Rate of Return

Debt Instruments and Markets

Professor Carpenter

Rate of Return

Reading: Veronesi, Chapter 7

Investment over a Holding Period

Rate of Return

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Consider an investment in any asset over a holding

period from time 0 to time T.

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Suppose the amount invested at time 0 is P and the

payoff at time T is F.

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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 over a Holding Period

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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:

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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.

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The annualized ROR with semi-annual compounding is

R = 2[(F/P)(1/(2T))-1]

so that F/P=(1+R/2)2T

Example of Holding Period Return

Rate of Return

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Suppose you invest $100 in an asset at time 0 and at

time 5 it is worth $150.

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Your un-annualized ROR is 150/100-1=50%.

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Class Problem: What is your annualized ROR with semiannual compounding?

2

Debt Instruments and Markets

Professor Carpenter

Rate of Return on a Zero:

Case 1) Maturity Equal to Investment Horizon

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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 = dt, F = 1 so

R = 2[(1/dt)(1/(2t))-1]=rt

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Example: If you buy a 1-year zero at 5.25% and

hold it to maturity your ROR over 1-year is

1

R = 2[(

)1/ 2 ?1] = 5.25%

2

1/(1+ 0.0525 /2)

€

Rate of Return on a Zero:

Case 2) Maturity Longer than Investment Horizon

Rate of Return

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If you buy a t-year zero-coupon bond and sell it at time

T ................
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