BOND VALUATION AND RISK Outline Start by valuing risk free bonds Zero coupon bonds Bonds that pay coupons Then introduce risk Zero Coupon Bonds Only two cash flows no intermediate coupon payments The bond s market price at the time of purchase The bond s face value at maturity Zero coupon bonds always sells at a discount a price lower than face value For example Treasury Bills are U S government zero coupon bonds with a maturity of up to one year Treasuries are generally regarded as risk free Valuing Zero Coupon Bonds Price of a zero coupon bond FV P 1 YTM n n Yield to maturity The discount rate that sets the present value of the promised bond payments equal to the current market price of the bond Yield to Maturity of an n Year Zero Coupon Bond YTM n FV P 1 n 1 Example YTM for zero coupon bonds Suppose the following zero coupon bonds are trading at the prices shown below per 100 face value Determine the corresponding yield to maturity for each bond Maturity 1 year 2 years 3 years 4 years Price 96 62 92 45 87 63 83 06 Solution YTM for zero coupon bonds Maturity 1 year 2 years 3 years 4 years Price 96 62 92 45 87 63 83 06 YTM n FV P 1 n 1 1 1 YTM1 100 96 62 1 3 50 1 2 YTM 2 100 92 45 1 4 00 1 3 YTM 3 100 87 63 1 4 50 1 4 YTM 4 100 83 06 1 4 75 Coupon Bonds Pays the face value at maturity plus regular coupon interest payment Two types of U S Treasury coupon securities are currently traded in financial markets Treasury notes original maturities from one to ten years Treasury bonds original maturities of more than ten years To compute the yield to maturity of a coupon bond we need to know the coupon payments and when they are paid Example Pricing a coupon bond Consider a five year 1000 bond with a 2 2 coupon rate and semiannual coupons Suppose the bond s yield to maturity is 2 expressed as an APR with semiannual compounding What price is the bond trading for Face value 1 1 1000 P 11 1009 47 1 10 10 0 01 1 01 1 01 Semi annual coupon Premium or Discount Coupon bonds may trade at a discount or at a premium But most issuers of coupon bonds choose a coupon rate so that the bonds will initially trade at or very close to par After the issue date the market price of a bond changes over time With changes to interest rates yields of similar bonds As time to maturity becomes shorter With changes in risk RISKY BONDS Credit Risk Most bonds are risky so their cash flows are not known with certainty E g corporate bonds mortgage bonds etc Some components of credit risk Probability of default How much is lost in default 100 recovery The timing when default is expected happen Valuing Risky Bonds The yield to maturity of a risky bond is not equal to the expected return of investing in the bond For a risky bond a higher yield to maturity does not even necessarily imply that its expected return is higher To value a bond we need to calculate the expected payments and discount the expected payments with the correct discount rate The correct discount rate is an expected return that takes into account the bond s systematic risk Risk and Interest Rates U S Treasury securities are considered risk free All other borrowers have some risk of default so investors require a higher interest rate Interest Rates on Five Year Loans for Various Borrowers March 2009 Example Valuing a risky bond Consider a one year 1000 zero coupon bond There is a 50 chance that the bond will repay its face value in full and a 50 chance that the bond will default and you will receive 900 Thus you would expect to receive 950 Assume that the discount rate expected return is 5 1 What s the price and yield to maturity of this bond The price of the bond is P 950 1 051 903 90 The promised yield to maturity us YTM FV 1 P 1000 1 903 90 1063 Bond Ratings Several companies rate the creditworthiness of bonds Three best known are Standard Poor s Moody s and Fitch These ratings help investors assess creditworthiness But investors should also do their own due diligence Bond Ratings Ratings range from C lowest quality to AAA highest quality Investment grade bonds BBB and higher Speculative bonds BB and lower Also called Junk bonds Cannot be held by many regulated financial institutions The rating depends on the risk of bankruptcy bondholders claim to assets in the event of bankruptcy recovery priority The problem s with credit ratings Ratings have been criticized for Being overly generous leading up to the financial crisis Being overly harsh e g many government bonds have been downgraded Agencies are paid by the issuers Potential conflict of interest Corporations and other bond issuers can choose which agencies to ask to rate them Potential selection bias Ratings are often used in financial regulation which can increase incentives for firms to try to influence their ratings