Question

Deposit Withdrawal Example: Date Fund Value before activity 1/1/99 2000 4/1/99 2060 9/1/99 2010 12/31/99 2405 The time-weighted yield rate is . 1111. Find X 300

Answer 1

Time-weighted yield rate = .1111

Formula for Time Weighted Return are as follows:

TWR ={ (1+HP₁ ) * (1+HP₂ ) * (1+HP₃ ).......* (1+HP_n )} - 1

TWR = Time Weighted Return

HP = (End Fund Value - Intial Fund Value + Cash Flow)/ Intial Fund Value + Cash Flow

n = Sub - period

In the question, HP return for the period from 1/1/99 to 4/1/99

HP = (2060-2000)/2000 = 0.03

HP return for the period from 4/1/99 to 9/1/99

HP =[ 2010-(2060-X)] / (2060-X) = (-50+X) / (2060-X)

HP return for the period from 9/1/99 to 12/31/99

HP = [2405-(2010+300)]/(2010+300) = 95/2310 = 0.0411

Now, we will apply the formula of time-weighted yield rate as follows:

[(1+0.03) * {1+(-50+X)/(2060-X)} * (1+0.0411)] - 1 = .1111

1.03 * {1+(-50+X)/(2060-X)} * 1.0411 = 1.1111

{1+(-50+X)/(2060-X)} = 1.1111/(1.03*1.0411)

{1+(-50+X)/(2060-X)} = 1.0362

(-50+X)/(2060-X) = .0362

-50+X = .0362(2060-X)

-50+X = 74.572 - .0362X

X +.0362X = 74.572+50

1.0362X = 124.572

X = 124.572/1.0362 = 120.22

Therefore, X = 120.22