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Chapter 5 - Term Structure of Interest Rates Interest rates vary by maturity of the instrument and by risk characteristics 3 mo T-bill 3 mo Commercial Paper Prime rate 10 yr. T-note 10 year A corporate 10 year Baa corporate 30 yr. fixed rate mortgage 30 yr. Treasury Bond Risk Premium - Feb. 2007 5.15% 5.25% 8.25% 4.79% 5.45% 6.30% 5.80% 4.87% Oct. 2016 0.33% 0.72% 3.50% 1.72% 2.78% 4.34% 3.54% 2.45% difference between the yield on a risky bond and the yield on a U.S. Treasury security of the same maturity We use the yield to maturity of \"on the run\" US Treasury securities as the benchmark rate \"on the run\" = most recently issued Ratings agencies scales Moody's Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa Ca C Standard & Poor's AAA AA+ AA AAA+ A ABBB+ BBB BBBBB+ BB BBB+ B BCCC CC C D Credit Quality Highest quality , least default risk High quality High quality High quality Medium quality Medium quality Medium quality Speculative issue Speculative issue Speculative issue Very speculative Very speculative Very speculative Highest likelihood of default Highest likelihood of default Highest likelihood of default Highest likelihood of default 2 Corporate yields are always higher than US Treasury yields because of risk premium Interest earned on US Treasuries is exempt from state income taxes Any non US Treasury bond is compared to a Treasury bond of the same maturity via Yield Spread = Bond Yield - US Treasury Yield Yield Spread is also called Risk Premiumor Benchmark Spread Comparable maturity Treasury yields are chosen as base rate 3 month Commercial Paper - 3 month TBill = .72 - .33 = .39% or 39 basis points 10 year Baa - 10 year Treasury = 4.34 - 1.72 = 2.62% or 262 basis points A Rated 10 year Municipal Bond Yield = 2.20% Yield Spread = 2.20- 1.72 = .48 3 www.wsj.com Bond Yields TREASURY ISSUES Tuesday, October 11, 2016 Prices and yields for on-the-run Treasurys, or the most recently issued U.S. Treasury securities, for various maturities. Data as of 3 p.m. ET. Maturity Coupon Current price Previous price Change Yield 11/03/16 ... 99.98 99.98 0.001 0.243 01/05/17 ... 99.92 99.92 -0.002 0.335 04/06/17 ... 99.78 99.78 -0.001 0.462 09/14/17 ... 99.40 99.41 -0.008 0.647 09/30/18 0.750 99.77 99.81 -0.039 0.866 09/15/19 0.875 99.59 99.66 -0.070 1.016 09/30/21 1.125 99.19 99.30 -0.117 1.294 09/30/23 1.375 98.66 98.80 -0.141 1.579 08/15/26 1.500 97.66 97.89 -0.234 1.760 08/15/46 2.250 94.88 95.42 -0.547 2.494 Source: Ryan ALM 4 Factors Influencing Yield Spread 1. Type of Issuer U.S. Government U.S. Government Agencies Municipal Governments Credit Market Industrial sector Utility sector Finance sector Non-corporate Foreign Government 2. Issuer's perceived credit worthiness Default risk can vary over time The default risk premium is generally higher during recessions and lower during booms, WHY? 3. Maturity of the bond - Term Structure 4. Liquidity Although liquidity is not rated, liquidity differentials show up as differences in yields Market participants are willing to give up yield for increased liquidity Treasury bonds are the most liquid of all bonds 5. Options written into the bond contract If options are given to issuer (call provision) then purchaser will demand higher yield If options are given to purchaser (put provision or conversion option) then purchaser will accept lower yield Option Adjusted Spread (OAS) = Yield Spread after adjusting (removing) the value of embedded options 5 6. Tax treatment of interest earnings Municipal Bonds yields are smaller than corporate bond yields since municipals are taxfree (state & local and federal income tax free) Consider a bond where: P = F= $10,000 