Question

You are given the following information on an investment account: 1/1/2017 5/1/2017 9/1/2017 1/1/2018 Account value before deposit or withdrawal 50,000 75,000 90,000 67,000 Deposit 15,000 Withdrawal 25,000 Calculate the absolute value of the difference in the yield rates by the dollar-weighted and time-weighted methods.

Answer 1

The answer is "2.33%"

Step-by-step explanation:

A = pre-payment or withdrawal account value= 50,000

B =end-of-year balance = 67,000

Deposit = 15000;

Withdrawal = -(1000)

Return rate annual dollar-weighted:

`= ((67000 - 50000 - 15000 + 25000))/((67000)( (12)/(12)) + (15000)((8)/(12)) - 25000((4)/(12)))\\\\= ((27000))/((67000)( 1) + (15000)((2)/(3)) - 25000((1)/(3)))\\\\= ((27000))/((67000 + 5000 * 2 - 8333.3))\\\\= ((27000))/((67000 + 10000 - 8333.3))\\\\ = (27000)/(68666.67) \\\\= 3.63 \%`

Method of timing: the time frame is 1 year from the table provided balance at the beginning

:

`B_0 = 50000 \\\\ B_1= 75000`

return rate=
`(1 + i) (12)/(12)\\\\`

`= ((B_1)/(B_0)) * ( (B_2)/(B_1+W_1)) * ( (B_3)/(B_2+W_2)) * ((B_4)/( B_3+W_3))`

`= ((75000)/(50000)) * ((90000)/(75000+15000)) * ((67000)/(90000 - 25000))\\\\= ((3)/(2)) * ((90000)/(90000)) * ((67000)/(65000))\\\\= ((3)/(2)) * (1 ) * ((67)/(65))\\\\= ((3)/(2)) * (1 ) * 1.03\\\\= (3.09)/(2)\\\\=1.5\\\\\to 1 + i = (1.5) * 1 * 1.03 \\\\= 2.307%`

`\therefore \\ i = 2.307 - 1 = 1.307`

Therefore, by dollar-weighted and timeweighted approaches the gap in involves collecting:

`=3.63 - 1.307 \\\\ =2.33 \%`