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By Root 2816 0

between value calculations of growth stocks and the famous Petersburg Paradox, which has challenged and confused mathematicians for more than two hundred years. The point I want to make here is that there is a special paradox in the relationship between mathematics and investment attitudes on common stocks, which is this: Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw therefrom. In forty-four years of Wall Street experience and study I have never seen dependable calculations made about common-stock values, or related investment policies, that went beyond simple arithmetic or the most elementary algebra. Whenever calculus is brought in, or higher algebra, you could take it as a warning signal that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.

The older ideas of common-stock investment may seem quite naïve to the sophisticated security analyst of today. The great emphasis was always on what we now call the defensive aspects of the company or issue—mainly the assurance that it would continue its dividend unreduced in bad times. Thus the strong railroads, which constituted the standard investment commons of fifty years ago, were actually regarded in very much the same way as the public-utility commons in recent years. If the past record indicated stability, the chief requirement was met; not too much effort was made to anticipate adverse changes of an underlying character in the future. But, conversely, especially favorable future prospects were regarded by shrewd investors as something to look for but not to pay for.

In effect this meant that the investor did not have to pay anything substantial for superior long-term prospects. He got these, virtually without extra cost, as a reward for his own superior intelligence and judgment in picking the best rather than the merely good companies. For common stocks with the same financial strength, past earnings record, and dividend stability all sold at about the same dividend yield.

This was indeed a shortsighted point of view, but it had the great advantage of making common-stock investment in the old days not only simple but also basically sound and highly profitable. Let me return for the last time to a personal note. Somewhere around 1920 our firm distributed a series of little pamphlets entitled Lessons for Investors. Of course it took a brash analyst in his middle twenties like myself to hit on so smug and presumptuous a title. But in one of the papers I made the casual statement that “if a common stock is a good investment it is also a good speculation.” For, reasoned I, if a common stock was so sound that it carried very little risk of loss it must ordinarily be so good as to possess excellent chances for future gains. Now this was a perfectly true and even valuable discovery, but it was true only because nobody paid any attention to it. Some years later, when the public woke up to the historical merits of common stocks as long-term investments, they soon ceased to have any such merit, because the public’s enthusiasm created price levels which deprived them of their builtin margin of safety, and thus drove them out of the investment class. Then, of course, the pendulum swung to the other extreme, and we soon saw one of the most respected authorities declaring (in 1931) that no common stock could ever be an investment.

When we view this long-range experience in perspective we find another set of paradoxes in the investor’s changing attitude toward capital gains as contrasted with income. It seems a truism to say that the old-time common-stock investor was not much interested in capital gains. He bought almost entirely for safety and income, and let the speculator concern himself with price appreciation. Today we are likely to say that the more experienced and shrewd the investor, the less attention he pays to dividend