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# Computing Your Investing Returns, Redux

http://www.fool.com/investing/small-cap/2005/08/01/computing-your-investing-returns-redux.aspx

Matt Richards
August 1, 2005

After my articles on how to compute your investing returns came out (here and here), I received a number of interesting emails from readers with follow-up questions. Below, I address some issues that may have been unclear or that seem to deserve further elaboration. For those of you who've not yet read the two pieces preceding this one, I'd suggest checking the links above -- since this latest installment might seem, well, a bit unclear if you haven't.

1. Calculating annualized returns after one year. In the original article, I calculated annualized returns by simply boosting the return-to-date (our example lasted less than one year) to a full-year return by dividing it by the percentage of the year that had gone by. One correspondent asked what to do after the first year, and this got me thinking that the calculation could be both improved and tracked on a daily basis by a small change to the spreadsheet.

So, I've modified the sample spreadsheet to show how to calculate a "since inception" rate of return. To do so, we use the following formula:

(End NAV/Start NAV)^(1/years) -1

In the formula, years is (current date - start date)/365. That number will generally be a fraction, not a whole number of years. Which is OK. The formula still works.

You can use the same concept to add columns for year-to-date, quarter-to-date, or whenever-to-date returns by selecting the appropriate start date and start NAV.

I've placed a copy of the updated spreadsheet here. Note that the "since inception" numbers will vary wildly in the early days of your return tracking, so don't take them too seriously. They will settle down over time and show you how well you're really doing. (You might even want to delete some of the early "since inception" return cells, since their contents can be a bit distracting. When you see "#####," it means the calculated return is so large, or small, that it won't fit in the cell. I'd delete those.)

2. Treatment of dividends. A reader asked whether dividends should be entered as cash-in transactions when computing returns. The answer to this is "no." Dividends simply increase the value of the account, just like capital gains do, so their effect on the return computation comes when you enter the total value of the account into the spreadsheet.

3. Stock sales. My choice of words in the second article implied to one reader that the proceeds from the sale of the Microsoft stock should be accounted for with a cash-in transaction, but, in fact, they should not. Cash-in and cash-out transactions are only required when you literally either deposit money into the account or withdraw money from it. Neither the Microsoft sale, nor the Yahoo buy required a transaction to be entered in the spreadsheet, because effectively, the amount of cash in the account remained the same.

4. Time-weighted IRR vs. dollar-weighted IRR. More than one reader pointed out that the TWIRR method I presented (and which is the standard for reporting returns) may not reflect the actual return experience of the investor. That is, perhaps, surprisingly true. The returns the investor actually receives (expressed as an internal rate of return) are properly computed using what is known as the "dollar-weighted" IRR, which takes into account the timing of cash flows and amounts invested at any given time.

The point of TWIRR is precisely to remove the effects of the timing of cash flows in and out of the account in order to give a proper measurement of the performance of the underlying investments. When we evaluate the performance of a given money manager, we don't want to use numbers that reflect what might have been his luck in, for instance, receiving a large deposit, which he then put into a stock that immediately went up. We want numbers that reflect his stock-picking ability, disregarding the influence and the timing of cash flows, so that we can compare the manager's returns with those of other managers.

To get such numbers, we enter the cash flows in and out of the account into the spreadsheet, so that the TWIRR process sees when they took place and factors them out of the computations. In general, the discrepancies that can arise between TWIRR and dollar-weighted IRR tend to result from fortuitous (or unfortunate) cash flows in or out of the account that occur near large changes in the prices of the stocks owned.

A number of readers sent in test cases that showed certain results of the TWIRR method that seemed odd to them. In each instance, the test included relatively gigantic cash flows (such as an initial input of \$1,000 followed by a later input of \$1,000 -- a doubling of investable funds) and large changes in the value of the account. These examples are unrealistic, because it is unlikely that the average investor would experience a doubling of investable funds without either inheriting a large sum or winning the lottery (see No. 6 for more on this subject). But they also do reflect the nature of TWIRR and the fact that it removes the effect of the timing of cash flows.

To sum up, if you properly define your investable funds, the results of the TWIRR calculations will seem reasonable and will correctly reflect your investing skill. They will also be comparable with the returns reported by other members of the investing community.

5. Taxes. A reader asked how taxes figure into return computations. The answer is that they do not. Returns are always reported before taxes. Specifically, the reader asked whether reinvested dividends should somehow have taxes taken into account when computing the cost basis for an investment. Taxes do not enter into the calculation of either cost basis or returns. Of course, when comparing taxable vs. non-taxable investment alternatives (or when investing from tax-privileged accounts) we do need to take taxes into account when evaluating potential investments. But when comparing "birds of a feather," we ignore taxes.

6. Investable funds. One emailer mentioned that the article hit on his personal weak spot in return calculation -- that of not properly assessing which funds constitute his "investable funds." This is a very important thing to do properly -- and honestly. To be true to yourself when calculating returns, you need to decide