Lecture206 - Lecture 6 The Term Structure of Interest Rates...

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Lecture 6 The Term Structure of Interest Rates Math Note: The text is an excellent book, however, it has some shortcomings. In this chapter, the text transforms annual yields to semi-annual yields by dividing the annual yield by 2 rather than y annual = (1+ y (1/n) ) n –1. Note that (1+ y (1/2) ) 2 -1= 2*y (1/2) + y (1/2) 2 ,for typical semi-annual yields approximating semi-annual yields with y annual /2 appears close enough. Unfortunately, even small differences in yields have large effects on the price of bonds as the maturity increases. Example: Recall the bond with a $1000 face value that matures in 10 years. This bond pays a 7% coupon ($35) 6-months from now and every 6-months thereafter until the maturity date. Suppose the annual yield to maturity on this bond is 8%. What is this bonds price? Use the present value formula. P= [a 1 /(1+y)] + [a 2 /(1+y) 2 ] + [a 3 /(1+y) 3 ] +…+ [(M+ a T )/(1+y) T ] Where y is the semi-annual yield to maturity. If we compute y correctly we find y = (1.08) 1/2 –1 = .03923 and P = $942.12. If we use the incorrect approximation y = .08/2, the price of the bond is $932.05. Even the small difference in discount rate of .04 -
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Lecture206 - Lecture 6 The Term Structure of Interest Rates...

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