THE QUANT by Richard Booth

CONTROL PREMIUMS & STOCKHOLDER DIVERSIFICATION

As I argue in Market Prices & Imbedded Discounts the price of a stock as set in an active market should usually be higher than the price set by a willing seller and a willing buyer in a one-on-one negotiation. Most stock is held by diversified investors who avoid company-specific risk. Thus, stock prices reflect the value of stocks as part of a portfolio and as if there is no company-specific risk involved. Less risk means higher price. The bottom line is that in most cases market prices are higher than they would be if they were set by well informed buyers and sellers of whole companies. In other words, the notion that market prices are inherently low is a total myth.

This analysis implies that when a bidder makes an offer for a target company at a premium over the market price, the real premium from the point of view of the bidder is bigger than it would appear to be in comparison to market price. In other words, the market acts as a natural barrier to takeovers motivated by marginal gains. The fact that bidders must clear this hurdle in order to make a bid, suggests that target managers should bear a significant burden in justifying takeover defenses (which generally they do).

It is also possible that bidders find targets by looking for companies that trade at a discount to the price that CAPM indicates should be the price. Indeed, I am sure that they do. But if the premium offered is nothing more than the difference between a market price that is depressed for some reason and the price calculated under CAPM, then really the premium is no premium at all. I am not aware of any studies that have sought to determine the extent to which takeovers are prompted by discounts rather than offering true premiums. It is also possible that many takeovers involve mixed motives, that is, exploitation of a discount combined with some amount of premium.

If it turns out that most takeovers (or even a significant number of them) are motivated by discounts, then the idea that a court in an appraisal proceeding should tack on a premium is nonsense.

To put it bluntly, if bidders use CAPM to find undervalued targets, and then bid up to the CAPM price, it makes no sense for a court to add on another premium.

MARKET PRICES & IMBEDDED DISCOUNTS

In disputes about the value of a business, the courts have ruled that the market price of a company's stock is an unreliable measure of value because of the notion that market price must reflect some discount for marketability (liquidity) or minority status. See, e.g., Rapid-American Corp. v. Harris, 603 A.2d 796 (Del. 1992); see also Tri-Continental Corp. v. Battye, 74 A.2d 71 (Del. 1950).

The idea seems to be that the market builds in a discount more or less in exchange for the ability to sell on demand. In other words, if one wants to sell a stock fast, one must accept a fire sale price.

Wrong. The price set in an active market should usually be higher than the price set between a willing seller and a willing buyer in a one-on-one negotiation. Investors who hold diversified portfolios can avoid all company-specific risk. Most stock -- at least two-thirds by value in the US -- is held by diversified investors -- such as mutual funds and pensions plans. Stock prices are set by the trading of these investors and reflect the value of stocks to them as part of a portfolio. In other words, prices are set as if there is no company-specific risk involved. Less risk means higher price. The bottom line is that in most cases market prices are higher than they would be if they were set by well informed buyers and sellers of whole companies.

This is not to say that the market is always right. There are many reasons why the market may get it wrong for an individual stock. The market for the stock may be inactive or thin. There may be inaccurate information at work in the market. Traders may have driven the price of a particular stock (or sector of stocks) up or down. So appraisal and similar remedies -- by which a court undertakes to determine the correct value of a company or stock -- make sense in some cases.

The standard method applied by the courts in such proceedings is based on the Capital Asset Pricing Model (CAPM). In essence, CAPM provides a way to determine the required rate of return for a particular stock by measuring the tendency of the subject stock to fluctuate relative to the market as a whole. For more on this see The Logic of Beta (coming soon).

To be sure, this method of determining the required rate of return is based on market prices of other stocks (and changes in such prices). Thus, sometimes appraisers will gross up the calculated value to eliminate the imbedded discount that supposedly affects all market prices. In other words, they presume that all market prices are too low by some percentage (usually 20 to 25 percent).

That's the rub. It makes no sense to assume that all market prices are too low. Although reasonable people may disagree about whether a particular stock is undervalued by the market at some particular time, the market rate of return is what it is. One might predict that the market as a whole will go up or down and cite any number of reasons for the prediction. And one might even refrain from selling or buying on the belief that the market will go up or down. But it is nonsense to say that the market as a whole is wrong.

The beauty of CAPM is that it is a way to calculate what the market price of a stock should be on the basis of three easily observed variables: the riskless rate of return, the market rate of return, and the volatility of the subject stock relative to the market -- the beta of the stock. In other words, one can use CAPM to double check the reported market price of a stock against what the price should be as part of a diversified portfolio.

In contrast, it may make sense to gross up the calculated value of a stock if one calculates the value using a market multiple (P/E) derived from a group of comparable companies. For example, if that sector has been the subject of a series of mergers or takeovers, it may be that prices in the entire sector are depressed for some reason.

The bottom line is that an imbedded discount can be a problem for an individual stock. But it is exactly the kind of problem that CAPM is designed to address. To adjust the price calculated under CAPM supposedly to eliminate an embedded discount is double-think.