# Time weighted return question - Geometric mean

Hi All

I understand how to derive the HPRs on a time weighted question, and my understanding was you needed to get the geometric mean of these figures (or so I have been doing so far correctly).

Until I saw the below question…

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:

A) 7.0%. B) 10.4%. C) 5.5%. -------------------------------------------------------------------------------- B 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%

Wouldn’t you do the highlighted to the power of 1/3 and then -1?

Thanks

P

Geomean is used when you have several annual periods to calculate compounded annual growth rate. In this question you are asked to calculate monthly returns within one year.

So Flashback, what you are saying is that regardless of the injection and withdrawals from the account, we don’t get to raise the returns to the power of the period (inverse) guving that we are dealing within a single year…that’s new… Pls reconfirm this… If this is true, then I have learnt something new… Waiting for confirmation.

If you want the (geometric) average return per period, then you compound the returns and take the third root.

If you want the total return over the holding period, then you compound the returns, but you don’t take the third root.

You are a life saver Magician.

Thanks for clarifying, S2000.

My pleasure.