Coupon = 10% i = YTM = 10% Annual coupon payments = $1,000 If this is a municipal bond, the before tax and after-tax yield is 10% since none of the $1,000 annual interest payments is subject to income tax If this bond is a corporate bond, and the bond holder is in the 28% marginal federal income tax bracket, then the bond holder keeps $1,000 (1 - .28)=$720 of the interest and pays $280 in federal income taxes After-Tax Yield = Pre-Tax Yield (1 - Marginal Tax Rate) .072 = .100 (1 - .28) Corp. Bond after-tax yield is 7.2% Muni Bond after-tax yield is 10% The muni bond can offer lower yield and still be competitive Equivalent Taxable Yield= Tax Exempt Yield ( 1Marginal Tax Rate ) 6 Why do bond prices and yields to maturity change? To answer this question it's useful to separate yield to maturity into 2 components: Benchmark and Spread Benchmark is usually the government bond yield with same maturity as bond in question Spread = Bond YTM - Benchmark YTM Benchmark reflects macroeconomic factors such as expected inflation, the business cycle, economic growth and exchange rates between currencies Spread reflects microeconomic factors such as: credit risk, liquidity, tax status, trading in comparable securities The Spread can also be influenced by macroeconomic factors (greater risk during recession, less risk during boom periods) Fixed rate bonds usually use on-the-run government bond of same maturity as benchmark Floating rate notes usually use LIBOR as benchmark If no benchmark exists for a specific bond's maturity, interpolation is used to derive an implied benchmark G-spread = Bond yield -Government bond yield The return for bearing greater risk (credit risk, liquidity risk) Euro denominated corporate bondsare priced over a Euro interest rate swap benchmark rather than a government bond I-spread (interpolated spread) = Bond yield -LIBOR swap rate in currency of same maturity 7 IBM bond maturing October 15, 2018 Coupon 7.625% Spread to benchmark is 57.93 basis points (5 year Treasury bond maturing 7/31/2018 1.375% coupon) G-spread = 51.5 basis points (interpolated to match maturity of T bonds) I-spread = 34.2 basis points compared to LIBOR The LIBOR spread is smaller than the G-spread since 5 year Treasury bond yields were smaller than 5 year LIBOR yields 8 Up to this point, we have used 1 discount rate to discount all the cash flows associated with a bond For a corporate bond, we might have selected a discount rate equal to the yield on a comparable maturity Treasury bond plus a risk premium Bond price = Present value of future cash flows In order to avoid the risk premium issue, consider a 5-year Treasury bond with a 12% coupon The cash flows are as follows Time 1 2 3 4 5 6 7 8 9 10 Cash flow 6 6 6 6 6 6 6 6 6 106 Each cash flow should be discounted by a rate appropriate for the time period in which the cash flows are received What should these interest rates be? Treat the bond as a package of zero coupon instruments The value of the bond should equal the sum of the valuesof the zero coupon instruments If not, it would be possible to make riskless profits by stripping off the coupons and creating a stripped coupon security Find the value of zero coupon Treasury bonds with the same maturity asthe cash flows. These are called spot rates A spot rate is an interest rate on a security that makes a single payment in the future The yield on a zero-coupon bond is considered to be the most accurate representation of a year T interest rate since there is no re-investment risk involved A forward rate is the rate of interest today for a single payment security that will be issued in the future 9 Forward rates can be derived from current spot rates Since there aren't comparable