Tài chính doanh nghiệp - Chapter 15: The term structure of interest rates

Chapter 15The Term Structure of Interest RatesThe relationship between yield to maturity and maturity.Information on expected future short term rates can be implied from yield curve.The yield curve is a graph that displays the relationship between yield and maturity.Three major theories are proposed to explain the observed yield curve.Overview of Term StructureYieldsMaturityUpward SlopingDownward SlopingFlat Yield CurvesExpected Interest Rates (Table 15.1)Expected One-Year Rates in Coming Years Year Interest Rate 0 (today) 8% 1 10% 2 11% 3 11%Pricing of Bonds using Expected RatesPVn = Present Value of $1 in n periodsr1 = One-year rate for period 1r2 = One-year rate for period 2rn = One-year rate for period nBond Prices using Expected RatesTime to Maturity Price of Zero* Yield to Maturity 1 $925.93 8.00% 2 841.75 8.995 3 758.33 9.660 4 683.18 9.993* $1,000 Par value zerofn = one-year forward rate for period nyn = yield for a security with a maturity of nForward Rates from Observed RatesExample of Forward Rates using Table 15.24 yr = 9.993 3yr = 9.660 fn = ?(1.0993)4 = (1.0966)3 (1+fn)(1.46373) / (1.31870) = (1+fn)fn = .10998 or 11%Note: this is expected rate that was used in the prior example.Downward Sloping Spot Yield Curve Zero-Coupon Rates Bond Maturity 12% 1 11.75% 2 11.25% 3 10.00% 4 9.25% 5Forward Rates Downward Sloping Y C1yr Forward Rates 1yr [(1.1175)2 / 1.12] - 1 = 0.1150062yrs [(1.1125)3 / (1.1175)2] - 1 = 0.1025673yrs [(1.1)4 / (1.1125)3] - 1 = 0.0633364yrs [(1.0925)5 / (1.1)4] - 1 = 0.063008 ExpectationsLiquidity PreferenceUpward bias over expectationsMarket Segmentation Preferred HabitatTheories of Term StructureExpectations TheoryObserved long-term rate is a function of today’s short-term rate and expected future short-term rates.Long-term and short-term securities are perfect substitutes.Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.Long-term bonds are more risky.Investors will demand a premium for the risk associated with long-term bonds.The yield curve has an upward bias built into the long-term rates because of the risk premium.Forward rates contain a liquidity premium and are not equal to expected future short-term rates.Liquidity Premium TheoryLiquidity Premiums and Yield CurvesYieldsMaturityLiquidity PremiumForward RatesObserved Yield CurveLiquidity Premiums and Yield CurvesYieldsMaturityLiquidity PremiumForward RatesObserved Yield CurveShort- and long-term bonds are traded in distinct markets.Trading in the distinct segments determines the various rates.Observed rates are not directly influenced by expectations.Preferred Habitat:Modification of market segmentationInvestors will switch out of preferred maturity segments if premiums are adequate.Market Segmentation and Preferred HabitatUsing Spot Rates to Price Coupon BondsA coupon bond can be viewed as a series of zero coupon bonds.To find the value each payment is discount at the zero coupon rate.Once the bond value is found, one can solve for the yield.It’s the reason that similar maturity and default risk bonds sell at different yields to maturity.Sample Bonds A BMaturity 4 years 4 yearsCoupon Rate 6% 8%Par Value 1,000 1,000Cash Flow in 1-3 60 80Cash Flow in 4 1,060 1,080Assuming Annual compoundingPrice Using Spot Rates Bond APeriodSpot RateCash FlowPV of Flow1.056057.142.05756053.653.0636049.954.0671,060817.80Total978.54Price Using Spot Rates Bond BPeriodSpot RateCash FlowPV of Flow1.058076.192.05758071.543.0638066.604.0671,080833.23Total1,047.56Solving For Yield to MaturityBond ABond Price 978.54YTM 6.63%Bond BPrice 1,047.56YTM 6.61%