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Letters to the Editor: An Exchange of Letters Regarding a Doomsday Analysis of Dividend Yields

Dear Dr. Niederhoffer:

I compiled data on the DJIA dividend yield from 1955 to 2004. The data came from this week's Barron's (see page M22, 9-12-2005). I did a two-tailed, t-distribution on the data, using a 95% confidence level. The results were tabulated using a TI-83+ calculator:

Mean: .03634, SD: .01265, N: 50, T: 2.0096

The range of values I totaled were .03274, .03994. I concluded with 95% confidence that the average yearly DJIA dividend yield falls between those two values above in any random sample of 50.

I noticed something ominous in the more recent data, however. When looking at the DJIA dividend yields between 1990 and 1999, the dividend yield on the DJIA declined from 3.94% to 1.47%.

At the same time, however, the value of the DJIA climbed from 2633.66 to 11497.12. One question immediately came to mind: Does the value of the DJIA average move inversely to yearly changes in the dividend yield of the DJIA?

If there is negative correlation between yearly changes in the DJIA dividend yield and the closing value of the DJIA, could it be that in order for the DJIA dividend yield to return to its long-term 50 year average, the value of the DJIA must decline in the future?

This begs the question of whether changes in dividend yields are predictive of price action in stocks generally? Or could increased dividend payouts from companies in the DJIA cause the DJIA dividend yield to increase when the value of the DJIA remains flat? If so, to what degree?

If the data I compiled are incorrect, I would love to know where (and what) I did wrong. Your reply and review would be most appreciated. Seems like the numbers cause one to ask more questions than provide answers.

Aaron Koral

Victor Niederhoffer Responds:

Your data don't take into account the increase in buybacks during this period, the decline in interest rates, or the change in tax rates. Nor do you look at future return as a function of dividend yield changes. Nor do you take account of changing cycles, or the obvious differences between the markets of today and 40 years ago. Data on dividend yields are available in the Standard and Poor's Statistical Price Record and the Dow Jones handbooks, as well as on the internet. Like Robert Shiller, you are taking historical figures that show no predictivity and making impressionistic negative comments about today based on statistically insignificant results that have no bearing on today.

Aaron Koral Responds:

It's been a while  since I did any statistics, so I freely admit that my results were rudimentary.  There is, however, one notion you touched upon in your reply, which was "looking at future returns as a result of dividend changes". If I were to focus on this notion, how would I go about proving the "predictive" nature of changes in dividend yields on equity prices?

Should I also be looking at the yearly changes in the DJIA and compare that to the changes in the dividend yield? What should I learn in statistics to pursue a better understanding of how changes in dividend yields cause changes in equity prices (or not)?

Victor Niederhoffer Responds:

Your response reminds me of Galton's to Darwin on the matter of pangenesis which is very poetic and Galton turned out to be right. You don't need fancy statistics. Just make a table of dividend yields in one column and future returns the next year in another. Then divide the dividend yields into four classes from low to high. For each class look at the mean future return . Then compare and see if you note differences. Do the same for changes in yield. Make sure the data in the first column are available and announced well ahead of the return in the second column.

Charles Kim adds:

Regarding Aaron Koral's dividend study and Vic's response, it got me to thinking about how rare it is to see regression analyses that do not take place over an extended time series of data. Are their any quant shops out there that look at how various pricing relationships correlate when conditions are varied against the speed of price changes, or by volatility as measured by option implied volatility

Jason Schroeder rings in:

Having lots of data in order to make strong inferences is required in the common usages of statistics. This part of the justification for making "The Triumph of the Optimists."

Making inferences on smaller amounts of data invites a requirement to figure out "why" one needs "so much" data to begin with. Some souls attempt to subdivide their datasets in order to synthesize more data assuming that more is indeed more.

In common usage, the ability to differentiate between a poor hypothesis and poor inference process renders small datasets useless. In centuries past, data was more expensive to obtain and curiously it did not seem to halt research.

Andrew West adds:

The Financial Analysts Journal has published a number of interesting studies looking at markets and dividend yields. Arnott and Asness wrote "Surprise! Higher Dividends = Higher Earnings Growth", (Jan/Feb 2003) concluding that contrary to conventional formulas, periods of high earnings retention tended to lead periods of slower earnings. Arnott & P. Bernstein also found dividend yield useful in evaluating market risk premiums in their article "What Risk Premium is Normal?" (Mar/Apr 2002).

Regardless of whether one agrees with Arnott's negative conclusions, the collection and presentation of the data relating to dividends, earnings and the market were very interesting.

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