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(L04)TermStruc(f)2

# (L04)TermStruc(f)2 - Lecture 4 The Term Structure of...

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Primbs/Investment Science 1 Lecture 4: The Term Structure of Interest Rates Reading: Luenberger Chapter 4, Sections 1 – 5

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Primbs/Investment Science 2 The Term Structure of The Term Structure of Interest Rates Interest Rates The yield curve Spot and forward rates Term structure explanations Expectation dynamics
Primbs/Investment Science 3 The yield curve Fact: In general, yields on bonds of different maturities are different. (i.e. interest rates are a function of time.) If we plot yield vs. time to maturity for bonds, we call the resulting curve the yield curve. yield time to maturity

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Primbs/Investment Science 4 Plot of yield curve from yahoo.com (9/12/2004)
Primbs/Investment Science 5 Plot of yield curve from yahoo.com (10/4/2005)

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Primbs/Investment Science 6 The yield curve The yield curve is not exactly what we want since there may be coupons, etc. We would really like to know the interest rate on a cash flow at time t, with no intermediate cash flows. t 0
Primbs/Investment Science 7 The Term Structure of The Term Structure of Interest Rates Interest Rates The yield curve Spot and forward rates Term structure explanations Expectation dynamics

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Primbs/Investment Science 8 Spot Rates Interest rates for a specific time are known as spot rates , s t . These spot rates can be quoted as being compounded (i) yearly (ii) m periods per year (iii)continuously When we plot the spot rates vs. time , this is known as the spot rate curve . spot rate time Also known as the term structure of interest rates .
Primbs/Investment Science 9 Present Value and Spot Rates Example: Consider the following cash flow stream -1 2 1 1 -2 x x x x 5% 6% 7% The spot rate curve is 1 2 3 4 When computing present value, the spot rate corresponding to the time of each cash flow must be used for discounting

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Primbs/Investment Science 10 Example Time 0 4 Cash Flow -1 1 Spot Rate 5% 6% 7% 7% 925 . 0
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(L04)TermStruc(f)2 - Lecture 4 The Term Structure of...

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