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The Term Structure of Interest Rates

Key Terms. Term structure of interest ratesYield curveSpot ratePure yield curveForward interest rateLiquidity premiumExpectations hypothesisLiquidity preference theoryTerm premiums. What is a Yield Curve?. A plotting of the set of yields, from 1 year through 40 years to maturity, for a give

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The Term Structure of Interest Rates

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    1. The Term Structure of Interest Rates Business 2039

    2. Key Terms Term structure of interest rates Yield curve Spot rate Pure yield curve Forward interest rate Liquidity premium Expectations hypothesis Liquidity preference theory Term premiums

    3. What is a Yield Curve? A plotting of the set of yields, from 1 year through 40 years to maturity, for a given class of fixed-income securities at one point in time. Vertical axis is Yield to Maturity Horizontal axis is years left to maturity.

    4. April 2006 Rate Structure

    5. Trends in Short, Medium and Long Term Rates April, 2006

    6. Useful Links Bloombergs Bond Yields Bank of Canada Selected Bond Yields Yield Curve dot com

    7. Term Structure of Interest Rates There are theories used to explain the term structure of interest rates Liquidity preference theory Expectations hypothesis Segmentation theory Inflation Premium theory

    8. Expectations Theory The current spot rate is the geometric average of the forward rates expected to prevail over the life of the investment. R1 = spot rate for a one year bond R2 = spot rate for a two year bond f = forward rate 1f2 = forward rate from time 1 to time 2 (1 + R2)2 = (1 + R1)(1 + 1f2) 1f2 = (1 + R2)2 / (1 + R1)

    9. Expectations Theory Obviously, the 1 year spot rate is made up (according to the Fisher Hypothesis) of a real rate of return plus an expected inflation premium. We know the recent rate of inflation (core in the past year has been 2.3%) If the one year spot rate for a zero coupon Government of Canada bond is 4.1% then the real rate of return is: Of course, our estimate of the expected rate of inflation has been naively estimated as the most recent trailing CPI rate of core inflation. Investors (the markets may well be using something else).

    10. Expectations Theory Example: The current spot rate for a one year R1 = spot rate for a one year bond = 4.1% R2 = spot rate for a two year bond = 3.97% f = forward rate 1f2 = forward rate from time 1 to time 2 (1 + R2)2 = (1 + R1)(1 + 1f2) 1f2 = [(1 + R2)2 / (1 + R1)] - 1 =(1+.0397)2 / (1+.041) = [1.080976 / 1.041] 1 = 3.84%

    11. Expectations Theory We can find the implied forward rate for year 2 to 3 as:

    12. Expectations Theory We can find the implied forward rate for year 3 to 4 as:

    13. Expectations Theory Example

    14. Expectations Theory Example

    15. Expectation Theory Sowhy do we care about this theory? How can we use this knowledge? By imputing the implied forward rates we can figure out what the market (the consensus of the smart money managers who dominate activity in the bond market) is forecasting for spot rates and by implication, the markets inflationary expectations. The market is supposed to give us the best unbiased estimate of the future that is the best available information that we have today (if you believe in EMH)

    16. Liquidity Preference Theory Investors require a premium for tying up their investment in bonds over a longer period of time.

    17. Inflation Premium Theory This theory says that risk comes from uncertainty associated with future inflation rates. Though the market may be the best source of an unbiased estimate of future ratesactual rates will no doubt differ from these expectations. The longer the term to maturity of a bondthe greater inflation risk the investor in long bonds will bear. The longer the term to maturity, the greater the inflation riskthe higher the yield to maturity.

    18. Market Segmentation Theory There may be separate supply/demand conditions present at the short, intermediate, or long-term part of the market. These conditions can cause the yield curve to be disjoint

    19. Key Points Understanding the term structure of interest rates and the theories used to explain them can assist you in making a variety of decisions including: Informing bond portfolio strategies Decisions regarding retirement Choice of mortgage financing options, etc.

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