The Term Structure of Interest Rates Chapter 15 The Term Structure of Interest Rates

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 Three major theories are proposed to explain the observed yield curve

Yield Curves Yields Maturity Upward Sloping Downward Sloping Flat

Expected Interest Rates in Coming Years (Table 15.1) 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

Long-Term Rates and Bond Prices using Expected Rates Time to Maturity Price of Zero* Yield to Maturity 1 $925.93 8.00% 2 841.75 8.995 3 758.33 9.660 4 683.18 9.993 * $1,000 Par value zero

Forward Rates from Observed Long-Term Rates fn = one-year forward rate for period n yn = yield for a security with a maturity of n

Example of Forward Rates using Table 15.2 Numbers 4 yr = 9.993 3yr = 9.660 fn = ? (1.0993)4 = (1.0966)3 (1+fn) (1.46373) / (1.31870) = (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 11.75% 2 11.25% 3 10.00% 4 9.25% 5

Forward Rates for Downward Sloping Yield Curve 1yr Forward Rates 1yr [(1.1175)2 / 1.12] - 1 = 0.115006 2yrs [(1.1125)3 / (1.1175)2] - 1 = 0.102567 3yrs [(1.1)4 / (1.1125)3] - 1 = 0.063336 4yrs [(1.0925)5 / (1.1)4] - 1 = 0.063008

Theories of Term Structure Expectations Liquidity Preference Upward bias over expectations Market Segmentation Preferred Habitat

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 short-term rates

Liquidity Premium Theory Long-term bonds are more risky Investors will demand a premium for the risk associated with long-term bonds Yield curve has an upward bias built into the long-term rates because of the risk premium Forward rates contain a liquidity premium and are not equal to expected future short-term rates

Liquidity Premiums and Yield Curves Yields Observed Yield Curve Forward Rates Liquidity Premium Maturity

Liquidity Premiums and Yield Curves Yields Observed Yield Curve Forward Rates Liquidity Premium Maturity

Market Segmentation and Preferred Habitat Short- and long-term bonds are traded in distinct markets Trading in the distinct segments determines the various rates Observed rates are not directly influenced by expectations Preferred Habitat Modification of market segmentation Investors will switch out of preferred maturity segments if premiums are adequate