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A bond's yield refers to the expected earnings generated and realized on a fixed-income investment over a particular period of time, expressed as a percentage or interest rate. The 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 or coupon yield.

Coupon Rate = Annual Interest Payment / Bond Face Value

However, if the annual coupon payment is divided by the bond's current market price, the investor can calculate the current yield of the bond. Current yield is simply the current return an investor would expect if he/she held that investment for one year, and this yield is calculated by dividing the annual income of the investment by the investment’s current market price.

Coupon Rate = Annual Interest Payment / Bond Market Price.

Yield to maturity (YTM) is the overall interest rate earned by an investor who buys a bond at the market price and holds it until maturity. Mathematically, it is the discount rate at which the sum of all future cash flows (from coupons and principal repayment) equals the price of the bond. YTM is often quoted in terms of an annual rate and may differ from the bond’s coupon rate. It assumes that coupon and principal payments are made on time. Further, it does not consider taxes paid by the investor or brokerage costs associated with the purchase.
The formula for calculating YTM is shown below:

In addition to evaluating the expected cash flows from individual bonds, yields are used for more sophisticated analysis. Investors may buy and sell bonds of different maturities to take advantage of the yield curve, which plots the interest rates of bonds having equal credit quality but differing maturity dates.
The slope of the yield curve gives an idea of future interest rate changes and economic activity. Investors may also look for difference in interest rates between different categories of bonds.

A yield spread is the difference between yields on differing debt instruments of varying maturities, credit ratings, issuer, or risk level, calculated by deducting the yield of one instrument from the other -- for example the spread between 5-year AAA corporate bonds and 5-year Gsec. This difference is most often expressed in basis points (bps) or percentage points.

A bond's face, or par value will often differ from its market value. This has to do with several factors including changes to interest rates, a company's credit rating, time to maturity, whether there are any call provisions or other embedded options, and if the bond is secured or unsecured. A bond will always mature at its face value when the principal originally loaned is returned.

Bond prices and yields act like a seesaw: When bond yields go up, prices go down, and when bond yields go down, prices go up. A bond that pays a fixed coupon will see its price vary inversely with interest rates. This is because bond prices are intrinsically linked to the interest rate environment in which they trade for example - receiving a fixed interest rate, of say 8% is not very attractive if prevailing interest rates are 9% and become even less desirable if rates move up to 10%. In order for that bond paying 8% to become equivalent to a new bond paying 9%, it must trade at a discounted price. Likewise, if interest rates drop to 7% or 6%, that 8% coupon becomes quite attractive and so that bond will trade at a premium to newly issued bonds that offer a lower coupon.