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2) The point I wanted to bring to attention is that the price you get on the reinvestment of the dividends is *not* the price on the ex-dividend date. You get the price of a few days later.

Unless you reinvest the dividend on the ex-dividend date instead of a few days later--then you get a price on the ex-dividend date, and not a price from a few days later :-D

And before you fire off your next reply about what a "fantasy" that is, re-read my last post carefully. Note that for special dividends--the only dividends that are (1) large enough for cash management to be anything close to a significant consideration and (2) large enough for this discussion to concern anything other than tiny fractions of a percent of one's portfolio, the dividend is paid on the entitlement date (or more precisely, exchange rules require the ex-dividend date to be the day after the payment date), thus appearing in one's account no later than the morning of the ex-dividend date. It is therefore completely reasonable for backtests to assume these are reinvested at the close of the ex-dividend date.

As for ordinary cash dividends, even there I would argue that reinvestment at the close of the ex-dividend date is at least a reasonable assumption. It would take a lot of diligence and careful cash management planning to keep track of dividends as they are announced and have the cash ready to reinvest on the ex-dividend dates, but it could be approximated fairly well. Just because you, personally, enroll in DRIP plans, which makes this impossible, does not make it an unreasonable assumption in backtests. But, to the extent that this is impractical, I agree with Elan: It is inconsequential due to the relative size of the amounts involved.

If you are still going to argue that this assumption amounts to "fantasy" because it's not what you personally do, then I would simply ask, then what backtest isn't a fantasy? Have you always traded precisely at open or close prices? Do you always rebalance at exactly the same interval? Philosophically, it seems you are entering the same radical subjectivist quagmire that tpoto is in when he argues that the only backtests that are relevant are those that assume trading on precisely the same dates on which he personally has traded.

3) No method of trying to take [dividend reinvestment] into account is accurate. Or even can be accurate.

By this standard, no backtest is accurate, or even can be accurate.

First, historical data of payment dates is shaky. Heck, even accurate data for dividend amounts and dates older than the last 20 or so years is often difficult to track down. I remember going to the Schaumburg library in the 1990's digging through the archives for the Dow 30 stocks, when Timberfool was working on validating the Foolish Four strategy. And approximately NOBODY was tracking payment dates, just ex-dividend dates.

This is clearly coming straight out of your ass, and doesn't warrant a reply, but I quote it as an another example of the "radical subjectivism" I referred to above. Just because you, personally, cannot find data, does not make the data "shaky", less real, or hard for others to obtain.

The ex-div date is important because that's when the money belongs to you. The payment date is not as important, because that's just the date when the money happens to get into your hand.

Again, given the provenance of your statements, this one doesn't warrant a reply either, except that I feel compelled to point out for everyone else's benefit that the IRS deems dividends to be paid, and thus taxable, as of the payment date, not the ex-dividend date, which is irrelevant. (There are, however, exceptions for some special end-of-year distributions entitled on the last day of the year, paid by some ETFs. If in doubt, simply check your brokerage 1099 statement.) This has been the case since the resumption of dividend taxation in 1950s, and was also the case during the prior period of dividend taxation during the Great Depression. So if you're completing your tax returns according to the RayVT doctrine, you're doing them wrong. And contrary to what he states, there is nothing fuzzy about dividend payment dates and they are not at all difficult to find (I scrape dividend data daily from six high-quality sources, and all six sources give the payment dates). The Wall Street Journal and New York Times have been publishing daily declared dividends, including payment dates, since at least the 1920s. Better sources, like Mergent (which has been the gold standard for over a century), have historical dividend data going back even further.

Whether it makes sense to tax dividends as of their payment dates rather than their entitlement dates, or even whether they should be taxed at all, is of course another subject.

The subsequent discussion has drifted into arcane considerations that in the regular course make differences of small fractions of 1% in price adjustments.

This is true for the vast majority of dividends, but not for special dividends, where the adjustment method can make a huge difference. I gave an example of this in my post, which you must have glossed over. I also linked to a thread on this forum where a large special dividend was discussed because of the wild distortion that CSI's adjustment method was producing in Yahoo!'s prices. And there is nothing "arcane" about what causes this distortion: It arises from the fact that

 A + C      A
------- != --- (Unless C = 0 or A = B).
B + C B

In words, ratios aren't preserved by addition of constants (except for the constant zero, or the ratio 1).

The correct total return on the ex-dividend date for a dividend reinvested at the close of the ex-dividend date is

 Px + D

where Px is the price of the stock on the ex-dividend date and Pe is the price of the stock on the entitlement date. However, according to the way CSI/Yahoo! adjusts prices for dividends, the total return on the ex-dividend date comes out to

Pe - D

This is not the same: Subtracting D from the numerator and denominator does not produce the same ratio. When D is small relative to Px and Pe, or when the ratios are close to 1, they are close, but for large special dividends, they can be wildly different.

While there is nothing wrong, in theory, with the way CSI/Yahoo! adjust for dividends (as RayVT states, there is no single correct way), the only way to arrive at their resulting total returns on ex-dividend dates is to assume "leveraging out" each dividend with a purchase of more stock on margin at the close of the entitlement date. For large special dividends, I do not consider this to be a "reasonable assumption" for backtests, so instead, GTR1 linearization uses the correct adjustments that correspond to reinvestment at the close of the ex-dividend date ("PXD").

Twenty years ago, discussions with this level of mathematical detail weren't considered "arcane", and were in fact quite common. What has changed? It could be related to this: (Binghamton University. "Early retirement can accelerate cognitive decline." ScienceDaily. ScienceDaily, 29 October 2019.). This is, after all, a message board dedicated to retiring early, and some here have done just that (e.g., RayVT).

Robbie Geary
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