VIEWS: 243 PAGES: 23 CATEGORY: Business POSTED ON: 7/23/2011 Public Domain
Pricing of Bonds Zvi Wiener Based on Chapter 2 in Fabozzi Bond Markets, Analysis and Strategies Fall-02 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Time value of money How to calculate price of a bond Why the price of a bond changes Relation between yield and price Relation between coupon and price Price changes when approaching maturity Floaters and inverse floaters Accrued interest and price quotes Zvi Wiener Fabozzi Ch 2 slide 2 Time Value of Money present value PV = CFt/(1+r)t Future value FV = CFt(1+r)t Net present value NPV = sum of all PV -PV 5 5 5 5 105 4 5 105 PV t 1 (1 r ) (1 r )5 t Zvi Wiener Fabozzi Ch 2 slide 3 Time Value You have $100 now and are going to deposit it for 5 years with 6% interest. What will be the final amount? It depends on calculation method! Yearly compounding: $100*1.065 Semiannual compounding: $100*1.0312 Monthly compounding: $100*1.00560 Zvi Wiener Fabozzi Ch 2 slide 4 Periodic Rate Annual interest rateA r= = Number of periods in a year n Effective Rate n A 1 r n 1 1 R n Zvi Wiener Fabozzi Ch 2 slide 5 Pricing of Bonds T Ct PV t 1 (1 r )t 100 Zero coupon bond price (1 r ) t Zvi Wiener Fabozzi Ch 2 slide 6 Pricing of Bonds T Ct PV t 1 (1 r )t Term structure of interest rates T Ct PV t 1 (1 rt ) t Zvi Wiener Fabozzi Ch 2 slide 7 Yield Yield = IRR = Internal Rate of Return T Ct Pr ice t 1 (1 y ) t How do we know that there is a solution? Zvi Wiener Fabozzi Ch 2 slide 8 Example Price calculation: 5 5 105 2 3 83.34 1.10 1.11 1.12 Yield calculation: 5 5 105 83 .34 1 y (1 y ) 2 (1 y ) 3 y 11.9278% Zvi Wiener Fabozzi Ch 2 slide 9 Price-Yield Relationship Price and yield (of a straight bond) move in opposite directions. price yield Zvi Wiener Fabozzi Ch 2 slide 10 General pricing formula n Ct P t 1 (1 r ) v (1 r )t 1 days between settlement and next coupon v days in six months period Zvi Wiener Fabozzi Ch 2 slide 11 Accrued Interest Accrued interest = interest due in full period* (number of days since last coupon)/ (number of days in period between coupon payments) Zvi Wiener Fabozzi Ch 2 slide 12 Day Count Convention Actual/Actual - true number of days 30/360 - assume that there are 30 days in each month and 360 days in a year. Actual/360 Zvi Wiener Fabozzi Ch 2 slide 13 Floater The coupon rate of a floater is equal to a reference rate plus a spread. For example LIBOR + 50 bp. Sometimes it has a cap or a floor. Zvi Wiener Fabozzi Ch 2 slide 14 Inverse Floater Is usually created from a fixed rate security. Floater coupon = LIBOR + 1% Inverse Floater coupon = 10% - LIBOR Note that the sum is a fixed rate security. If LIBOR>10% there is typically a floor. Zvi Wiener Fabozzi Ch 2 slide 15 Price Quotes and Accrued Interest Assume that the par value of a bond is $1,000. Price quote is in % of par + accrued interest the accrued interest must compensate the seller for the next coupon. Zvi Wiener Fabozzi Ch 2 slide 16 Home Assignment Chapter 2 Questions 2, 3, 7, 8, 11 Zvi Wiener Fabozzi Ch 2 slide 17 FRM-99, Question 17 Assume a semi-annual compounded rate of 8% per annum. What is the equivalent annually compounded rate? A. 9.2% B. 8.16% C. 7.45% D. 8% Zvi Wiener Fabozzi Ch 2 slide 18 FRM-99, Question 17 (1 + ys/2)2 = 1 + y (1 + 0.08/2)2 = 1.0816 ==> 8.16% Zvi Wiener Fabozzi Ch 2 slide 19 FRM-99, Question 28 Assume a continuously compounded interest rate is 10% per annum. What is the equivalent semi-annual compounded rate? A. 10.25% per annum. B. 9.88% per annum. C. 9.76% per annum. D. 10.52% per annum. Zvi Wiener Fabozzi Ch 2 slide 20 FRM-99, Question 28 (1 + ys/2)2 = ey (1 + ys/2)2 = e0.1 1 + ys/2 = e0.05 ys = 2 (e0.05 - 1) = 10.25% Zvi Wiener Fabozzi Ch 2 slide 21 Mortgage example You take a mortgage $100,000 for 10 years with yearly payments and 7% interest. What is the size of each payment? 10 x 100 ,000 t 1 (1 0.07 ) t 10 1 100 ,000 x t x 14.2378 t 1 1.07 Zvi Wiener Fabozzi Ch 2 slide 22 Mortgage example How much do you own bank after 3 first payments? 7 14 .2378 1.07 t 76 .7314 t 1 What is the fair value of your debt if interest rates are 5%? 7 14 .2378 1.05 t 82 .3849 t 1 Zvi Wiener Fabozzi Ch 2 slide 23