zero coupon Treasuries in the market to match to every cash flow, we must construct a theoretical spot rate curve Only 4 week, 13 week, 26 week and 52 week Treasury issues are zero-coupon We can use the following in construction of the theoretical spot rate curve 1. On the run Treasury issues 2. On the run and off the run Treasury issues 3. All Treasury coupon securities 4. Stripped coupon Treasuries - observed yield are the spot rates Construct 60 semi-annual spot rates ranging from 6 months to 30 years using \"on the run\" Treasury issues On the run Treasury issues - most recently auctioned issues Use the 6 month and one year T-Bills yields since these are zero-coupons Treasury securities with maturities greater than 1 year are coupon bonds For coupon bonds not trading at par, we find the yield necessary to make them trade at par(this is the coupon rate on the bond) The resulting curve is called the par coupon curve www.wsj.com Bond Yields TREASURY ISSUES Tuesday, October 11, 2016 Prices and yields for on-the-run Treasurys, or the most recently issued U.S. Treasury securities, for various maturities. Data as of 3 p.m. ET. Maturity Coupon Current price Previous price Change Yield 11/03/16 ... 99.98 99.98 0.001 0.243 01/05/17 ... 99.92 99.92 -0.002 0.335 04/06/17 ... 99.78 99.78 -0.001 0.462 09/14/17 ... 99.40 99.41 -0.008 0.647 09/30/18 0.750 99.77 99.81 -0.039 0.866 09/15/19 0.875 99.59 99.66 -0.070 1.016 09/30/21 1.125 99.19 99.30 -0.117 1.294 09/30/23 1.375 98.66 98.80 -0.141 1.579 08/15/26 1.500 97.66 97.89 -0.234 1.760 08/15/46 2.250 94.88 95.42 -0.547 2.494 10 \"On the run\" issues available are: 6 month, 1 year, 2, 3, 5, 7, 10 and 30 year maturities These are listedin the following table One method of estimating the missing maturities is linear interpolation: Yield at higher maturityYield at lower maturity Number of semiannual periods between the maturity points+1 Period Year 1 .5 2 1.0 3 1.5 4 2.0 5 2.5 6 3.0 7 3.5 8 4.0 9 4.5 10 5.0 11 5.5 12 6.0 13 6.5 14 7.0 15 7.5 16 8.0 17 8.5 18 9.0 19 9.5 20 10.0 .015 . . . 60 30.0 On the run Issues .00462 .00647 .006985 .0075 .008125 .00875 .009375 .01 .010625 .01125 These are coupon rates .01375 .0225 For the 1.5 year maturity .0075.00647 =.000515 .00647 + .000515 = .006985 2 For the 2.5 year maturity .00875.00757 =.000625 .0075 + .000625 = .008125 2 For maturities 3.5 to 4.5 .01125.00875 =.000625 4 Problems 1. Wide gaps between 10 and 30 year 11 2. Yields for \"on the run\" issues are understated since they offer financing opportunities in the REPO market (higher liquidity) 12 Par Coupon Curve Period Year 1 .5 2 1.0 3 1.5 4 2.0 5 2.5 6 3.0 7 3.5 8 4.0 9 4.5 10 5.0 On the run Issues .00462 = z1 .00647 = z2 .006985 .0075 .008125 .00875 .009375 .01 .010625 .01125 1. Find the Cash Flows .5 year .006985 x 100 x .5 = .34925 1 year .006985 x 100 x .5 = .34925 1.5 year .006985 x 100 x .5 + 100 =100.34925 2. Find Present Value of Cash Flows .34925 .34925 100.34925 PV = + + 3 1+ z1 (1+ z 2)2 (1+ z 3) Use of the 6-month and 1-year spot rates for z 1 and z2 z1 = .00462 / 2 = .00231 z2 = .00647 / 2 = .003235 .34925 .34925 100.34925 PV = + + =100 2 3 1.00231 1.003235 (1+ z 3) Since the price of the 1.5 year coupon bond from the Par yield Curve is 100, the PV above must = 100 Solve this equation for z3 100=.3484451+.3470013+ 99.3045536= 100.34925 3 (1+ z 3 ) 100.34925 3 (1+z 3) (1 + z3)3 = 1.01052013 1+z3 = 1.010520131/3 = 1.003494483 z3 = .003494483 is the half year spot rate multiply by 2 to get annual spot rate for 1.5 year maturity (.006988966) 13 Once we have the Par Yield Curve, we use Bootstrapping to find the Theoretical Spot Rate Curve BOOTSTRAPPING Suppose the Par Yield Curve is as