Question

This is Actuarial Science

Problem 3 - Dollar-weighted and Time-weighted rate of returns


An investment account has a value of $7000 on 1/1/2014. A deposit of XX is made on 5/1/2014, a withdrawal of $400 is made on 9/1/2014, and a deposit of $300 is made on 11/1/2014. The balance on December 31, 2014 is $8074.

Find the amount of the first deposit if the dollar-weighted rate of return is 6%

X=

Problem 8 - Dollar-weighted and Time-weighted rate of returns

For an investment account, you are given the following information during calendar years 2014 and 2015:

Account for 2014

Date	Fund Value Before Activity	Deposit	Withdrawal
January 1, 2014	150
March 1, 2014	165	20
July 1, 2014	160		15
November 1, 2014	165	15
December 31, 2014	X

Account for 2015

Date	Fund Value Before Activity	Deposit	Withdrawal
January 1, 2015	X
September 1, 2015	197	10
December 31, 2015	Y

During 2014, the dollar-weighted return equals 8%. During 2015, the time-weighted return equals 10%. Determine the value of the fund at the end of 2014 and 2015.
X=
Y=

Problem 10 - Dollar-weighted and Time-weighted rate of returns

You are given the following information about the activity in 2 different investment accounts:

Account A

Date	Fund Value Before Activity	Deposit	Withdrawal
January 1, 2014	400
September 1, 2014	445		X
November1, 2014	425	2X
December 31, 2014	445

Account B

Date	Fund Value Before Activity	Deposit	Withdrawal
January 1, 2014	400
April 1, 2014	445		X
December 31, 2014	415.5

During 2014, the dollar-weighted return for investment account A equals the time-weighted return for investment account B, which is equal to ii.
Compute i

Answer 1

Problem 3). Let the amount deposited be x.

Using the dollar-weighted return of 6%, we have

7,000*(1+6%)^1 + x*(1+6%)^(7/12) - 400*(4/12) + 300*(1+6%)^(2/12) = 8,074

x*(1+6%)^(7/12) = 758.917

x = 758.917/1.0346 = 733.56 or 734

Problem 8).

Calculation of X using dollar-weighted return of 8%:

X = 150*(1+8%)^(12/12) + 20*(1+8%)^(10/12) - 15*(1+8%)^(6/12) + 15*(1+8%)^(2/12) = 182.93

Calculation of Y using the time-weight return of 10%:

Time-weighted return = [(balance before deposit/initial balance)*(final balance/balance after deposit)] -1

10% = [(197/182.93)*(Y/198)] -1

Y = 1.10*198*182.93/197 = 202.24

answered by: anonymous