Tutorial 5

# Tutorial 5 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Tutorial 5 1 Review 1.1 Yield Rates C t is the contribution (cash inﬂow) at time t . r t is the returns (cash outﬂow) at time t . R t is net cash ﬂow ( r t - C t ) at time t . P ( i ) = n X t =0 v t R t = 0 1.2 Money-weighted Rates of Return B = A + C + I I = iA + X i C t · 1 - t i t Exact yield rate: 1 - t i t = (1 + i ) 1 - t - 1 Approximate yield rate: 1 - t i t = (1 - t ) i i = I A + t C t (1 - t ) 1.3 Time-weighted Rates of Return 1 + j k = B k B 0 k - 1 1 + i = (1 + j 1 )(1 + j 2 ) ··· (1 + j m ) 1

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1.4 Reinvestment Rates 1. Single payment 1 + is n e i 2. Annuity payments ( Annuity - immediate : AV = n + i ( Is ) n - 1 e j Annuity - due : AV = n + i ( Is ) n e j 2
2 Exercises 1. An investor makes payments of 8,000 at times 0 and 1 and receives returns of 900 at times 1, 2, . .., 25. Write the yield rate equation. Use annuity calculations to show the yield rate is between 2.75% and 3%.
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## This note was uploaded on 04/17/2011 for the course STAT 1802 taught by Professor Dr.k.c.yuen during the Spring '08 term at HKU.

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Tutorial 5 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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