follows: Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 YTM=Coupon Rate(%) 5.25 5.50 5.75 6.00 6.25 6.50 6.75 6.80 7.00 7.10 7.15 7.20 7.30 7.35 7.40 7.50 7.60 7.60 7.70 7.80 The 6 month and 1 year yields are spot rates since these issues are zero-coupon Given these 2 spot rates we can find the spot rate for the theoretical 1.5 year zero-coupon Price = Present Value of 3 cash flows from the 1.5 year coupon Treasury (period 3) 14 1. Find the Cash Flows .5 year .0575 x 100 x .5 1 year .0575 x 100 x .5 1.5 year .0575 x 100 x .5 + 100 = 2.875 = 2.875 =102.875 2. Find Present Value of Cash Flows 2.875 2.875 102.875 PV = + + 1+ z 1 (1+ z 2)2 (1+ z 3)3 Use of the 6-month and1-year spot rates for z 1 and z2 z1 = .0525 / 2 = .02625 z2 = .055 / 2 = .0275 2.875 2.875 102.875 PV = + + =100 1.02625 (1.0275)2 (1+ z 3 )3 Since the price of the 1.5 year coupon bond from the Par yield Curve is 100, the PV above must = 100 Solve this equation for z3 100=2.801461+2.723166+ 94.47537= 102.875 3 (1+ z3 ) 102.875 3 (1+ z 3) (1+z3)3 = 1.088908 z3 = .0287987 Doubling this value gives the theoretical spot rate for the 1.5 year maturity (.057596) Given this rate we can now find the 2 year spot rate .5 year .06 x 100 x .5 = 3.00 1 year .06 x 100 x .5 = 3.00 1.5 year .06 x 100 x .5 = 3.00 2.0 year .06 x 100 x .5 + 100 =103.00 PV = 3.00 3.00 3.00 103.00 + + + =100 2 3 1.0265 (1.0275) (1.0287987) (1+ z 4) 4 91.48011= 103.00 (1+ z 4 )4 (1+z4)4 = 1.125927 z4 = .030095 Doubling this value gives the theoretical spot rate for the 2 year maturity (.06019) 15 Continuation of this process results in the Theoretical Spot Rate Curvebelow Theoretical Spot Rate Curve Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 SpotRates(%) 5.25 5.50 5.76 6.02 6.28 6.55 6.82 6.87 7.09 7.20 7.26 7.31 7.43 7.48 7.54 7.67 7.80 7.79 7.93 8.07 One could use yields from the zero coupon Treasury market instead of going through the complicated procedure just described, but this also has problems 1. The coupon bond market has greater liquidity than the strips market The strip yields contain a liquidity premium 2. The tax treatment of strips is different from coupon bonds The accrued interest on strips is taxed The yield on strips reflects the tax disadvantage 3. Foreign tax authorities allows advantageous treatment of strips Foreign investors are willing to accept lower yield on strips since their governments allow the difference between maturity value and purchase price as a capital gain which is taxed at lower rates than interest income The theoretical spot rate curve is the correct Treasury yield curve Use the Theoretical Spot Rate Curve to properly value bonds instead of discounting all the cash flows by one discount rate 16 Theoretical value of the 10 year Treasury = $115.429 if the issue is purchased and stripped Here, we are using the theoretical spot rates to present value the cash flows on the 10-year 10% Treasury bond 17 If one used the yield curve YTM of 7.8% as the discount rate for the 10-year bond Value of a 10-year 10% Treasury Bond (PAR=100) using a 7.8% discount rate Period Year Cash PV 1 0.5 5 4.81232 2 1.0 5 4.631684 3 1.5 5 4.457829 4 2.0 5 4.290499 5 2.5 5 4.129451 6 3.0 5 3.974447 7 3.5 5 3.825262 8 4.0 5 3.681676 9 4.5 5 3.543481 10 5.0 5 3.410472 11 5.5 5 3.282457 12 6.0 5 3.159246 13 6.5 5 3.04066 14 7.0 5 2.926526 15 7.5 5 2.816675 16 8.0 5 2.710948 17 8.5 5 2.60919 18 9.0 5 2.511251 19 9.5 5 2.416989 20 10.0 105 48.85155 115.0826 If this bond sold for $115.0826, we could buy the bond, strip it, and sell the zero coupon bonds for $115.429. We would make an arbitrage profit of $.3464 per $100 of par If you purchase $10,000,000 of these bonds stripped them and sold them, you would make a $34,640 profit This