Question

100 is deposited into an investment account on January 1, 1998. You are given the following information on investment activity that takes place during the year:

April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
The amount in the account on January 1, 1999 is 115. During 1998, The annual effective dollar weighted yield is 0%, and the annual effective time weighted yield is y. Calculate y.

Answer 1

y = - 0.681 % ≈ -0.7 %

Explanation:

Given:

April 19,1998 October 30, 1998

Value immediately prior to deposit 95 105

Deposit 2X X

amount in the account on January 1, 1999 = 115

effective dollar weighted yield = 0%

annual effective time weighted yield = y

To find:

Calculate y

Solution:

Given that the dollar weighted return is 0%

100 is deposited into investment account on January 1, 1998. So, add 100 to the deposits 2X X

100 + 2x + x = 115

3x = 115 - 100

3x = 15

x = 15/3

x = 5

Compute y

1 + y = (95/100)(105/105)(115/110)

1 + y = 0.95 * 1 * 1.045

1 + y = 0.99318

y = 0.99318 - 1

y = - 0.0068 * 100

y = - 0.681 % ≈ -0.7 %

y = -0.7 %