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Unformatted text preview: p. 5 of 17 B. Term Structure of Interest Rates 1. Yield Curves: {BKM §15.1} Table 1. ANNUAL RATES & YIELDS 17 Jun ‘08 FED Discount 2.25% U.S. Core Inflation 2.30% a) On a given day, one can Federal Funds 2.10% Five year CD 3.85% observe many interest rates. T Bills (6 mo.) 2.35% Fixed 30 yr Mortgage 6.39% It’s not surprising, given the T Notes (5 yr) 3.63% U.S. Prime Rate 5.00% amount of variation in the T Bonds (30 yr) 4.70% Money Market 2.41% default risk, maturity, and TIPS (7 yr) 1.39% Comm. Paper (90 day) 2.52% liquidity of debt security State & Local 4.59% Corporate Aaa 5.68% issues. {Hull §4.1} b) The relationship between YTM and term to maturity, ceteris paribus, is the term structure of interest rates. In order to analyze the term structure, we compare securities in the same risk class (i.e., same DP and LP). We like Treasuries because DP = LP = 0. ry c) Yield curves. Normal 1) Yield curves graph ry against T for a pic Fig. 2 ture of term structure at a given time. Humped 2) Because of interest rate risk (MP), we Flat expect upward sloping (normal) yield Inverted curves. But we often find flat, humped or T even inverted curves. [Fig. 2] 3) 30 JUN 2008 US Treasury yields are shown at right. 2. Using Term Structure to Deduce Forward Interest Rates: {Hull §4.5  4.6; BKM §15.2  15.3} a) Simplifying assumptions for a “pure yield curve.”4 #1 No uncertainty or risk, not even IR risk, on bonds: RP = 0. #2 Bonds are zero coupon pure discount securities. • We get ready made pure yield curve from Treasury strips or “T zeros” if we assume no interest rate risk (MP = 0), because rc = 0 and DP = LP = 0. • We get pure yi = V0e0.06e0.11 = V0e0.17, which is larger. 3) If f2 = 9%, no one would buy the 1 year note in 2008. They would buy the 2 year note to lock in the greater rate of return: • With the 2 year bond, V2 = V0e0.08(2) = V0e0.16 • With rollover, V2 = V0e0.06e0.09 = V0e0.15, which is smaller. f) With “pure yield curves,” the shape of the curve is dictated by the forward rates. 1) The yield curve slopes up if forward rates are rising, and down if they are falling. 2) Let r0(1) ≡ f1 = 6%, f2 = 10%, and f3 = 12%. By the term structure equation: • R0(1) = 6% • 2r0(2) = r0(1) + f2 = 6% + 10% = 16% ⇒ ry(2) = 8% • 3r0(3) = r0(1) + f2 + f3 = 6% + 10% + 12% = 28% ⇒ ry(3) = 9.33% • The yield curve is upward sloping. g) The shape of yield curves, inflationary expectations, and risk free rates. 1) If there is no risk or uncertainty, then the short rate rt = deduced forward rate ft, and both are the risk free rate rf. 2) But risk free rates are not constant over time, because they incorporate an inflation premium IP based on investor expected inflation rates: • r(f)t = r* + E(it), where r* is a “minimum compensatory” interest rate. 3) If expectations E(it) are rising, then r(f)t will be rising and the yield curve slopes up. Ec 174 INTEREST RATE RISK p. 7 of 17 C. Forward Rate Agreements...
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 Winter '08
 Foster,C

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