Bond Prices and Yields nFixed income security qAn arragement between borrower and purchaser qThe issuer makes specified payments to the bond holder on specified dates nFace or par value nCoupon rate qZero coupon bond nIndenture qThe contract between the issuer and the bondholder Bond Characteristics Different Issuers of Bonds nU.S. Treasury qNotes and Bonds qRanging from 10 to 30 years qIn denominations $1.000 or more qMinimum reduced in 2008 to $100 qSemiannual payments q n bod30611_1401 n Accrued Interest and Quoted Bond Prices nQuoted prices are not the prices that investor pay for the bond nQuoted price does not include the interest that accrues between coupon payments dates n Commercial bonds nCorporations qMost of them traded in OTC markets by bond dealers nMunicipalities nInternational Governments and Corporations nInnovative Bonds qFloaters and Inverse Floaters qAsset-Backed qCatastrophe nIndexed Bonds n Figure 14.2 Corporate Bond Listings Innovative Bonds qFloaters and Inverse Floaters nSame as floating-rate bonds nCoupon rate on these bond falls when the general level of interest rates rises qAsset-Backed nIncome from a specified group of assets is used to service the debt nWalt Disney Bonds qCatastrophe nWay how to transfer catastrophe risk in capital market qIndexed bonds nPayments are tied to a general price index or a price of a commodity qTIPS q n Table 14.1 Principal and Interest Payments for Treasury Inflation Protected Security bod30611_t1401 Bond Pricing nRepayments occur months or years in the future qDepend on the future value and present value nNominal risk free rate qReal risk free rate + compensation for expected inflation nNot riskless qAdditional premium nDefault risk, liquidity, taxation, call risk, etc. q nPB = Price of the bond nCt = interest or coupon payments nT = number of periods to maturity ny = semi-annual discount rate or the semi-annual yield to maturity Bond Pricing Ct = 40 (SA) P = 1000 T = 20 periods r = 3% (SA) Price: 10-yr, 8% Coupon (SA), Face = $1,000 nAt a higher interest rate qPV is lower nBond price will fall as market interest rates rise nThe negative shape (Bond Price x Interest Rate) qInverse relationship between prices and yields qAn increase in the interest rate results in a price decline that is smaller than the price gain resulting from decrease in the interest rate nconvexivity Figure 14.3 The Inverse Relationship Between Bond Prices and Yields bod30611_1403 nThe inverse relation between price and yield is a central feature of fixed-income securities nInterest rate fluctuations represent the main source of risk nGeneral rule in evaluating bonds price risk qKeeping all other factors same qThe longer the maturity of the bond, the greater the sensitivity of price to fluctuations in the interest rate q nThis is why short-term T securities are considered to be the safest qFree not only of default risk but also largely price risk Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually bod30611_t1402 Yield to Maturity nA investor considering the purchase of a bond is not quoted qUse bond price, maturity day, coupon payment to infer return offered by the bond over its life nYield to maturity qInterest rate that makes the PV of a bond’s payments equal to its price nThe average rate of return that will be earned on a bond if it is bought now and held until maturity Yield to Maturity nInterest rate that makes the present value of the bond’s payments equal to its price. nSolve the bond formula for r n Yield to Maturity Example 10 yr Maturity Coupon Rate = 7% Price = $950 Solve for r = semiannual rate r = 3.8635% Effective annual yield nAnnualized interest rate on a security computed using compound interest techniques. nThe yield on an investment in one year, taking into account the effects of compounding. nAEY=(1+periodic rate)^period – 1 nNumber of period representing a year nEg. Semiannualy → periods = 2 Effective annual yield nFor example, if one has a fixed-income investment such as certificate of deposit that pays 3% in interest each month, the annual percentage yield is more than 3% because compounding the interest results in a (slightly) higher return each month. n Effective annual yield nIn this example, the annual effective yield is calculated thus: Annual percentage yield = (1.03)^12 - 1 = .43 = 43%, where 1.03 is 1 plus the monthly interest and 12 is the number of times in a year interest is compounded. It is also known as the annual effective yield. nUse for comparison with e.g. bonds with different coupon periods n Yield to Call nYield to maturity qHold till maturity nYield to Call n Figure 14.4 Bond Prices: Callable and Straight Debt bod30611_1404 Example 14.4 Yield to Call n n n n n n nYield to call = = 6,64% nYield to maturity = 6,82% Exp 14_4 Realized Yield versus YTM nReinvestment Assumptions qAll coupons from return realized over life if all coupons are reinvested at an interest rate equal to the bond’s yield to maturity qExample: a 2-year bond, paying 10% coupon once a year nWhen reinvestment rate equal to the 10% qRealized compound return equals yield to maturity qIf not - reinvestment rate risk nChanges in interest rate n n Figure 14.5 Growth of Invested Funds bod30611_1405 Bond Prices Over Time nBond prices are set according to the PV qIf coupon rate > market interest rate nIncome is greater than that available elsewhere in the market nPrice of these bonds above their par values qIf coupon rate < market interest rate nIncome is lower than that available elsewhere in the market nPrice of these bonds under their par values q Holding-Period Return: Single Period nHPR = [ I + ( P0 - P1 )] / P0 nwhere nI = interest payment nP1 = price in one period nP0 = purchase price n Holding-Period Example nCR = 8% YTM = 8% N=10 years nSemiannual Compounding P0 = $1000 nIn six months the rate falls to 7% n P1 = $1068.55 nHPR = [40 + ( 1068.55 - 1000)] / 1000 nHPR = 10.85% (semiannual) nRating companies qMoody’s Investor Service qStandard & Poor’s qFitch nRating Categories qInvestment grade qSpeculative grade Default Risk and Ratings Figure 14.8 Definitions of Each Bond Rating Class bod30611_1408 Junk Bonds nHigh-yield bonds nBefore 1977 – fallen angels nAfter 1977 – original-issue junk nDrexel Burnham Lambert – Michael Milken qNetwork of potential investors into junk bonds nTill 1980’s nCoverage ratios qEarnings to fixed costs qLow or falling – cash flow difficulties nLeverage ratios qDebt-to-equity ratio nLiquidity ratios qCurrent: qQuick (without inventories) nProfitability ratios nCash flow to debt Factors Used by Rating Companies Table 14.3 Financial Ratios and Default Risk by Rating Class, Long-Term Debt bod30611_t1403 nSinking funds qTo help ensure the commitment to spread payment problems over several years nSubordination of future debt qFactor that determine bond safety is total outstanding debt of the issuer nDividend restrictions nCollateral Protection Against Default Default Risk and Yield nYield to maturity and expected yield qMaximum possible yield vs. yield with possibility of default nDefault premiums qTo compensate for the possibility of default qYields compared to ratings qYield spreads over business cycles Figure 14.11 Yields on Long-Term Bonds, 1954 – 2006 bod30611_1411