tailieunhanh - Lecture Investments (6/e) - Chapter 15: The term structure of interest rates

In this chapter we explore the pattern of interest rates for different-term assets. We attempt to identify the factors that account for that pattern and determine what information may be derived from an analysis of the so-called term structure of interest rates, the structure of interest rates for discounting cash flows of different maturities. | Chapter 15 The Term Structure of Interest Rates The 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 Structure Yields Maturity Upward Sloping Downward Sloping Flat Yield Curves Expected Interest Rates (Table ) Expected One-Year Rates in Coming Years Year Interest Rate 0 (today) 8% 1 10% 2 11% 3 11% Pricing of Bonds using Expected Rates PVn = Present Value of $1 in n periods r1 = One-year rate for period 1 r2 = One-year rate for period 2 rn = One-year rate for period n Bond Prices using Expected Rates Time to Maturity Price of Zero* Yield to Maturity 1 $ 2 3 4 * $1,000 Par value zero fn = one-year forward rate for period n yn = yield for a security with a maturity of n Forward | Chapter 15 The Term Structure of Interest Rates The 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 Structure Yields Maturity Upward Sloping Downward Sloping Flat Yield Curves Expected Interest Rates (Table ) Expected One-Year Rates in Coming Years Year Interest Rate 0 (today) 8% 1 10% 2 11% 3 11% Pricing of Bonds using Expected Rates PVn = Present Value of $1 in n periods r1 = One-year rate for period 1 r2 = One-year rate for period 2 rn = One-year rate for period n Bond Prices using Expected Rates Time to Maturity Price of Zero* Yield to Maturity 1 $ 2 3 4 * $1,000 Par value zero fn = one-year forward rate for period n yn = yield for a security with a maturity of n Forward Rates from Observed Rates Example of Forward Rates using Table 4 yr = 3yr = fn = ? ()4 = ()3 (1+fn) () / () = (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 2 3 4 5 Forward Rates Downward Sloping Y C 1yr Forward Rates 1yr [()2 / ] - 1 = 2yrs [()3 / ()2] - 1 = 3yrs [()4 / ()3] - 1 = 4yrs [()5 / ()4] - 1 = Expectations Liquidity Preference Upward bias over expectations Market Segmentation Preferred Habitat Theories of Term Structure Expectations Theory Observed 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 .