•1Chapter 9Bond Prices and Yield2/1/2006 FIN 3710 - Investments - Professor Rui Yao 2Debt Classes: Payment Type A security obligating issuer to pay interests and principal to the holder on specified dates,¾ Coupon rate or interest rate, e.g. 4%, 5 3/4%, etc. ¾ Face, par value or principal payment, e.g. $1000¾ Maturity, e.g. 3 month, 1 year, 30 year, etc. Bond can be classified according to its attributes¾ Payment type, e.g. semi-annual coupon¾ Issuer, e.g. government, agency, corporate, etc.¾ Maturity, e.g. short, medium, long, etc.¾ Security, e.g. secured, unsecured, etc.•22/1/2006 FIN 3710 - Investments - Professor Rui Yao 3Debt Classes: Payment Type Pure discount bond or zero-coupon bond¾ No coupon payments prior to maturity¾ Bond’s face value paid at maturity Coupon bond¾ A stated coupon paid periodically prior to maturity.¾ Bond’s face value paid at maturity Perpetual (Consol) bond ¾ A stated coupon paid at periodic intervals forever Self-amortizing bond ¾ Certain amount of principal paid at each period¾ No balloon payment at maturity2/1/2006 FIN 3710 - Investments - Professor Rui Yao 4Debt Classes: Issuers End of Q2:2003•32/1/2006 FIN 3710 - Investments - Professor Rui Yao 5Debt Classes: Corporate Bonds Credit RatingMoody S&P Quality of Issue Aaa AAA Highest quality. Very small risk of default. Aa AA High quality. Small risk of default. A A High-Medium quality. Strong attributes, but potentially vulnerable. Baa BBB Medium quality. Currently adequate, but potentially unreliable. Ba BB Some speculative element. Long-run prospects questionable. B B Able to pay currently, but at risk of default in the future. Caa CCC Poor quality. Clear danger of default . Ca CC High specullative quality. May be in default. C C Lowest rated. Poor prospects of repayment. D - In default. 2/1/2006 FIN 3710 - Investments - Professor Rui Yao 6Source of Risks for Bond Holders Interest rate risk (Market risk)¾ The major factor affecting bond prices¾ The price of bond changes in the opposite direction of interest rate change¾ All bonds are exposed to interest rate risk Inflation risk¾ Inflation reduces purchasing power¾ Partially captured by market interest rate¾ All bonds are exposed to inflation risk, though floating-rate and inflation-indexed ones are to a lesser degree•42/1/2006 FIN 3710 - Investments - Professor Rui Yao 7Source of Risks Credit risk¾ Inability of issuer to pay coupon and/or principal¾ Corporate¾ Emerging market¾ High-yield bonds Liquidity risk¾ Inability to unload position without substantial costs¾ Municipal, corporate, and emerging market bond2/1/2006 FIN 3710 - Investments - Professor Rui Yao 8Bond Pricing Discounted cash flow approach¾ Identify cash flows in coupon and principal payment¾ Apply one discount rate (market interest rate / yield-to-maturity) to discount all future cash flows Quoting conventions for bond coupon rates¾ APR (annual percentage rates) Also called BEY (bond equivalent yields) APR / # of periods per year = rate per-period Convert APR to EAY (effective annual yield)¾ EAY accounts for compounded interest¾ 1+EAY=(1+rate per period)n= (1+APR/n)n•52/1/2006 FIN 3710 - Investments - Professor Rui Yao 9Bond Pricing Bond Value, P¾ C: Coupon per period in dollars¾ r : Interest rate (discount rate) per period¾ Price of a 8% semi-annual coupon 30 year T-bond? F = $1,000, C = $40, T = 60 When market interest rate is 8%, r = 4%, then P =? When market interest rate is 10%, r = 5%, then P =?TTTTttTTrFrrCrFrCrFrCrCrCP)1(])1(11[)1()1()1()1()1()1(12+++−×=+++=++++++++=∑="2/1/2006 FIN 3710 - Investments - Professor Rui Yao 10Bond Pricing Bond price higher if¾ Market interest rate is lower Price converges to par as a bond approaches maturity if market interest rate stays constantCoupon Rate = 8% F = $1,000 C = $40Year T4% 6% 8% 10% 12% 14%1 2 1038.83 1019.13 1000.00 981.41 963.33 945.762 4 1076.15 1037.17 1000.00 964.54 930.70 898.385 10 1179.65 1085.30 1000.00 922.78 852.80 789.2910 20 1327.03 1148.77 1000.00 875.38 770.60 682.1830 60 1695.22 1276.76 1000.00 810.71 676.77 578.82Market Interest Rate (APR)MaturityPremium Bond P > par valueDiscount Bond P < par valuePar Bond P=par value•62/1/2006 FIN 3710 - Investments - Professor Rui Yao 11Bond Yield-to-Maturity Yield to Maturity (YTM)¾ The interest rate (or discount rate) that makes the PVof bond cash flow equal to its price¾ YTM is the “average” return of holding a bond to maturity total return from holding the bond for one period if the market interest rate stays constant YTM is different from current yield ¾ Current yield ignores the capital gain (loss) component of total holding period return (HPR)pricemarketBondcouponAnnualYieldCurrent =2/1/2006 FIN 3710 - Investments - Professor Rui Yao 12Bond Yield-to-Maturity Q: what is the relationship between coupon rate, current yield and ytm? A: It depends on the type of bond¾ 1. premium bondCoupon rate > current yield > ytm¾ 2. par bondCoupon rate = current yield = ytm¾ 3. discount bondCoupon rate < current yield < ytm•72/1/2006 FIN 3710 - Investments - Professor Rui Yao 13YTM vs. Current Yield – An Example Example: What’s YTM of a bond with F = $1,000, C = $40, T = 60, P = $1,276.76 ?¾ We refer rBEYas commonly used YTM¾ Notice the differences/similarities among coupon rate, market interest rate (YTM/APR/rBEY), per-period discount rate r,rEAY, and current yield%09.61)1(%,62%,3)1(000,1)1(4076.276,1)1()1(2606011=−+==×==+++=⇒+++=∑∑==rrrrrrrrFrCPEAYBEYttTTtt2/1/2006 FIN 3710 - Investments - Professor Rui Yao 14Bond Yield-to-Call A callable bond gives the issuer the right to buy back a bond from the investor at a specified price after the protection period¾ Q: When will a firm call its bond?¾ Putable bond; convertible bond Yield-to-Call¾ The discount rate which makes the PV of cash flow up to call date equal to the current price Cash flow includes coupon payment and call price¾ Often used for premium bond•82/1/2006 FIN 3710 - Investments - Professor Rui Yao 15An Example of Yield-to-Call Example: Yield-to-call for a bond with¾ 20 year maturity, 5 year call at $1,050, 9% coupon, priced at P = $1,098.96¾ Implied YTM = 8% ¾ Yield to call: r = 3.72%, rBEY= 7.44%¾ Q: Which yield measure is more relevant to the bond
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