expected_inflation

# expected_inflation - U NIVERSITY OF E SSEX D EPARTMENT OF E...

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UNIVERSITY OF ESSEX DEPARTMENT OF ECONOMICS EC372 Economics of Bond and Derivatives Markets Nominal Bonds, Real Bonds and Expected Inﬂation This note uses zero-coupon (ZC) bonds to explore the so-called ‘Fisher relationship’ between rates of return and the rate of inﬂation: nominal rate of return = real rate of return + expected rate of inﬂation Strictly, as will be shown below, the relationship should be written (the Fisher relationship is an approximation 1 ): ( 1 + nominal rate of return ) = ( 1 + real rate of return ) × ( 1 + expected rate of inﬂation ) 1. Expected rate of inﬂation Suppose that the prices of goods and services (the ‘price level’) change by a factor Z n between today and n years from now. Then the average annual rate of inﬂation over the coming n years can be deﬁned as the π n that satisﬁes: ( 1 + π n ) n = Z n or π n = Z 1 / n n - 1 (1) For example, if the price level is 1 . 5 times higher in ﬁve years than it is today, then Z 5 = 1 . 5 and the average annual rate of inﬂation over over the coming ﬁve years equals π 5 = ( 1 . 5 ) 1 / 5 - 1 8 . 45%. 2 As of today, the price level at any date in the future cannot be known for sure. Hence, Z n should be interpreted as an expectation (i.e., based on investors’ beliefs – exactly whose beliefs will be discussed later). Bond yields (see Economics of Financial Markets , chapter 12, for details) Two ZC bonds are assumed to exist: nominal ZC bonds and real ZC bonds, both with a maturity n years from today. For example, suppose that n = 5 and the face value of each bond equals m = \$100. Notation (deﬁned below): Spot yields Nominal Real Nominal ZC bond y n y * n Real ZC bond e y n e y * n (Summary: * denotes real yields ; e denotes real bonds .) Nominal ZC bonds : The nominal spot yield on a nominal ZC bond is its yield to maturity , the rate of return that is obtained if the bond is held to maturity. Hence, y n satisﬁes: p n = m ( 1 + y n ) n that is: p 5 = 100 ( 1 + y 5 ) 5 (2) 1 The Fisher relationship is an exact equality if rates of return are

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## This note was uploaded on 03/15/2012 for the course EC 372 taught by Professor R.e.bailey during the Spring '12 term at Uni. Essex.

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expected_inflation - U NIVERSITY OF E SSEX D EPARTMENT OF E...

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