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Postby pooja923 » Thu May 12, 2016 5:41 am

On January 1, Jonathan Wood invests $50,000. At the end of March, his investment is worth $51,000. On April 1, Wood deposits $10,000 into his account, and by the end of June, his account is worth $60,000. Wood withdraws $30,000 on July 1 and makes no additional deposits or withdrawals the rest of the year. By the end of the year, his account is worth $33,000.
The time weighted return for the year is closest to:
1. 10.4%.
2. 7.0%.
3. 5.5%.
January March return = 51,000 / 50,000 − 1 = 2.00%
April June return = 60,000 / (51,000 + 10,000) − 1 = 1.64%
July December return = 33,000 / (60,000 − 30,000) − 1 = 10.00%
Time weighted return = [(1 + 0.02)(1 − 0.0164)(1 + 0.10)] − 1 = 0.1036 or 10.36%
Which method is used here? If I use Holding period return for each time period and then compound it, the answer will be different.
Kindly explain me how to solve this type in time wtd return calculation.


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Postby edupristine » Thu May 12, 2016 8:16 am

Hi Pooja

The time-weighted returns are what they are and will not be affected by cash inflow and outflow.
The time-weighted formula is essentially a geometric mean of a number of holding period returns that are linked together or compounded over time.

Compounded time-weighted rate of return, for N holding periods = [(1 + HPR1)*(1 + HPR2)*(1 + HPR3) ... *(1 + HPRN)] - 1.
HPRs is done by
(a) adding 1 to each sub-period HPR, then
(b) multiplying all 1 + HPR terms together, then
(c) subtracting 1 from the product

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