Question

You are given the following information about an investment account:

(i) The value on January 1 is 10.
(ii) The value on July 1, prior to a deposit being made, is 12.
(iii) On July 1, a deposit of X is made.
(iv) The value on December 31 is X.

Over the year, the time-weighted return is 0%, and the dollar-weighted (money-weighted) return is Y.
Calculate Y.

Answer 1

Answer / Explanation

To properly understand this question let us define some terms used in the question:

Investment Account: An Investment account is a monetary account that is owned by an individual or group of people and they are eat liberty to use the investment account for such purpose as transaction purpose, purpose of taxation, receiving of profit or income earned such as (interest, sales proceeds, insurance benefit, etc).

Time Weighed Return (TWR): This can be defined or refers to as a method used in calculating the expected returns on investment.

With the understanding of the above defined, Referencing back to the question asked, we not that since the time–weighted return is 0%, 12 / 10 . x / 12 + x = 1.

So, x = 60

Hence, The dollar–weighted return 'y' satisfies the equation below:

B - A - ∑Ck / A + ∑Ck ( 1 - tk ) = i

Therefore:

y = 10 +60 - 60 / (10) (1) + (60) (1/2)

Solving the above further,we arrive at

Y= - 0.25

Now, if we convert the above value to percentage, we have

Y= - 25%

Explanation:

Answer 2

The calculated dollar-weighted rate of return, Y = -25%.

Explanation:

The time-weighted rate of return is 0%

Therefore, (12/10)*( X/(12 + X)) = 1

12X = 120 + 10X -> X = 60

The dollar-weighted rate of return,Y is calculated below as:

Y = (X-(10 + X))/(1*10+X/2)

Y = (60-(10+60))/(1*10+60/2)

Y = (60 - 70)/(10+30)

Y= -10/40

Y = -25%

Therefore, the calculated dollar-weighted rate of return, Y = -25%.