Section 5 - ECON 136: Financial Economics Section 5 (Sep...

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ECON 136: Financial Economics Section 5 (Sep 25th) Xing Huang 1 Economics Department, UC Berkeley 1 Bond Pricing 1.1 Review General formula: P = X PV ( payments ) = C (1 + R ) 1 + C (1 + R ) 2 + ±±± + C (1 + R ) T + F (1 + R ) T = C R " 1 ² 1 1 + R ± T # + F (1 + R ) T Some Facts: 1. P goes up, R goes down; R goes up, P goes down. 2. C/F = R implies P=F; C/F > R implies P > F; C/F < R implies P < F. 3. Longer maturity implies higher sensitivity of price to changes of yield (generally). Yield curve / term structure of interest rates 1.2 Example Question 1 There is a coupon bond with $10,000 face value and a 9% coupon rate, which makes semi-annual coupon payments. The maturity of the bond is 7 years. Take the annual interest (or discount) rate a) Find the price of this coupon bond. Step 1: Determine the dollar amount of the coupon payments, C . Many coupon bonds pay semi-annual payments. For these bonds, it is typical to quote the coupon rate as 2 times the percentage of the face value which a single coupon payment would consist of. Thus for our bond, C = $10 ; 000 ³ 9% 2 = $450 You may notice that this is using the arithmetic mean, which we just made a point of saying was the wrong way of annuualizing a return. This is simply an institutional convention in the way that 1 Thank you all very much !! 1
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coupon bonds are described, so we just need to remember it and not get confused. Step 2: Take the annualized interest rate given in the problem and convert it to the appropriate half-year interest rate so we can discount the semi-annual coupon payments. 1 +
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Section 5 - ECON 136: Financial Economics Section 5 (Sep...

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