what is a bond yield 
a bond yield is the return an investor realizes on a bond put simply a bond yield is the return on the capital invested by an investor bond yields are different from bond prices both of which share an inverse relationship the yield matches the bond s coupon rate when the bond is issued bond yields can be derived in different ways including the coupon yield and current yield additional calculations of a bond s yield include yield to maturity ytm among others investopedia daniel fishelunderstanding bond yieldsbonds are essentially a loan to bond issuers they are considered safe investments that s because bond values don t change the same way stock prices do they offer investors a reliable stream of income and provide bondholders with a fixed form of income investors earn interest on a bond throughout the life of the asset and receive the face value of the bond upon maturity investors can purchase bonds for more than their face value at a premium or less than the face value at a discount whichever they buy will change the yield they earn on the bond bonds are rated by services approved by the securities and exchange commission sec and ratings range from aaa as investment grade with the lowest risk to d which are bonds in default or junk bonds with the highest risk 1the return realized by a bond investor is called the yield there are a couple of different yield related concepts these include the formula and calculation of a bond yieldthe simplest way to calculate a bond yield is to divide its coupon payment by the face value of the bond this is called the coupon rate 2coupon rate annual coupon payment bond face value text coupon rate frac text annual coupon payment text bond face value coupon rate bond face valueannual coupon payment if a bond has a face value of 1 000 and made interest or coupon payments of 100 per year then its coupon rate is 10 or 100 1 000 bonds are essentially a loan to bond issuers they are considered safe investments that s because bond values don t change the same way stock prices do they offer investors a reliable stream of income and provide bondholders with a fixed form of income bond yield vs bond priceprice and yield are inversely related this means that as the price of a bond goes up its yield goes down conversely as the yield goes up the price of the bond goes down if an investor purchases a bond with a face value of 1000 that matures in five years with a 10 annual coupon rate the bond pays 10 or 100 in interest annually if interest rates rise above 10 the bond s price will fall if the investor decides to sell it 3if the interest rate for similar investments rises to 12 the original bond will still earn a coupon payment of 100 which would be unattractive to investors who can buy bonds that pay 120 as interest rates have risen to sell the original 1000 bond the price can be lowered so that the coupon payments and maturity value equal a yield of 12 if interest rates fall the bond s price would rise because its coupon payment is more attractive the further rates fall the higher the bond s price will rise in either scenario the coupon rate no longer has any meaning for a new investor but if the annual coupon payment is divided by the bond s price the investor can calculate the current yield and get an estimate of the bond s true yield current yield annual coupon payment bond price text current yield frac text annual coupon payment text bond price current yield bond priceannual coupon payment the current yield and the coupon rate are incomplete calculations for a bond s yield because they do not account for the time value of money maturity value or payment frequency and more complex calculations are required additional bond yield calculationsas noted above there are additional calculations of a bond s yield these include the ytm bond equivalent yield bey and effective annual yield eay a bond s yield to maturity is equal to the interest rate which makes the present value of all a bond s future cash flows equal to its current price these cash flows include all the coupon payments and maturity value solving for ytm is a trial and error process that can be done on a financial calculator but the formula is as follows price t 1 t cash flows t 1 ytm t where ytm yield to maturity begin aligned text price sum t t 1 frac text cash flows t 1 text ytm t textbf where text ytm text yield to maturity end aligned price t 1 t 1 ytm tcash flowst where ytm yield to maturity in the previous example a bond with a 1 000 face value five years to maturity and 100 annual coupon payments is worth 927 90 to match a new ytm of 12 the five coupon payments plus the 1 000 maturity value are the bond s six cash flows finding the present value of each of those six cash flows with an interest rate of 12 will determine what the bond s current price should be bond yields are quoted as a bond equivalent yield which adjusts for the bond coupon paid in two semi annual payments in the previous example the bonds cash flows were annual so the ytm is equal to the bey however if the coupon payments were made every six months the semi annual ytm would be 5 979 the bey is a simple annualized version of the semi annual ytm and is calculated by multiplying the ytm by two in this example the bey of a bond that pays semi annual coupon payments of 50 would be 11 958 5 979 x 2 11 958 the bey does not account for the time value of money for the adjustment from a semi annual ytm to an annual rate investors can define a more precise annual yield given the bey for a bond when considering the time value of money in the calculation in the case of a semi annual coupon payment the effective annual yield would be calculated as follows eay 1 ytm 2 2 1 where eay effective annual yield begin aligned text eay left 1 frac text ytm 2 right 2 1 textbf where text eay text effective annual yield end aligned eay 1 2ytm 2 1where eay effective annual yield if an investor knows that the semi annual ytm was 5 979 they could use the previous formula to find the eay of 12 32 because the extra compounding period is included the eay will be higher than the bey a bond rating is a grade given to a bond and indicates its credit quality the rating takes into consideration a bond issuer s financial strength or its ability to pay a bond s principal and interest in a timely fashion there are three bond rating agencies in the united states that account for approximately 95 of all bond ratings and include fitch ratings standard poor s global ratings and moody s investors service 4bond yield calculation issuessome factors skew the calculations in determining a bond s yield in the previous examples it was assumed that the bond had exactly five years left to maturity when it was sold which is rare the fractional periods can be defined but the accrued interest is more difficult to calculate assume a bond has four years and eight months to maturity the exponent in the yield calculations can be turned into a decimal to adjust for the partial year however this means that four months in the current coupon period have elapsed with two remaining which requires an adjustment for accrued interest a new bond buyer will be paid the full coupon so the bond s price will be inflated slightly to compensate the seller for the four months in the current coupon period that have elapsed bonds can be quoted with a clean price that excludes the accrued interest or a dirty price that includes the amount owed to reconcile the accrued interest when bonds are quoted in a system like a bloomberg or reuters terminal the clean price is used 