Examples 4 and 5, if the second purchase occurs exactly halfway through the overall period, the modified Dietz method has the same result as the simple Dietz method. 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. In this case, the Modified Dietz return is less than the Simple Dietz return. 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. In this case, the Modified Dietz return is greater than the Simple Dietz return. 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. This is still noticeably less than the 10 percent time weighted return. Linked returns methods 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. Such an approximate time-weighted return method is prone to overstate or understate the true time-weighted return. Linked Internal Rate of Return (LIROR) is another such method that is sometimes used to approximate the true time-weighted return. It combines the true time-weighted rate of return method with the internal rate of return (IRR) method. 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%. If the regular time periods are not years, then calculate either the un-annualized holding period version of the IRR for each time interval or the IRR for each time interval firstly, then convert each one to a holding period