Rate of Return Lecture - Debt Instruments and Markets...

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Debt Instruments and Markets Professor Carpenter Rate of Return 1 Rate of Return Reading: Veronesi, Chapter 7 Investment over a Holding Period Consider an investment in any asset over a holding period from time 0 to time T . Suppose the amount invested at time 0 is P and the payoff at time T is F . F might not be known at time 0. In general, the payoff F is not known until the investment horizon date T. Invest P Get Payoff F Time 0 Time T
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Debt Instruments and Markets Professor Carpenter Rate of Return 2 Rate of Return over a Holding Period To compare the performance of different investments, and adjust for scale, one might consider the gross or unannualized rate of return (ROR) on the investment: Unannualized ROR = F/P - 1. To adjust for differences in the length of the holding period as well, one might annualize the ROR. We'll use semi-annual compounding to be consistent with US bond market interest rate quote conventions. The annualized ROR with semi-annual compounding is R = 2[( F / P ) ( 1 /( 2T )) -1] so that F / P =(1+ R /2) 2 T Example of Holding Period Return Suppose you invest $100 in an asset at time 0 and at time 5 it is worth $150. Your un-annualized ROR is 150/100-1=50%. Class Problem : What is your annualized ROR with semi- annual compounding?
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Debt Instruments and Markets Professor Carpenter Rate of Return 3 Rate of Return on a Zero: Case 1) Maturity Equal to Investment Horizon If you buy a zero-coupon bond and hold it to maturity, the ROR on your investment is the zero rate at which you bought the bond: T = t, P = d t , F = 1 so R = 2[(1/d t ) (1/(2 t )) -1]= r t Example: If you buy a 1-year zero at 5.25% and hold it to maturity your ROR over 1-year is R = 2[( 1 1/(1 + 0.0525/2) 2 ) 1/ 2 1] = 5.25% Rate of Return on a Zero: Case 2) Maturity Longer than Investment Horizon If you buy a t-year zero-coupon bond and sell it at time T<t, the ROR on your investment depends on market conditions at the selling time T.
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