# Additional+Slides+for+Bond+Market - The Bond Pricing...

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The Bond Pricing Equation t t r) (1 FV r r) (1 1 - 1 C Value Bond + + + = 7-1

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More general format 7-2 n n yt n yt yt t n t t e c e c e c y c y c y c - - - + + + = + + + + + + = ...... P ) 1 ( ...... ) 1 ( ) 1 ( P 2 1 2 1 2 1 0 2 1 0 The below formula applied to more general future cash flow, more general discounting For example, c1=c2=….=c(n-1)=c, c(n)=c+Par and ti=I The next case is when we discount by continuous compounding rate.
Bond Pricing Theorems Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond This is a useful concept that can be transferred to valuing assets other than bonds Think of Risk-Return Tradeoff, law of one price and no arbitrage. 7-3

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Risk and Return and Bond Evaluation*** One common misconception - In present value model, we always think of the discount rate as interest rate and then apply this relationship to bond valuation. This is true for interest rate for example short rate (risk free rate, risk neutral world, 3 month treasury bill), the present value relationship holds. Think of interest rate in this case as percentage return on risk free asset. If the asset is risk free , the return should be low (you have estimated this in your homework 2 for Treasury bill). We can not apply interest rate as discount factor to value risky bond. Then, present value would be the market price if we apply the appropriate discount rate not necessary interest rate (no default risk) , or we may think of it as market discount rate or market required return or the new term we just learnt - yield 7-4
Risk and Return and Bond Evaluation*** 7-5 If you want to link present value to price and it’s discount rate to interest rate, note that the equality in (*) only holds in Risk- Neutral World – The world where there is no risk. In this world all assets have same risk free return. In economics, we think of investors or more generally economic agent to be risk averse or in reality we live in Risk Averse World. Remember, in the risk-return trade-off slide, the higher return asset should be the more risky. Two assets with the same return should have the same risk, otherwise violating No Arbitrage Assumption There should be a premium for bearing the risk (in our case future uncertainty)

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