process would cause the price of the security to increase. Arbitrage would cease when the price became $115.429 Arbitragewould push the price to its correct value(where the cash flows are discounted by the theoretical spot rates) The theoretical Treasury Spot ratesare the correct base rates to use along with a risk premium to value a non-Treasury bond 18 Yield Curves - plot yield to maturity v. term to maturity for securities with same risk profile US Treasury yield curve plots Treasury YTM v. Term to maturity Swap yield curve shows fixed LIBOR swap rates v. Term to maturity Yield curves are typically upward sloping since long term bonds are riskier than short term bonds Calculate a constant yield spread over the government spot rate curve Z-spread = zero volatility spread The Z-spread for the IBM bond was 42.5 bp The Z-spread over the benchmarks calculated from the following: PV = PMT PMT PMT + FV + +. ..+ 1 2 (1+ z 1+ Z ) (1+ z 2+ Z) (1+ z n + Z)n z1, z2, . . . zn are spot rates from Treasury yield curve Z is Z-spread per period and is same for all time periods OAS = Option Adjusted Spread on callable bond = Z-spread - Option value in bp Example 6% corporate bond with annual coupons 4% government bond annual coupons 2 years to maturity 2 years to maturity P = 100.125 P = 100.75 1 year and 2 year gov't spot rates z1 = .0210 z2 = .03635 Find YTM for Corp. and Govt. bond a) Find G-spread 232.7 bp 19 b) Find Z-spread We need to solve the following equation for Z 100.125= 6 106 + 1 (1.0210+ Z) (1.03635+ Z)2 Use Solver in EXCEL Put =(6/(1.021+A13))+(106/(1.03635+A13)^2) Put guess for Z in A13 Click on Solver Set objective $A$12 To Value of 100.125 by changing variable cells $A$13 in cell A12 Click Solve Z = .023422 or 234.22 bp The price of the corporate bond is the PV of its cash flows discounted at: .021+.023422 = .044422 and .03635+.023422 = .059772, respectively 100.125= 6 106 + 1 2 (1.044422) (1.059772) 20 Term Structure of Interest Rates Investor with a 1 year horizon has 2 alternatives 1. Buy a 1 year bond 2. Buy a 6 month bond and when it matures buy another 6 month bond The 1 year spot rate is known (z2) The 6 month spot rate is known (z1) The 6 month spot rate 6 months from now is unknown; this is called a forward rate (f) f is the 6 month rate 6 months from now that makes the investor indifferent between alternatives 1 & 2 Total $ at end of 12 months (1 + z2)2 1 + z1 100(1 + z2)2 1 + f1 t t+6 months 100(1 + z1)(1 + f1) t+12 months For the investor to be indifferent between the 2 alternatives, the following must hold: 100(1 + z1)(1 + f1) = 100(1 + z2)2 (1 + f1) = 100(1 + z2)2 / 100(1 + z1) f 1= (1+ z 2)2 1 (1+ z 1) Doubling f1 gives the bond equivalent yield The theoretical spot rates shown above are: z1= .0525 / 2 = .02625 z2 = .055 / 2 = .0275 f 1= (1.0275)2 1=.028751523 (1.02625) 2f1 = .057503046 To Maximize Return If f = .0575 then we are indifferent between the 2 alternatives If f .0575 then invest in 6 month bond & reinvest proceeds in another 6 month bond 21 In general, the relationship between a t-period spot rate, the current 6 month spot rate and the 6 month forward rates is: zt = [(1 + z1)(1 + f1)(1 + f2)(1 + f3) . . . (1 + ft-1)]1/t - 1 f1 embodies the market's expectation for the future 6 month rate six months from now f2 embodies the market's expectation for the future 6 month rate 12 months from now f3 embodies the market's expectation for the future 6 month rate 18 months from now . . . How well do forward rates do at predicting future interest rates? Not very well Future interest rates are difficult to predict Treasury Yield Curve - Plot YTM v. Term to Maturity This is known as the Term Structure of Interest Rates 6 5 4 Yield to