Renuka Chitnis May 4 14 Section 6 1 Bond Terminologies Chapter 6 Notes Bond is a security sold by governments and corporations to raise money from investors today in exchange for a promised future payment Bond certificate amounts and dates of all payments to be made Maturity date the final repayment date of a bond Term time remaining until the repayment date Face value par value principal amount notional amount of a bond used to compute its interest payments Generally due at the bond s maturity Some bonds also promise additional payments called coupons the promised interest payments of a bond paid periodically until the maturity date of the bond Coupon rate determines the amount of each coupon payment of a bond Coupon rate is expressed as an APR and is set by the issuer and stated on the bond certificate Coupon Payment Coupon Rate x Face Value Number of Coupon Payments per Year Section 6 2 Zero Coupon Bonds o Only two cash flows Zero coupon bonds a bond that makes only one payment at maturity Pay the bond s current market price Then at the maturity date we receive the bond s face value Simplest type of bond Prior to its maturity date the price of a zero coupon bond is ALWAYS less than its face value Investor only receive the face value on maturity date Treasury bills zero coupon bonds issued by the US government with a maturity of up to one year STRIPS Separately Tradable Registered Interest and Principal Securities Zero coupon bonds always trade at a discount a price at which bonds trade that is less than their face value Pure discount bonds zero coupon bonds Yield to Maturity of a Zero Coupon Bond o With zero coupon bonds the price is the cost of the bond o Coupon bond rate of return is the discount rate at which the present value of all future cash flows from the bond equals the price of the bond o Yield to maturity the rate of return of an investment in a bond that is held to its maturity date or the discount rate that sets the present value of the promised bond payments equal to the current market price for the bond o 1 YTM n Face Value 1 n Price Section 6 3 A default free zero coupon bond that matures on date n provides a risk free interest rate equals the yield to maturity on such a bond Yield to maturity of the appropriate maturity zero coupon risk free bond the risk free interest rate Spot interest rates default free zero coupon yields because these rates are offered on the spot at tat point in time Zero coupon yield curve a plot of the yield of risk free zero coupon bonds as a function of the bond s maturity rate Coupon bonds pays investors their face value at maturity Bonds that pay regular coupon interest payments up to maturity when the face value is also paid 2 types of US treasury coupon securities o Treasury notes a type of US treasury coupon security currently traded in financial markets with original maturities from 1 10 years o Treasury bonds which have original maturities of more than 10 ears o Original maturity is the term of the bond at the time it was originally issued Coupon Bond Cash Flows o Return on a coupon bond can come from 2 sources 1 Any different between the purchase price and the principal value 2 Its periodic coupon payments o Yield to maturity of the bond is the single discount rate that equates the present value of the bond s remaining cash flows to its current price o Yield will be a per coupon interval o Yields are typically quoted as APRs so we multiple by the number of coupons per year thereby converting the answer into an APR quote with the same couponing interval as the coupon rate Coupon Bond Price Quote o We can convert any price into a yield and vice versa o Prices and yields are used interchangeably o Yield is independent of the face value Section 6 4 Why Bond Prices Change Zero coupon bonds always trade for a discount so prior to maturity the price is less than the face value Coupon bonds may trade at a discount or at a premium a price at which coupon bonds trade that is greater than their face value Par a price at which coupon bonds trade that is equal to their face value US Treasury sets coupon rates on its notes and bonds in this way After the issue date the market price of a bond generally changes over time for two reasons o 1 As time passes the bond gets closer to its maturity date the present value of the bond s remaining cash flows changes as the time to maturity decreases o 2 Changes in the market interest rates affect the bond s yield to maturity and its price the present value of the remaining cash flows Interest Rate Changes and Bond Prices o If a bond sells at par investors will only get return in the form of coupons Coupon rate will equal yield to maturity o As interests rates in the economy change yields that investors demand also change o If the yield price is 8 and 9 the price of the 8 will lower until it becomes as appealing as the 9 this often means selling it at a discount below par o If a bond trades at a discount the investor will get a return from both receiving the coupons and from receiving a face value that exceed the price paid for the bond As a result if a bond trades at a discount its yield to maturity will exceed its coupon rate o A bond tat pays a coupon can also trade at a premium to its face value trading above par o If the interest rate is low an investor s return from the coupons is diminished by receiving a face value less than the price paid for the bond Thus a bond trades at a premium whenever its yield to maturity is less than its coupon rate Always better to buy at a discount When you buy a bond the price exactly equals the present value of the bond s cash flows so that you earn a fair return o A higher yield to maturity means that investors demand a higher return for investing They apply a higher discount rate to the bond s remaining cash flows reducing their present value and hence the bond s price The reverse holds when interest rates fall o Investors then demand a lower yield to maturity reducing the discount rate applied to the bond s cash flows and raising the price o Therefore as interest rates and bond yields rise bond prices will fall and vice versa o Interest rates and bond prices ALWAYS move in the opposite direction LOOK AT PAGE 157 o If a bond s yield to maturity does not change Then the rate of return of an investment in the bond equals its yield to maturity …