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topic01_note - EC372 Bond and Derivatives Markets Topic#1...

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EC372 Bond and Derivatives Markets Topic #1: Bond Markets & Fixed Interest Securities R. E. Bailey Department of Economics University of Essex Outline Contents 1 Bonds and bond markets 1 2 Zero-coupon (ZC) bonds 3 2.1 Real ZC bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Coupon-paying bonds 5 3.1 Macaulay Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Valuation of bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Risks of bond portfolios 7 5 Term structure of interest rates 8 5.1 Implicit forward rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6 What determines the term structure? 9 6.1 Pure Expectations Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6.2 Liquidity Preference Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 6.3 Preferred Habitat Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Reading: Economics of Financial Markets , chapters 12, 13 1 Bonds and bond markets What’s special about bonds? A bond’s indenture is a contract that requires the issuer to take specified, deliberate actions typically to make a definite sequence of payments until a specified terminal date unlike equity, for which future payoffs (dividends) are discretionary Bonds are low-risk – the payoffs are contractual – but risk , especially of default , remains! 1
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Most bonds can be summarised by just two numbers: 1. Interest rate – the bond’s yield to maturity 2. Time to maturity – time to the date at which the obligation ceases Understanding bond markets (suggested approach) Central bank fixes the short-term interest rate (monetary policy) Bond yields adjust (via price changes) to balance supply and demand for all bonds. The Unit Time Period While rates of return are conventionally measured at an annual rate, other relevant time intervals need not coincide with a calendar year. Returns may be compounded more or less frequently than once per year, investors may have planning horizons longer or shorter than a year, and they may take the opportunity to revise their decisions many or few times each year. Unless explicitly noted, it should be assumed that the unit time interval corresponds to ‘one year’. The complications that occur when it is necessary to consider intervals of different length will be addressed as they arise. What defines a bond? Maturity date, after which the bond ceases to exist Let T denote the maturity date. If t is ‘today’, n = T - t is the bond’s time to maturity (its ‘life’) Bonds are commonly redeemed at a specified face value, m Callable bonds : issuer can terminate before T Convertible bonds : holders can exchange bond for another asset Perpetuities : no specified maturity date Sinking fund : issuer redeems bonds over an extended period Coupons : a sequence payments from the issuer to the holder c t +1 , c t +2 , . . . , c T , typically constant , c , paid twice per year Coupon rate c/m (typically used to define the coupon) Other sorts of bonds include: Floating rate bonds: coupons linked to another interest rate Index linked bonds: payoffs linked to the price level Timing of coupon payments. Although coupons are almost always expressed at annual rates, their payment is commonly split into instalments, typically made at six-monthly intervals. For example,
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