Maturity 3 9/21/2006 9/22/2008 9/22/2015 9/22/2016 2 1 0 1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr 30 yr Term to Maturity 22 The relationship between yields and maturity varies over time Usually the yield curve is upward sloping (2008, 2015, 2016) Occasionally we observe an inverted yield curve (2006) Why does the slope of the yield curve vary over time? Empirical facts that term structure theories must explain 1. Interest rates on bonds of different maturities move together over time 2. When short-term rates are low, the yield curve is likely to be upward sloping. When short- term rates are high, the yield curve is likely to be downward sloping. 3. Yield curves almost always slope upward. Theories of the Term Structure 1. Expectations Theory - Assumption: Bond buyers have no preference about maturity They are indifferent between holding short term or long term bonds Implication: Investors care only about expected return Since investors hold both long term and short term bonds, they must expect the same return on long bonds as they do on short bonds Long-term bond yield = Average of short-term rates that people expect to occur over the life of the long term bond Consider an investment of $1 z1 = interest rate today on a one-period bond f1 = expected interest rate on a one-period bond next period z2 = interest rate today on a two-period bond You have 2 investment choices 1. You invest $1 in a two-period bond and hold it for two periods Your expected yield is:z2 2. You invest $1 in a one-period bond today. When it matures, you purchase another one-period bond Your expected yield is: [(1 + z1) (1 + f1)]1/2 - 1 23 eg. 5 period time horizon Investors are indifferent between (1) holding 5-period bond (2) holding5 1-period bonds, 5 years in a row as long as expected return is same a) Assume that 1-periodforward yields are expected to be:f 1=.06, f2=.07, f3=.08, f4=.09over the next 4periods and that the present 1-period yield is z 1 = .05 If the expectations theory is correct then 1 /2 2-year bond must yield z 2=[ ( 1.05 ) ( 1.06 ) ] 1=.05499 1/ 3 3- year bond must yield z 3=[ ( 1.05 ) ( 1.06 ) (1.07 ) ] 1=.05997 4- year bond must yield z 4=[ (1.05 )( 1.06 )( 1.07 ) (1.08)]1 /4 1=.06494 5-year bond must yield 1 /5 z 5=[ ( 1.05 ) ( 1.06 ) (1.07 )( 1.08 )( 1.09 ) ] 1=.0699 The yield curve will slope upwards b) Suppose short rates are expected to fall by 1% per year in the future f1=.04, f2=.03, f3=.02, f4=.01 z1 = .05 If the expectations theory is correct then z 2=[ ( 1.05 ) ( 1.04 ) ]1 /21=.04499 z 3=[ ( 1.05 ) ( 1.04 ) ( 1.03 ) ]1/ 31=.03997 z 4 =[ ( 1.05 ) ( 1.04 ) ( 1.03 ) (1.02)]1/ 41=.03494 1/ 5 z 5=[ ( 1.05 ) ( 1.04 ) ( 1.03 )( 1.02 ) ( 1.01 ) ] 1=.0299 The yield curve will slope downwards c) Suppose short rates are expected to rise then fall in the future f1=.07, f2=.09, f3=.07, f4=.05 z1 = .05 If the expectations theory is correct then 1 /2 z 2=[ ( 1.05 ) ( 1.07 ) ] 1=.05995 1 z 3=[ ( 1.05 ) (1.07 )( 1.09 ) ] 3 1=.069875 z 4=[ (1.05 )( 1.07 )( 1.09 ) (1.07)]1 /4 1=.069907 z 5=[ ( 1.05 ) ( 1.07 ) (1.09 )( 1.07 ) ( 1.05 ) ]1 /51=.065895 The yield curve will have both upward and downward sloping portions 24 8 7 6 5 Yield to Maturity 4 3 2 1 0 1 2 3 4 5 Term to Maturity Does the Expectations theory explain the 3 empirical facts? Empirical fact 1 and 2 are explained by the theory. Empirical fact 3 is not. Since yield curves are usually upward sloping, expected future short term rates would usually be expected to rise in the future. But future short term rates are just as likely to fall as rise Therefore the theory suggests that the typical yield curve should be flat 2. Segmented Markets Theory Bonds of different maturities are not perfect substitutes People prefer bonds of a given maturity to another maturity There is a market for 1-year bonds, 2-year bonds, . . . 