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**Unformatted text preview: **2010 Topic 5 Interest Rate theory and Bond Valuation 6-1 Part I I n t e r e s t R a t e T h e o r y 6-2 s D e t e r m i n a n t s o f i n t e r e s t r a t e s s T h e t e r m s t r u c t u r e a n d y i e l d c u r v e s s I n v e s t i n g o v e r s e a s Nominal vs. Real rates r = represents any nominal rate r* = represents the real risk-free rate 6-3 of interest. Like a T-bill rate, if there was no inflation. Typically ranges from 1% to 4% per year. r RF = represents the rate of interest on Treasury securities . Determinants of interest rates r = r* + IP + DRP + LP + MRP quired return on a debt security 6-4 r = required return on a debt security r* = real risk-free rate of interest IP = inflation premium DRP = default risk premium LP = liquidity premium MRP= maturity risk premium Premiums added to r* for different types of debt IP MRP DRP LP S-T Treasury c 6-5 L-T Treasury c c S-T Corporate c c c L-T Corporate c c c c Yield curve and the term structure of interest rates s Term structure relationship between interest rates (or yields) and 5 6 Yield (% ) 6-6 maturities. s The yield curve is a graph of the term structure . s The November 2005 Treasury yield curve is shown at the right. 1 2 3 4 0.25 0.5 2 5 10 30 Maturity (years) Constructing the yield curve: Inflation s Step 1 Find the average expected inflation rate over years 1 to N: 6-7 N INFL IP N 1 t t N = = Constructing the yield curve: Inflation Assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter. IP 1 = 5% / 1 = 5.00% 6-8 IP 10 = [5% + 6% + 8%(8)] / 10 = 7.50% IP 20 = [5% + 6% + 8%(18)] / 20 = 7.75% Must earn these IPs to break even vs. inflation; these IPs would permit you to earn r* (before taxes). Constructing the yield curve: Maturity Risk s Step 2 Find the appropriate maturity risk premium (MRP) . For this example, the following equation will 6-9 be used find a securitys appropriate maturity risk premium. ) 1- t ( 0.1% MRP t = Constructing the yield curve: Maturity Risk Using the given equation: MRP 1 = 0.1% x (1-1) = 0.0% RP 0.1% x (10 ) = 0.9% 6-10 MRP 10 = 0.1% x (10-1) = 0.9% MRP 20 = 0.1% x (20-1) = 1.9% Notice that since the equation is linear, the maturity risk premium is increasing as the time to maturity increases, as it should be. Add the IPs and MRPs to r* to find the appropriate nominal rates Step 3 Adding the premiums to r*. r RF, t = r* + IP t + MRP t 6-11 t Assume r* = 3%, r RF, 1 = 3% + 5.0% + 0.0% = 8.0% r RF, 10 = 3% + 7.5% + 0.9% = 11.4% r RF, 20 = 3% + 7.75% + 1.9% = 12.65% Hypothetical yield curve s An upward sloping yield curve . s Upward slope due 15 Interest Rate (%) Maturity risk premium 6-12 to an increase in expected inflation and increasing maturity risk premium....

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