Bond valuation and riskOutlineZero-Coupon BondsValuing Zero-Coupon BondsExample: YTM for zero-coupon bondsSolution: YTM for zero-coupon bondsCoupon BondsExample: Pricing a coupon bondPremium or Discount?Risky bondsCredit RiskValuing Risky BondsRisk and Interest RatesExample: Valuing a risky bondBond RatingsBond RatingsThe problem(s) with credit ratings?BOND VALUATION AND RISKOutline • Start by valuing risk-free bonds — Zero-coupon bonds — Bonds that pay coupons • Then introduce riskZero-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-freeValuing Zero-Coupon Bonds Price of a zero-coupon bond 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: (1 )=+nnFVPYTM1 1= −nnFVYTMPExample: 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 $83.06Solution: YTM for zero-coupon bonds 1/111/221/331/44(100/96.62) 1 3.50%(100/92.45) 1 4.00%(100/87.63) 1 4.50%(100/83.06) 1 4.75%YTMYTMYTMYTM= −== −== −== −=1 1= −nnFVYTMPMaturity 1 year 2 years 3 years 4 years Price $96.62 $92.45 $87.63 $83.06Coupon 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? 10 101 1 100011 1 $1009.470.011.01 1.01P=× − +=Semi-annual coupon Face valuePremium 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 riskRISKY BONDSCredit 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 happenValuing 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 riskRisk 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 • The (promised) yield to maturity us 950 $903.901.051= =P1000 1 1 .1063903.90= −= −=FVYTMPBond 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