Econ173A_topic8

Econ173A_topic8 - Ec 173A FINANCIAL MARKETS Foster, UCSD...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Ec 173A – FINANCIAL MARKETS LECTURE NOTES Foster, UCSD 22-Nov-08 A. Bond Prices and Yields [BKM, Ch. 14] 1. Review: 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. Examples: Corporate bonds. US Treasury Bonds and Notes. State and local govt municipal bonds (“munis”). Federal agency debt (bonds issued by Fannie Mae, Ginnie Mae, Freddie Mac, etc.) b) Basic bond value equation and definitions. 1) Annual interest I = r c M. Most bonds pay semiannually ($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 interest rates rise from 4.0% to 4.5%, they have increased by 50 basis points. 2. Yield to Maturity: 1 a) YTM -- pure discount bonds. 1) If B 0 grows to M in T years, r y is found by solving the following growth equation: 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 -- annual coupon interest. 1) If the bond pays $I interest at the end of each year, a financial calculator finds r y by solving the equation below (corresponding to the bond value equation above) using an iterative algorithm: B 0 = I × PVA r,T + M × PV r,T 2) A formula for approximating YTM is available: 1 See the Appendix for E XCEL spreadsheet formulas to compute YTM, accrued interest, and bond duration. Bond Notation B 0 current price of bond ($) 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 + + + + + + + = 3 2 0 0 B M T B M I r y + - +
Background image of page 1

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

View Full DocumentRight Arrow Icon
Ec 173A BONDS & INTEREST RATES p. 2 3) Numerical example. Given: B 0 = $982, M = $1,000, I = $60/yr, T = 15 years Using E XCEL , r y = 6.188%. Using the approximation, r y ≈ 6.194%. c) YTM -- semi-annual coupon interest. 1) If the bond pays $I/2 every 6 months, a financial calculator finds r y by solving the following equation using an iterative algorithm: B 0 = I/2 × PVIFA r/2,2T + M × PVIF r/2,2T 2) This corresponds to the bond value equation below. The algorithm computes r/2, then report r y = 2 (r/2), an annual percentage rate (APR). 3) Numerical example. Given: B 0 = $982, M = $1,000, I = $30 per 6 months, T = 15 years Using E XCEL , r y = 6.186%. 3.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/30/2009 for the course ECON 173A taught by Professor Foster during the Spring '09 term at UCSD.

Page1 / 15

Econ173A_topic8 - Ec 173A FINANCIAL MARKETS Foster, UCSD...

This preview shows document pages 1 - 3. Sign up to view the full document.

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