AT THE start of 1998, Apple, a computer maker, was in deep trouble. Its shares bounced around wildly and were far more volatile than those of, say, IBM, a blue-chip rival. And yet, calculated according to conventional financial theory, Apple's cost of equity (the return that investors demanded to compensate them for the risk of owning its shares) was 8% -- below IBM's 12%. More puzzling still, when Apple's situation improved in the spring, and its shares became less volatile, its theoretical cost of equity actually rose to 11%.

Has theory lost touch with common sense? Jim McNulty and Max Ziff, two bankers at Warburg Dillon Read (WDR), think so. The culprits seem to be a pair of Greeks, alpha and beta. These are cornerstones of the capital-asset pricing model (CAPM), the academically kosher way to value securities. Because it often reaches outlandish conclusions, says Mr Ziff, the model is considered by many of his clients to be useless. Fortunately, however, he reckons that his bank has fixed it.

The basic insight of the CAPM is this. Investors require higher returns from riskier investments; but risk has two parts. One, called alpha, is specific to a particular share (bad management, for example). In a big share portfolio, all the alphas, in effect, cancel one another out. So investors tend to focus on the second part of risk: that the stockmarket might crash, taking their shares down too. They then price each share according to how much it moves with market swings. The degree of that volatility is expressed as a beta factor.

So what to make of Apple? Just when its future was most in doubt and its shares most volatile, its beta was only 0.47-in other words, it appeared to be half as volatile as the overall stockmarket. IBM's beta was 1.09, roughly in line with the market.

Probably, what had happened is that Apple had become such a basket-case that it simply decoupled from the stockmarket altogether.

So as IBM and its peers rose and fell with the rest of Wall Street, Apple shares reacted solely to news about he company, at times-by coincidence-bucking the market's trend. Beta thus created the false impression that Apple shares were more stable than the stockmarket.

This also means, says Mr Ziff, that beta is not much use to anyone who is not thinking in terms of a total portfolio. A company considering taking over Apple, for instance, is not planning to buy scores of other companies as well. It would value Apple by projecting its cashflows and discounting them by its cost of capital. Using beta, that discount-rate would be unreasonably low, overstating Apple's worth.

Mr Ziff accordingly proposes to replace beta with a measure of total risk. It so happens that markets already provide this information, in the form of the premium of a call option on the company's share-price. The more volatile the share, the higher this premium-since the share is more likely to rise above the option's strike price. Translate the premium into an annual rate and you have the cost of equity.

Using this method, WDR would have put Apple's cost of equity at 18% in January 1998-above IBM's, and more in line with common sense. When Apple shares became less volatile in the spring, the model would have cut the cost of equity to 16%.

Bye-bye CAPM? Not so fast, say loyalists. So long as any investors are able to mix enough shares into a portfolio to diversify away specific company risk, they will bid up the price of those shares until they reflect only market risk. A mutual fund, say, that specialises in "distress stocks" might put a thousand Apples in its basket, each rotten but for different reasons. For such investors, beta is still hard to beat.