With the average price of a share in the small-cap group at about $3%, using the 45% spread in the 1931 to 1935 period, the bid would be about $2,625 and the asking price $4.00. The buyer, according to Banz, could blithely waltz in and buy any amount of stock in the middle ( ), and not pay any commission to boot, which on small stocks could be as high as 3% of the price. The lucky buyer in 1941 could do the same thing. This assumption is key to a large part of academic financial research, which assumes markets are efficient and therefore transaction costs are a non-factor.* In addition to commissions, Banz also ignores that even tiny amounts of buying, possibly only 100 shares, could drive the stock price up 8 1 , which is why these prices often skyrocketed.

Just how far-fetched some of this analysis is can be seen from the following calculations. If someone were willing to pursue such a strategy, and buy every share of the small-cap group traded on average on any day during the 1931 to 1935 period, the theoretical cost would only be $111,422. But if you tried to do so, the trading volume would be doubled, which would drive prices much higher than the $111,422 figure. This only considers shares that traded; remember that 58% of the pint-sized group did not trade at all on any given day during this five-year period. Remember too that the spread on the stocks that didnt trade was enormous. If an investor wanted to buy $1 million worth of these surefire winners, or if a savvy mutual fund wanted to put $100 million into this group, the prices would be driven up tenfold, maybe more, making the cost of this strategy inane.

Two clear-cut examples of how thin these markets were come from the second quarter of 1933 and the third quarter of 1932. Examining the second quarter of 1933 first, the supposedly midget companies returned an astonishing 319%, against 91% for their large-sized brethren. Small wonder the investor in the Fortune chart is jubilant.

But as Thomas Carlyle noted in the 1830s, "statistics are the greatest liars of them all." The small-cap statistics would not likely change Car-lyles opinion. In the second quarter of 1933 the market price was $1.35 for the average stock in the group and the average market value was only $263,000 for each company. These shares traded an average of 94 shares a day at the beginning of this period.

* This is not the only time that this conclusion has resulted in severely flawed ideas. The 1987 crash is the classic example. See my Forbes articles written before and after the crash-"Doomsday Machine," 3/23/87; "Thanks, Professor," 11/16/87; and "The Nominees Are ...," 3/21/88.

t Taking the average trading volume of 240 shares of the 139 companies in the bottom 20% resulted in this figure.

* Taken again from the closing prices from The New York Times and The Wall Street Journal at the end of each quarter in the period. No bid/ask information for this period is available from any computer database that I am aware of, and not from CRSP.

If you bought every stock that traded in the group, the total cost would have been a pittance: $17,470. Many readers IRAs or other retirement funds Im sure exceed this figure-even in constant dollars. But it gets worse. You could only buy 27% of the stocks traded; 73% of these stocks simply did not trade.

What was the average spread between the bid and oiTer of the 73% of these the stocks that didnt trade? It was an amazing 117%. If you wanted to buy 100 shares, you would have had to pay double the market price. That alone would wipe out 50% of the advantage of small over large cap stocks in their finest hour. With markets this thin, one shudders to diink what 100,000 shares would push the price to.

The third quarter of 1932, when midget companies rose 160.7%, vs. 90.5% for the large caps, is a nearly identical example. The average market price for the bottom 20% was $1.09, the average volume was 32 shares, and 83% of the group did not trade. The total trading volume for the bottom 20% was $4,817 a day.

The 1941 to 1945 period, the best in the sample, shows again how little liquidity existed for pint-sized companies, even for those trading on the NYSE. The companies were minuscule, with the average size of the bottom 20% at $1.9 million. The average trading volume was very low, only 482 shares a day when this group of "big winners" was selected at the beginning of I94I.* The spread between the bid and the offer price was still large at 17%. Although the price was higher than in I93I, it would have only cost an investor about $335,000 to do all the trading on the NYSE in this group on a given day. Add the fact that more than 37% of the group did not trade on any trading day, and you can see that even a marginal increase in demand for these stocks would have driven prices through the roof, which is exactly what happened.

Without the two periods where pint-sized companies sparkled in the Banz study, I93I to 1935 and I94I to 1945, small stocks actually did no better than the market, with a far greater risk of going under. The new professors did not consider any of these factors.

But was the liquidity problem solely one affecting small-cap stocks or did it also apply to their larger brethren? The answer is that liquidity was lower for all stocks throughout this period, but it had a disproportionate effect on the smaller companies. For the large stocks the spread in 1931 to 1935 was 4.6%. (The median spread for large caps was 1.3% in 1931

to 1935, while small caps was 20%.) The average large-cap volume was 4,842 shares, or 20 times that of the pint-sized group. In 1941 the spread was only 1.6%, and the volume was about six times that of the small group. Fewer of the larger companies did not trade on any single day, 13.2% vs. 58.1% of the small-cap group in the 1931 to 1935 period, and 11.0% versus 37.3% in the 1941 to 1945 period. Liquidity in bigger companies was a fraction of what it is today, but you could buy or sell them, which meant you could carry out a real, rather than a hypothetical, strategy.

A final problem that Banz and his blue-ribbon academic committee missed is connected to the others and magnifies the liquidity problem enormously. Numbers of the smaller-sized companies in the 1931 to 1945 period were in serious operating difficulties, particularly if they were once larger, financially sound firms. That was what originally won them their spurs to trade on the Big Board. An improvement in outlook would likely trigger a manifold price increase in one of the most illiquid securities markets in the nations history. When the U.S. entered World War II, many firms which had barely stayed alive began to prosper.

The war was an enormous one-time boost to small cap companies, many of which had accumulated major losses in the past. Improving business and prior losses meant they paid little or no income taxes, rebuilding often drained financial resources. The larger companies, on the other hand, often profitable through the thirties, paid excess profit taxes up to 100%. The war was a splendid one-time boost to troubled small cap companies, a boost that the solid blue chips didnt get.

The 1930 to 1945 period happened once, and only once in American economic history, brought about by the worst crash and depression on record, followed by the nations largest recovery. Add to this some of the most extreme illiquidity in market history. The key point is that it was extraordinary conditions, not rapidly growing small-sized firms, that accounted for the rocketlike retums.

In short this was a strategy that could not have been used by any but a handful of investors buying a few hundred shares here and there. Yet the Banz study is used to justify billions of dollars and millions of investors mshing in to buy small-sized companies. Its almost like locating a bridge on a map that does not detail its size or composition, and concluding the bridge is a steel span on a superhighway when it is in fact constmcted of rope.

When I showed their results were problematical a year later, and the low P/E effect was very much alive, there was nary a word from the -