2_Interest Rates.pdf

Year payment pv of the payment 05 3 1 3 15 3 2 103

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Year Payment PV of the payment 0.5 3 \$ 1 3 \$ 1.5 3 \$ 2 103 \$ Sum \$ A 0 = A t e Rt

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Bond pricing: Example Fin330 26 l Recall that the PV of investment with continuous compounding is l The flow of funds for an investor: l Theoretical price of the bond is \$98.39. Year Payment PV of the payment 0.5 3 \$ 1 3 \$ 1.5 3 \$ 2 103 \$ Sum \$ 98.39 A 0 = A t e Rt 3 e 0.05 × 0.5 3 e 0.058 × 1.0 3 e 0.064 × 1.5 103 e 0.068 × 2.0
Bond pricing: arbitrage l In the previous example: l What could investors do if the market price of the bond were above its theoretical price? Answer: l What could investors do if the market price of the bond were below its theoretical price? Answer: Fin330 27

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Bond’s Yield l A bond’s yield is a single discount rate that, when applied to all cash flows, gives the bond’s value equal to the bond’s price. l In the example above: What single yield y should we apply to discount the payments, so that their present value equals to the bonds price of \$98.39? Answer: y=6.76% (check this!). Fin330 28 Year Payment PV of the payment 0.5 3 \$ 1 3 \$ 1.5 3 \$ 2 103 \$ Sum \$ 98.39 3 e y × 0.5 3 e y × 1.0 3 e y × 1.5 103 e y × 2.0
Term structure of interest rates l The term structure of interest rates ( yield curve ) is the relationship between bond yields and different terms or maturities. l YTM is the internal rate of return of an investment in the bond with a given maturity made at the observed price. l Bond prices are often quoted in terms of YTM. l The U.S. Treasury Yield Curve is the benchmark for the credit market, because it represents the yields of risk-free fixed income investments across a range of maturities. l Typically, the Treasury yield curve is upward-sloping (longer- term investments require higher yields). Fin330 29

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U.S. Treasury Yield Curve Fin330 30 Source:
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• Spring '16
• Chang

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