30-year bonds Different yield curve patterns are accounted for by differing supply and demand conditions in markets of various maturities. Generally, people prefer short-term bonds since they have less risk. Short term bonds have higher demand than long term bonds which implies higher prices and lower interest rate for short term bonds than long term bonds. The theory predicts that yield curves will usually be upward sloping (fact 3) Problem: Theory cannot explain facts 1 and 2 Since bond markets are segmented, there is no reason why a change in the rate for bonds of one maturity should influence bonds of another maturity. 25 It cannot explain why bonds of differing maturities move together. Neither can it explain empirical fact 2 since it is unclear how demand and supply for long versus short-term bonds change with the level of short-term interest rates P i P i S P30 i30 S P1 i1 D D One Year Market 3. 30 Year Market Liquidity Premium Theory Bonds of different maturities are substitutes but not perfect substitutes Investors prefer short-term bonds to long-term bonds. If investorsare to assume the risk associated with the long-term bond, they must be compensated for the risk. Interest rates on a long-term bond will equal the average of short term rates expected to occur over the life of the long-term bond plus a liquidity premium that responds to supply and demand conditions for that bond This is a combination of the first two theories The interest rate on an n period bond zt ={[(1 + z1)(1 + f1)(1 + f2)(1 + f3) . . . (1 + ft-1)]1/t- 1} + Lt whereLt is a liquidity premiumon the t period bond Ltincreases with the term to maturity This theory explains all 3 empirical facts. 1. Rates on bonds of different maturities move together over time, as was the case with the expectations hypothesis. 26 2. When short-term rates are low the yield curve is upward sloping When short- term rates are high, the yield curve slopes downward. 3. Yield curves typically slope upward since Lnttypically rises with maturity n. The yield curve can slope downward if rates are expected to drop so much that the drop dominates the liquidity premium FIN 423 / MBA 623 Fall 2016 Project 1 DUE November 7 This project involves construction of the theoretical spot rate curve from \"on the run\" U.S. Treasury securities on Friday October 28, 2016. Data concerning the \"on the run\" securities is shown below. 1. First, construct the par coupon curve for each maturity between 6 months and 5 years. Create a table with the maturities and the par coupon values. 2. From the par yield curve, use bootstrapping to construct the theoretical spot rate curve. Create a table with the spot rates for each maturity between 6 months and 5 years. 3. Using the spot rates in part 2, find the price of a 5 year Treasury security with a 2% coupon. Attach and email me an EXCEL spreadsheet that shows your calculations for each of the above. Clearly label your answers for each part. Bond Yields TREASURY ISSUES Friday, October 28, 2016 Prices and yields for on-the-run Treasurys, or the most recently issued U.S. Treasury securities, for various maturities. Data as of 3 p.m. ET. Maturity Coupon Current price Previous price Change Yield 11/25/16 ... 99.99 99.99 0.001 0.162 01/26/17 ... 99.93 99.93 0.002 0.284 04/27/17 ... 99.76 99.76 0.004 0.483 10/12/17 ... 99.38 99.37 0.007 0.652 10/31/18 0.750 99.78 99.73 0.047 0.861 10/15/19 1.000 99.98 99.90 0.078 1.008 10/31/21 1.250 99.64 99.58 0.063 1.325 10/31/23 1.625 99.92 99.87 0.055 1.637 08/15/26 1.500 96.91 96.94 -0.031 1.847 08/15/46 2.250 92.48 92.77 -0.281 2.615