturity. This discounted price has to make up for the fact that the buyer receives a lower rate of return (yield to maturity) over the life of your bond than from bonds. We summarize what key concepts of Bonds, Bond Valuation & Bond Pricing. also demonstrate that there is an inverse relationship between yields and bond prices: With a price of $, what is the bond's yield to maturity?.

Bond Price Function The price or market value of an investment bond is based on the rate of interest the bond pays -- called the coupon rate -- compared to the current market yield for similar bonds. If a bond's coupon rate is higher than market rates, the value of the bond will be higher than the face amount to bring the yield an investor earns in line with current rates.

This is called a premium bond.

A discount bond is priced below the face amount, because the bond's coupon rate is lower than current market rates. Bond prices move inversely to interest rate changes. Factors Affecting Price Volatility Two features of bonds affect the price volatility in response to changes in market interest rates.

- Bond Pricing
- The Relation Between Time to Maturity & Bond Price Volatility
- The Relationship Between a Bond's Price & Yield to Maturity

A bond with a lower coupon rate will be more volatile than a bond with a higher coupon rate. Also, longer-term bonds are more volatile than bonds with a shorter time to maturity. Volatility in this case is the amount a bond's price changes in response to a specific change in interest rates.

Bond Duration The mathematical concept of bond duration can be used as a measure of the volatility or risk of a bond. Duration is similar to maturity but is a measure of the cash flow of a bond: Treasury Treasury securities are issued by the U. These are free of default risk, which is the risk that the investor will not receive all promised payments.

They are not taxed by state and local governments, but are taxed at the federal level. Treasuries can be classified by their maturities as follows: Treasury bills — the maturity is one year or less; the currently available maturities are 4 weeks, 13 weeks, 26 weeks and 52 weeks Treasury notes — the maturity ranges between 1 and 10 years; the currently available maturities are 2, 3, 5, 7 and 10 years Treasury bonds — the maturity ranges between 20 and 30 years; the currently available maturity is 30 years Another key difference between these securities is that Treasury bills are sold at a discount from their face value and redeemed at face value; Treasury notes and bonds are sold and redeemed at face value and pay semi-annual coupons to investors.

### The Relation Between Time to Maturity & Bond Price Volatility | Finance - Zacks

These bonds offer a higher promised coupon rate than Treasuries, but expose investors to default risk. The riskiest corporations offer the highest coupon rates to investors as compensation for default risk. Occasionally, municipalities do default on their debts; inthe city of Detroit filed for bankruptcy as a result of being unable to pay its debts. Municipal bonds offer an extremely favorable tax treatment to investors.

They are not taxed by federal, state or local governments as long as the bond holder lives in the municipality in which the bonds were issued. As a result, municipal bonds can be issued with very low yields.

If they are denominated in a foreign currency, they are known as eurobonds.