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The Term Structure of Interest Rates
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  1. The Term Structure of Interest Rates

  2. Overview of Term Structure of Interest Rates • The relationship between yield to maturity and maturity. • Information on expected future short term rates (short rate) might be implied from the yield curve. (short rate vs. spot (average) rate) • 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.

  3. Spot Rates on Yield Curves Yields Upward Sloping Flat Downward Sloping Maturity

  4. Expected Interest Rates in Coming Years Expected One-Year Short Rates in Coming Years YearInterest Rate 0 (today) 8% 1 10% 2 11% 3 11%

  5. Pricing of Zero Coupon Bonds using Expected Rate PVn = Present Value of $1 in n periods r1 = One-year short rate for period 1 r2 = One-year short rate for period 2 rn = One-year short rate for period n yn= yield for a zero coupon security with a maturity of n

  6. Thus Short rates  Spot rates • But what about the other way around?

  7. 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

  8. Example of Forward Rates 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.

  9. Downward Sloping Spot Yield Curve Zero-Coupon RatesBond Maturity 12% 1 11.75% 2 11.25% 3 10.00% 4 9.25% 5

  10. 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

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

  12. 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.

  13. Liquidity Premium Theory • Long-term bonds are more risky. • Investors will demand a premium for the risk associated with long-term bonds. • The 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.

  14. Liquidity Premiums and Yield Curves Yields Observed Yield Curve Short Rates Liquidity Premium Maturity

  15. Liquidity Premiums and Yield Curves Yields Observed Yield Curve Short Rates Liquidity Premium Maturity

  16. 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.