Interest Rate Risk

Interest Rate Risk - Econ 174 FINANCIAL RISK MANAGEMENT...

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Econ 174 – FINANCIAL RISK MANAGEMENT LECTURE NOTES Foster, UCSD October 16, 2011 INTEREST RATE RISK A. Bond Yields, Risk, and Duration [Review] 1. Bonds and Fixed-Income Securities: a) Fixed-income securities -- medium and long-term bonds or debt instruments involving a promise to pay a certain fixed amount (principal) to the holder at a certain future date (maturity), often with fixed “coupon” interest payments along the way. b) Basic bond value equation and definitions. 1) Annual interest I = r c M. Most bonds pay semi-annually ($I/2 every 6 months). 2) Yield to maturity r y is the discount rate that equates DCF with current price B 0 . It is like the annual rate of return on the bond. 3) Basis point -- 1/100 of a percentage point; if the interest rate rises from 4.0% to 4.5%, it has increased by 50 basis points. 2. Yield to Maturity: 1 a) YTM -- pure discount bonds (“zeros”). 1) If B 0 will grow to M in T years, YTM is found by solving the following for r y : M = B 0 (1+r y ) T Ln(1+r y ) = Ln(M/B 0 )/T = γ, 1+r y = e γ 2) Numerical example. B 0 = $887, M = $1,000, T = 34 months (2.83 years) γ = Ln(1000/887)/2.83 = 0.0423, e 0.0423 = 1.0432, r y = 4.32% b) YTM -- semi-annual coupon interest. 1) If the bond pays $I/2 every 6 months, a financial calculator finds r/2 solving the following equation using an iterative algorithm, then reports r y = 2 (r/2): B 0 = I × PVA r/2,2T + M/(1+r/2) 2T 2) Numerical example. Given: B 0 = $982, M = $1,000, I = $30 per 6 months, T = 15 years Using E XCEL , r y = 6.186%. c) r y = compound annual rate of return on investment of $B 0 if bond held to maturity . 1) This is easy to see with zero coupon bonds. 1 See the Appendix for E XCEL spreadsheet formulas to compute YTM, accrued interest, and bond duration. Bond Notation B 0 current price of bond ($) M par or face value (usually $1,000) T term to maturity (years) r c coupon interest rate (%/yr) I annual coupon interest ($) r y yield to maturity (YTM, %/yr) T y y y r M I r I r I B ) 1 ( ) 1 ( ) 1 ( 2 0 + + + + + + + =
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Ec 174 INTEREST RATE RISK p. 2 of 21 2) It is only true with coupon bonds if the bondholder reinvests each future coupon payment at today’s r y . 3. Bond Prices: a) Initial issue bond pricing and convergence to M. 1) Before 2008, there were 10-12 new corporate bond issues every day. Issuers pick coupon rate r c so that the bonds sell close to par in primary market ( i.e. , so that B 0 = M). 2) If coupon rate on a given bond equals YTM on bonds of other companies with same credit rating at the time, then r c = r y = r, I = rM and B 0 = M. Proof: 3) As t approaches the date of bond maturity: T 0 PVA r,T 0 1/(1+r) T 1 Bond price B t M (net of accrued interest b) Bond price, accrued interest, and day-count conven-tions: 1) Bonds that pay coupon interest usually make pay-ments every 6 months. The date of these payments can be deduced from the date of maturity (the date of the final semi-annual payment). If it matures April 15, interest is paid April 15 and October
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Interest Rate Risk - Econ 174 FINANCIAL RISK MANAGEMENT...

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