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## Time-weighted return |

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**Time-weighted returns** is a measure of the compound rate of return of a portfolio over a stated period of time. It requires a set of sub-period returns to be calculated whenever there is an external cash flow, such as a deposit or withdrawal from the portfolio. In essence, it calculates the geometric total and mean return as opposed to the arithmetic total and mean return. This method does not include or have any distortions created when money is deposited or withdrawn from a portfolio. This is in contrast to Money-weighted returns. In order for firms to meet Global Investment Performance Standards, they must use time-weighted returns as opposed to money-weighted returns.

Time-weighted returns assume that all cash distributions (i.e. dividends, interest, etc) are reinvested back into the portfolio. It also eliminates the effect of cash flows in and out of the portfolio, in essence treating the portfolio as if there were a single investment at the beginning of the measurement period.

A quick example would help illustrate the point. Assume your portfolio's value was $1,000 at the beginning of the month, and $1900 at the end of the month. On the 10th day of the month, you deposit $250, and on the 20th day of the month you deposit another $250. The overall value of your portfolio (after the deposits are made) on the 10th day is $1,300, and $1,700 on the 20th day. Therefore, there are three "sub-periods"- the first includes days 1-10, the second days 11-20, and finally the third is for days 21-30.

In order to calculate the time weighted return, we first need to calculate the return of each subperiod.

- The return of subperiod one is: [ ($1,300-$250)-$1,000 ] / $1,000 = 5%.
- The return of subperiod two is: [ ($1,700-$250)-$1,300 ] / $1,300 = 11.5%
- The return of subperiod three is: [ ($1,900-$1,700) ] / $1,700 = 11.8%

Finally, we compound the returns together to calculate the overall time-weighted rate of return:

- Time-weighted rate of return: [(1+0.05)*(1+0.115)*(1+0.118)]^0.33 -1 = 9.39%

The main difference between time weighted and money weighted returns is that time weighted returns ignores the effect of cash inflows/outflows, whereas money-weighted returns incorporate the size and timing of cash flows. The money-weighted rate of return internalizes both the timing and size of external cash flows (such as deposits and withdrawals), whereas time-weighted return correct for this by allowing different "subperiods" to have different returns.

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