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25 percent per year. In the geometric average, each term is given equal weight, because the two periods are of the same length. If the annual returns are expressed as continuously compounding returns ln(1 + r), as shown, then the familiar arithmetic average can be used to arrive at the same result. 56 percent. The weighting in this averaging is what the “time-weighted” aspect of time-weighted returns refers to. In light of the preceding, the original concept of “time-weighted return” referred to the geometric average or compound annual return.

3 Notice that the IRR does not require valuations at the times of cash flows, only at the beginning and at the end of a period. Of course, if there are no cash flows over a period, then the IRR gives exactly the same result as the familiar holding period return. 3 See David G. Luenberger, Investment Science (New York: Oxford University Press, 1998), p. 35, for a basic algorithm. CHAPTER 5 Returns in the Presence of Cash Flows 35 An approximation of a true time-weighted return can therefore be calculated as follows: 1.

00 percent. Finally, suppose we assume that the inflow occurred at the beginning and the outflow occurred at the end. The beginning value immediately after the inflow would be 140 + 30 = 170, while the ending value immediately before the outflow would be 168 + 10 = 178. 71 percent. The calculated return in this example clearly depends on the timing assumption. Whatever assumption is used, it should be used consistently. Changing the assumption after calculating the returns may be misleading. Even if the timing of the cash flows is known, a drawback of the unit value method and time-weighted returns is that a portfolio valuation must be available at every cash flow.

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