MGTC71-3 - MGTC71-Lecture 3 Interest Rates & Duration...

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1 MGTC71-Lecture 3 Ata Mazaheri
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2 Types of Rates Treasury rates LIBOR rates Repo rates
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3 Measuring Interest Rates The compounding frequency used for an interest rate is the unit of measurement The difference between quarterly and annual compounding is analogous to the difference between miles and kilometers
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4 Continuous Compounding In the limit as we compound more and more frequently we obtain continuously compounded interest rates $100 grows to $100e RT when invested at a continuously compounded rate R for time T $100 received at time T discounts to $100e - RT at time zero when the continuously compounded discount rate is R
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5 Conversion Formulas Define R c : continuously compounded rate R m : same rate with compounding m times per year ( 29 R m R m R m e c m m R m c = + = - ln / 1 1
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6 Zero Rates A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T Maturity (years) Zero Rate (% cont comp) 0.5 5.0 1.0 5.8 1.5 6.4 2.0 6.8
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7 Bond Pricing To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate In our example, the theoretical price of a two-year bond providing a 6% coupon semiannually is 3 3 3 103 98 39 0 05 0 5 0 058 1 0 0 064 1 5 0 068 2 0 e e e e - × - × - × - × + + + = . . . . . . . . .
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8 Bond Yield The bond yield is the discount rate that makes the present value of the cash flows on the bond equal to the market price of the bond Suppose that the market price of the bond in our
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MGTC71-3 - MGTC71-Lecture 3 Interest Rates & Duration...

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