The Term Structure of Interest Rates CHAPTER 13


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1 The Term Structure of Interest Rates CHAPTER 13
2 Chapter Summary Objective: To explore the pattern of interest rates for differentterm assets. The term structure under certainty Forward rates Theories of the term structure Interpreting the term structure 132
3 Overview of Term Structure of Interest Rates 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 Two major theories are proposed to explain the observed yield curve 133
4 Important Terms Bond yields Spot rates Forward rates Yield curve Term structure or pure yield curve Structure of forward rates Using observed rates to predict future rates 134
5 Yield Curves Yields Upward Sloping Flat Downward Sloping Maturity 135
6 Spot Rates, Bond Pricing and the Yield Curve Spot rates can be found by discounting zerocoupon bonds of various maturities For maturities longer than one year zerocoupon bonds are created artificially, by stripping regular coupon bonds and selling each coupon separately Coupon bonds are priced by discounting each cash flow by the appropriate spot rate The pure yield curveis a plot of the spot rates against their respective maturities 136
7 Table 13.1 Yields and Prices to Maturity on ZeroCoupon Bonds ($1,000 Face Value) 137
8 Figure 13.2 Two 2Year Investment Programs 138
9 Figure 13.3 Short Rates versus Spot Rates 139
10 Summary Reminder Objective: To explore the pattern of interest rates for differentterm assets. The term structure under certainty Forward rates Theories of the term structure Measuring the term structure 1310
11 Forward Rates from Observed Rates (1 + y n n ( 1 + fn) = n 1 (1 + yn 1) f n = oneyear forward rate for period n y n = yield for a security with a maturity of n n n 1 ( 1 + y ) = (1 + y ) (1 + f ) n n 1 n ) 1311
12 Example of Forward Rates using Figure yr = 8.00% 3yr = 7.00% fn =? (1.08) 4 = (1.07) 3 (1+f n ) (1.3605) / (1.2250) = (1+f n ) f n =.1106 or 11.06% Note: this is expected rate that was used in the prior example
13 Downward Sloping Spot Yield Curve ZeroCoupon Rates Bond Maturity 12% % % % %
14 Forward Rates for Downward Sloping Yield Curve 1yr Forward Rates 1yr [(1.1175) 2 / 1.12] 1 = yrs [(1.1125) 3 /(1.1175) 2 ]1 = yrs [(1.1) 4 /(1.1125) 3 ]1 = yrs [(1.0925) 5 /(1.1) 4 ]1 =
15 Uncertainty and Forward Rates Under certainty investors are indifferent between a shortterm bond and a longterm bond sold before maturity, or between one longterm investment and a sequence of rolledover shortterm investments Under uncertainty the strategy whose return does not depend on an unknown future bond price is less risky 1315
16 Summary Reminder Objective: To explore the pattern of interest rates for differentterm assets. The term structure under certainty Forward rates Theories of the term structure Measuring the term structure 1316
17 Theories of Term Structure The Expectations Hypothesis Forward rates are expectations of future short term rates Liquidity Preference Upward bias over expectations 1317
18 Expectations Theory Observed longterm rate is a function of today s shortterm rate and expected future shortterm rates Longterm and shortterm securities are perfect substitutes Forward rates that are calculated from the yield on longterm securities are market consensus expected future shortterm rates 1318
19 Liquidity Premium Theory Longterm bonds are more risky Investors will demand a premium for the risk associated with longterm bonds Yield curve has an upward bias built into the longterm rates because of the risk premium Forward rates contain a liquidity premium and are not equal to expected future shortterm rates 1319
20 Figure 13.4 Yield Curves (with Liquidity Premiums) 1320
21 Figure 13.4 Yield Curves (with Liquidity Premiums) 1321
22 Summary Reminder Objective: To explore the pattern of interest rates for differentterm assets. The term structure under certainty Forward rates Theories of the term structure Interpreting the term structure 1322
23 What does the record say? Yield curves are mostly upwardsloping Liquidity premiums are hard to estimate and may not be constant Inverted yield curves generally point to declining interest rates Steeply rising yield curves are generally interpreted as signaling impending rate increases 1323
24 Figure 13.5 Yield Volatility of Long Term Bonds,
25 Figure 13.6 Yields on LongTerm Versus ShortTerm Government Securities: Term Spread,
26 Forward Rates as Forward Contracts Forward rates are also market interest rates We can contract forward loans by buying and selling zero coupon bonds of varying maturities Suppose f 2 is the forward rate between periods 1 and 2 Then you sell 1+f 2 twoyear zeros for every one year zero that you buy This is a loan arranged today for period 2 at interest rate f
27 Figure 13.7 Engineering a Synthetic Forward Loan 1327
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