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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online