The time-weighted return is a measure of the historical performance of an investment portfolio which compensates for external flows.
External flows refer to the net movements of value into or out of a portfolio, stemming from transfers of cash, securities, or other financial instruments.
These flows are characterized by the absence of a concurrent, equal, and opposite value transaction, unlike what occurs in purchases or sales.
Furthermore, they do not originate from the income generated by the portfolio's investments, such as interest, coupons, or dividends.
The time-weighted return is found by multiplying together the growth factors for each year, i.e. the growth factors before and after the second transfer into the portfolio, then subtracting one, and expressing the result as a percentage: We can see from the time-weighted return that the absence of any net gain over the two-year period was due to bad timing of the cash inflow at the beginning of the second year.
However, by reflecting the performance each year compounded together on an equalized basis, the time-weighted return recognizes the performance of the investment activity independently of the poor timing of the cash flow at the beginning of Year 2.
The growth factor is: External flows during the period being analyzed complicate the performance calculation.
The return is: and the corresponding growth factor is: Suppose that the portfolio is valued immediately after each external flow.
The value of the portfolio at the end of each sub-period is adjusted for the external flow which takes place immediately before.
If they have no control over the timing of flows, then compensating for the timing of flows, applying the true time-weighted return method to a portfolio, is a superior measure of the performance of the investment manager, at the overall portfolio level.
Internal flows are transactions such as purchases and sales of holdings within a portfolio, in which the cash used for purchases, and the cash proceeds of sales, is also contained in the same portfolio, so there is no external flow.
It is internal to the portfolio, but external to both the stock and the cash account when they are considered individually, in isolation from one another.
The time-weighted method only captures the effect attributable to the size and timing of internal flows in aggregate (i.e., insofar as they result in the overall performance of the portfolio).
The time-weighted return of a particular security, from initial purchase to eventual final sale, is the same, regardless of the presence or absence of interim purchases and sales, their timing, size and the prevailing market conditions.
Unless this feature of the time-weighted return is the desired objective, it arguably makes the time-weighted method less informative than alternative methodologies for investment performance attribution at the level of individual instruments.
Is this poor timing apparent, from the time-weighted (holding-period) return of the shares, in isolation from the cash in the portfolio?
Then the first sub-period growth factor, preceding the second purchase, when there are just the first 10 shares, is: and growth factor over the second sub-period, following the second purchase, when there are 15 shares altogether, is: so the overall period growth factor is: and the time-weighted holding-period return is: which is the same as the simple return calculated using the change in the share price: The poor timing of the second purchase has made no difference to the performance of the investment in shares, calculated using the time-weighted method, compared, for instance, with a pure buy-and-hold strategy (i.e., buying all the shares at the beginning and holding them until the end of the period).
Other methods exist to compensate for external flows when calculating investment returns.
The internal rate of return is commonly used for measuring the performance of private equity investments, because the principal partner (the investment manager) has greater control over the timing of cash flows, rather than the limited partner (the end investor).
The Simple Dietz method[3] applies a simple rate of interest principle, as opposed to the compounding principle underlying the internal rate of return method, and further assumes that flows occur at the midpoint within the time interval (or equivalently that they are distributed evenly throughout the time interval).
The simple Dietz returns of two or more different constituent assets in a portfolio over the same period can be combined to derive the simple Dietz portfolio return, by taking the weighted average.
Applying the Simple Dietz method to the shares purchased in Example 4 (above): so which is noticeably lower than the 10% time-weighted return.
If the second purchase is earlier than halfway through the overall period, the gain, which is 5 dollars, is still the same, but the average capital is greater than the start value plus half the net inflow, making the denominator of the modified Dietz return greater than that in the simple Dietz method.
If the second purchase is later than halfway through the overall period, the gain, which is 5 dollars, is still the same, but the average capital is less than the start value plus half the net inflow, making the denominator of the modified Dietz return less than that in the simple Dietz method.
No matter how late during the period the second purchase of shares occurs, the average capital is greater than 100, and so the Modified Dietz return is less than 5 percent.
Calculating the "true time-weighted return" depends on the availability of portfolio valuations during the investment period.
If valuations are not available when each flow occurs, the time-weighted return can only be estimated by linking returns for contiguous sub-periods together geometrically, using sub-periods at the end of which valuations are available.
The internal rate of return is estimated over regular time intervals, and then the results are linked geometrically.
For example, if the internal rate of return over successive years is 4%, 9%, 5% and 11%, then the LIROR equals 1.04 x 1.09 x 1.05 x 1.11 – 1 = 32.12%.
give identical results - it is only the various ways they handle flows that makes them different from each other.