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RayVT is of course quite right that reinvesting dividends at the close of the ex-dividend date (i.e., the dividend reinvestment strategy I abbreviated as PXD in https://boards.fool.com/intro-to-event-partition-linearizati...) is practically impossible for a portfolio seeking 100% investment in non-marginable positions at all times, especially in retirement accounts where all positions are non-marginable. And even where margin is available, PXD assumes "free leverage" (as I called it in https://boards.fool.com/gtr1-trading-suspensions-20765833.as...) on the dividend amounts from ex-dividend date close to payment date close. However, when designing GTR1 linearization, I considered these mostly non-issues for reasons that I didn't go into in great detail in the otherwise very thorough posts (possibly the longest two posts in the history of the message board!) that I just linked to:

1. The impracticality only really exists with ordinary cash dividends. For special dividends and distributions of other stock, the payment date is almost always the entitlement date, a.k.a. the cum-distribution date, i.e., the market day before the ex-distribution date. Thus it is perfectly practical to re-invest a special dividend at the next day's close, or to sell a spin-off and reinvest the proceeds in the distributing stock at the next day's close.

2. What minor practical impossibilities there are (mainly "free leverage") in PXD as applied to ordinary cash dividends can be mitigated by assuming a 1-2% cash buffer is reserved in the portfolio at all times for PXD. While doing this would slightly reduce CAGR, it would also slightly reduce drawdowns and other risk metrics as well, and most importantly for those whose primary performance metric is Sharpe Ratio, adding a permanent cash buffer as a percentage of the portfolio value has, by design, zero impact on Sharpe Ratio, which is invariant under changes in assumed allocations between the underlying investment and cash or margin (subject to certain other assumptions, of course).


However, RayVT is wrong on a couple points:

1. The reason "we" use PXD with ordinary cash dividends is not that it's "the only data we have". In designing GTR1 linearization, I could have simulated reinvesting all ordinary cash dividends at the close of payment dates by making every ex-dividend date a "critical date" in the language of EPL. The reason I opted against this wasn't lack of data (I have declaration dates, record dates, ex-distribution dates and payment dates on all historical dividends), but that it would result in massively larger linearized databases while having negligible effects on backtests for the reasons just given.

2. Yahoo! Finance (or rather, their historical data source, Commodity Systems Inc.), does not use PXD (and has not used it for quite some time). The adjustment method detailed by Randy is a correct description of how CSI, Norgate, QuoteMedia, and virtually all other data sources besides the GTR1 backtester and most academic databases (e.g., CRSP and Compustat) adjust for distributions, but if you think about it carefully, it does not correspond to reinvestment of the distribution at the close of the ex-distribution date. Some of these sources actually claim to use "the CRSP method" of adjusting for distributions, but these claims are false.

So what reinvestment strategy does the CSI method underlying Yahoo!'s data assume? It turns out to be one that is far less practical than PXD. Furthermore, the impracticality of the reinvestment strategy impacts all distributions, not just ordinary cash dividends, and in the case of large special dividends, it can result in a significant distortion of returns. The net result is actually a measurable distortion of returns to the downside as a result of the asymmetry of leveraged daily stock returns.

The reinvestment strategy underlying the CSI method of adjustment (which is really everyone's except GTR1 and academia) is this: At the close of the entitlement date (i.e., market day before the ex-dividend date), purchase enough additional shares of the distributing security on margin (notionally on margin, if the portfolio has cash available) so that the entitled distributions, as valued on the entitlement date, exactly pay off the notional margin debt, keeping in mind that any shares purchased at the entitlement date close are also entitled to the same distributions. Furthermore, if the distributions include other stock, then short the entitled number of shares (using when-issued shares, if necessary) at the close of the entitlement date (again, keeping in mind that the additionally purchased shares in the distributing security are themselves entitled to the distribution of stock, and also that one is liable for any distributions to which the shorted shares are entitled) so that the short positions are exactly closed out on the ex-distribution date.

If that sounds complicated, it is, and because of that, I'll omit the proof that these assumptions are equivalent to the CSI method of adjustment. And if it sounds like a ridiculously convoluted and impractical method of actually reinvesting distributions, you're of course right. But as I've said, this is the "industry norm" outside of academia and the GTR1 backtester (and possibly the Portfolio123 backtester also, given that it uses Compustat data, though of course Portfolio123 is free to apply their own linearization method, and they may well go with the "industry norm").


The CSI Method and Return Distortion

To demonstrate the kind of distortion that the CSI method entails, suppose that a stock trading around $20 per share is to pay out a $10 special dividend as a first step in liquidation (not an uncommon scenario) or buy-out. Assume the stock closes at exactly $20 at the close of the entitlement date (which is identical to the payment date for a dividend this large) of 11/25/2019, and the next day (the ex-distribution date), the stock closes at $8.

Using PXD (the GTR1/academic method), the total return on the ex-dividend date is simply ([$8 value of 1 remaining share at the close of 11/26/2019] + [$10 dividend available for reinvestment at the close of 11/26/2019])/[$20 value of 1 share held on 11/25/2019] = 18/20 = 0.9, i.e., -10%.

Using the CSI ("industry norm") method, the total return on the ex-dividend date is [$8 value of 1 remaining share at the close of 11/26/2019]/([$20 value of 1 share held on 11/25/2019] - [$10 dividend]) = 8/10 = 0.8, i.e., -20%.

Why is the loss on the ex-dividend date twice as bad using the CSI adjustment method versus the PXD method? Simply put, because the position went into the ex-distribution date 2x leveraged using the implied CSI reinvestment method.

Of course, the implied leverage of the CSI method can also distort returns to the upside. However, there are two critical points: First, for reasons that I won't go into unless there is interest, "the market's" recognition of returns more closely matches PXD assumptions than those of the CSI adjustment method, and second, leveraged returns are asymmetrical on a compounding basis.

For example, if the same stock distributed another special dividend of $4 per share with entitlement date/payment date 11/26/2019, but this time the stock closed up (on an adjusted basis) on the ex-dividend date at price of $4.8889, then PXD produces a total return of (4 + 4.8889)/8 ~= 11.11%, which by design, cancels out the previous day's loss. However, by the CSI method, the investor is still in the hole after the gain on 11/26/2019: The return on the second ex-dividend date is only 4.8889/(8 - 4) ~= 22.22%, which is insufficient to compensate for the -20% loss on a compounded basis.

A hypothetical example wasn't even necessary. The issue of the CSI method distorting returns has come up on this message board before when screen picks have made large special dividends (for example, see https://boards.fool.com/pip-squeak-32566361.aspx?sort=whole#...).


So, why is the CSI method the "industry norm" when it so distortionary?

The CSI adjustment method is universally applied outside of academia because it has one very appealing property for traders and real-time data consumers in general: Throughout the ex-dividend date (and in fact, from the moment the market closes on the entitlement date), the adjusted closing price of the distributing security on the entitlement date is fixed. That is, the "previous close" at 3pm on the ex-dividend date is the same as it was at 11am, or at any other time of the day. By contrast, PXD has the peculiar (and undesirable, for traders) property that the adjusted previous closing price for the distributing security fluctuates throughout the ex-dividend date and doesn't settle down until the market closes on the ex-dividend date. This fluctuation would cause massive confusion if PXD were used in real-time stock quotes on brokerage websites, in trading software, etc, so for that reason alone, PXD is completely impractical, in spite of it actually being more realistic for both backtesting and market valuation.


Robbie Geary
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