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Unformatted text preview: Economics 106V Investments : Lecture Note7 Daisuke Miyakawa UCLA Department of Economics July 11, 2008 7th lecture (note: this lecture is onehour) covers the following items for the further discussion of bond pricing: (1) The concept of yield curve, (2) forward rate, (3) expectation hypothesis, and (6) some other theories for the term structure of interest rate. After discussing those items, we will have a midterm exam. 1 Bond Pricing2 1.1 Yield Curve Recall the following expression for the price of zerocoupon bonds introduced in the previous lecture: P 1 = FV (1+ y 1 ) T ; P 2 = FV (1+ y 2 ) T & 1 ; & & & ; P t = FV (1+ y t ) T & ( t & 1) ; P t +1 = FV (1+ y t +1 ) T & t ; & & & ; P T = FV (1+ y T ) HPR t = P t +1 & P t P t = P t +1 P t ¡ 1 where T : Maturity of the zerocoupon bond P t : The price for a bond at the beginning of period t y t : YTM at the beginning of period t Here, P 1 is the price of a zerocoupon bond which matures in T years from now and y 1 is its YTM over the next T years, both of which are computed at the beginning of year1. Also, P t +1 is the price of a zerocoupon bond which matures in ( T ¡ t ) years from the point (i.e., the term to maturity) and y t +1 is its YTM over the next ( T ¡ t ) years, both of which are computed at the beginning of year ( t + 1) . These represent the evolutions of the price and yield (or YTM) of one speci&c zerocoupon debt, which is illustrated in Figure1. Year Year1 Year2 Year3 YearT Year(T1) P 1 P 2 P 3 P T1 P T YTM=y 1 YTM=y 2 YTM=y 3 YTM=y T1 YTM=y T Figure1: The Evolution of the Price One Annual Debt 1 How can we summarize the prices and yields of debts with di∕erent maturities at a speci&c year? Here, our interest is summarized in Figure2 Year Year1 Year2 Year3 YearT Year(T1) P T,1 P T1,1 P T2,1 P 2,1 P 1,1 YTM=y T,1 YTM=y T1,1 YTM=y T2,1 YTM=y 2,1 YTM=y 1,1 Figure2: The Illustration of Yield Curve as of Year1 The notation in Figure2 is the following: P &; 1 : The year1 price of zerocoupon bond which matures in & years from now y &; 1 : The year1 yield of zerocoupon bond over the next & years As you may guess from the discussion on the last lecture, there are the following relationship between those two objects: P T; 1 = FV (1+ y T; 1 ) T ; P T & 1 ; 1 = FV (1+ y T & 1 ; 1 ) T & 1 ; & & & ; P 2 ; 1 = FV (1+ y 2 ; 1 ) 2 ; P 1 ; 1 = FV 1+ y 1 ; 1 The plot of those yields for a &xed timing (i.e., t = 1 on this example) is called as a yield curve. And the structure of the yield curve is called as a term structure of interest rate. Figure3 illustrates various types of yield curves....
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 Summer '08
 Miyakawa
 Economics, Interest Rates, Yield Curve, Zerocoupon bond

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