Lecture_17-spring

Lecture_17-spring - The Term Structure of Interest Rates...

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The Term Structure of Interest Rates

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Review of Last Lecture
t t t w CF y ice = + ( ) 1 Pr t w t D T t = × = 1 CF CashFlow for period t t = Duration: Calculation Duration is the weighted average of the times until each payment. The weights are equal to the fraction of the price received at different points in time (they sum to 1).

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We can use duration to measure the sensitivity of the bond price to changes in yield to maturity. There is a close relation between price changes and the bond’s modified duration D*. The percentage change in the bond price is the product of modified duration and the bond’s change in yield. P/P = -D x [ (1+y) / (1+y)]= -D x [ y / (1+y)] D * = modified duration Defining D * = D / (1+y) P/P = - D * x y Modified Duration
Term Structure of Interest Rates We can look at the yield to maturity of bonds of different maturity. Plotting ytm against maturity gives the yield curve. • The ytm on short term bonds (T-bills) is often called the short rate. • Differences in ytm may be related to market expectations about future short rates.

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Figure 15.1 Treasury Yield Curves
Shape of the Yield Curve A upward-sloping yield curve is one in which longer maturity bonds have a higher yield compared to shorter- term bonds due to the risks associated with time. An inverted yield curve is one in which the shorter-term yields are higher than the longer-term yields, which can be a sign of upcoming recession. A flat, or humped) yield curve is one in which the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition. The slope of the yield curve is also seen as important: the greater the slope, the greater the gap between short- and long-term rates. 7

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Yield Curve The yield curve is a graph that displays the relationship between yield and maturity. Pure yield curve Curve for zero-coupon treasury bonds (strips) On-the-run yield curve Yield for recently issued coupon bonds selling at par value 9

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Expected Future Short rates What might determine the shape of the yield curve: Assume that everybody in the market knows that the one year interest rates (the interest rate for one year investments) for the coming years will be: year interest rate 0-1 (today) 5% 1-2 4.5% 2-3 4.4% 3-4 4.2%
Pricing of Bonds We can use these interest rates to find the present value of \$1000 in 1, 2, 3, and 4, years. • In 4 years: PV=\$1000/[(1+r1)(1+r2)(1+r3)(1+r4)] • PV=\$1000/(1.05*1.045*1.044*1.042) = 837.77 • We can calculate bond prices and yields to maturity on 1, 2, 3, and 4 year zero-coupon bonds. • Yields to maturity on zero-coupon bonds are sometimes called spot rates

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Prices & ytm using expected rates Time to maturity price of zero yield to maturity 1 \$952.38 5.00% 2 \$911.37 4.75% 3 \$872.96 4.633% 4 \$837.77 4.525% • These are prices of zero coupon bonds with par value equal to \$1,000.
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This note was uploaded on 04/17/2008 for the course ECON 171A taught by Professor Yusim during the Spring '08 term at Brandeis.

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Lecture_17-spring - The Term Structure of Interest Rates...

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