Alternative Market Capitalization Measures

As the major stock market indexes have swung up and down, newspapers have breathlessly reported that trillions of dollars of value that have appeared and disappeared from our economy in a matter of hours or days. I share the guilt, having done so in other posts.

The market capitalization of a company is typically determined by multiplying the number of shares it has outstanding by the current share price of the stock. The market capitalization of the market is typically determined by using percentage changes in a value weighted index of the total market, and using the aggregate market capitalization of the companies that make up the index at a given point as a baseline.

While this measure has the virtue of responsiveness to economic conditions in the firm valued and in the market generally, this is also a very volatile measure of value in the case of companies which, our intuition tells us, shouldn't experience much variation in value from day to day under most circumstances. The vast majority of shareholders of a publicly held company, on any given day, do not trade their shares. Implicitly, by not selling, these shareholders are stating that the shares are currently undervalued or properly valued. Market value is set only by the tiny minority skittish enough to sell shares or buy them on a given day who are most pessimistic about the company's value.

Market value certainly has many worthwhile purposes, particularly if you are contemplating selling your shares or buying shares. But, in a market capitalization calculation, it ignores the judgment of the vast majority of shareholders about a market capitalization value, in favor of a tiny minority.

Indeed, there is every reason to believe from the way that market participants organize themselves in the real world, that a large share of all trading, and hence all market price setting, is done by market participants who value shares using methods quite different from those of long term investors, and are influenced by different considerations. Day traders and long term value and growth investors operate differently. Hot money, short term investors are subject to different kinds of pressures than buy and hold investors.

The experience of tender offers, when an acquirer offers to buy a control block of shares in a company, motivating shareholders not willing to sell at the current market price by offering a premium from the current market price to sellers, suggests that the real collective valuation of a typical target company is a third to a half higher than a typical market valuation of the company by existing shareholders. Tender offer buyers, meanwhile, implicitly are stating that the company, when properly managed, can have an even higher value -- "new management value."

Of course, tender offers are unusual too. On any given day, and indeed, in any given year, only a small percentage of publicly held companies are the subject of tender offers. And, one expects that companies with particularly low share prices relative to the intrinsic value of the company's assets are the most likely to be the subject of a takeover attempt.

There is no particularly good reason to believe that "majority value" representing a price that would have to be offered to succeed in a tender offer for a majority of a company's shares, has a reliable relationship to "market value" in the stock market on a given day, in the vast majority of companies that aren't subjected to tender offers. While majority value (and hence a more realistic measure of market capitalization) should almost always be higher than a market capitalization based upon market value, there is no particularly good reason that these two valuations should have the same ratio to each other in all companies.

Tender offer premiums may suggest the order of magnitude of the typical difference between majority value and market value, but can only tell us so much. Other financial ratios, like price to earnings ratios, and price to book value per share ratios, typically very greatly by industry and from company to company within an industry. A price to "majority value" per share ratio, if there was a way to measure it, would also likely very a great deal form industry to industry, and from company to company.

One can imagine some measures that would compensate for the thinness of trading much of time.

A fairly simple measure, which would greatly reduce volatility, but is still subject to the fact that it depends over much upon short term investor psychology, would be to look at average price during the time period over which a number of shares equal to half of the shares currently outstanding have changed hands.

A measure similar to the way that capital assets were traditionally valued for accounting purposes, could measure the average basis that shareholders of a company have in their shares -- the aggregate shareholder purchase price of the company, so to speak. Or, one could measure the purchase price of shareholders of median duration of ownership in the company.

One could, instead, use a more analytical model that would look at the relationship between sales volume in a company's shares and changes in share price, in a large number of companies, to so if this relationship predicted tender offer premiums in any predictable way. A similar methodology is used to accurately predict the likelihood of rare extreme natural disasters like big floods, major earthquakes and long droughts. This data concerning the share prices and trading volumes of the company in the real world over an arbitrary time period would then be collected and applied to the formula that predicts "majority value." Other data that might be relevant to such a formula would be insider trading activity.

In the same vein, a formula might, for example, value a company at not less than the highest price shares have traded for in the period over which aggregate volume of trading has equalled a majority of shares in the company. This would still probably undervalue a company that had a stable value (even if old share prices were corrected for inflation or overall market fluctuations), and would be less responsive to changes in a company's value over time, but does make some theoretical sense.

Rather than trying to pin down an actual price, another way to report share prices would be to include a "margin of error," in a given day's valuation, based upon statistical volatility and sample size principles, over a time period measured in either time or percentage of total shares outstanding that have been traded, or simply raw numbers of trades conducted (since statistical margin of error is far more strongly influenced by sample size than by population size in most circumstances with the kind of daily trading volumes and numbers of outstanding shares seen in the stock market). This measure would add insight to situations like those we have seen in the last few weeks, where wild upward and downward swings in share prices reflect uncertainty in the market over the true value of the assets that the market is attempting to value. In heavily traded stocks, it might also be possible to do a Monte Carlo analysis of the likely range within share prices should fall.

Similarly, one might flag share prices as being more or less significant, in much the same way that one might use p values to describe statistical significance, by ranking them based upon volume relative to the number of shares outstanding. The heavier trading is in a company, the more one would expect the current market price to be close to the majority price. The thinner trading was in a company, the less reliable market share prices could be assumed to be as a measure of the majority value of shares of the company. Once again, it might also turn out to be the case that share price significance by this measure is related in some formulatic way to the majority price to market price ratio of a company. Or, perhaps "margin of error" and "share price significance" taken together might in compensation be predictive of a majority price to market price ratio.