Rethinking CAPM

William F. Sharpe says his pioneering work on the Capital Asset Pricing Model is ready for a makeover.

The 42-year-old model — which earned Mr. Sharpe a Nobel Memorial Prize in economics in 1990 — is being revamped because Mr. Sharpe says he found a better way for portfolio managers and business-school students to learn about how portfolios are constructed and securities are priced.

CAPM, along with portfolio theory, developed by Mr. Sharpe's mentor and co-Nobel winner Harry Markowitz, is the foundation of every finance program in the country, if not the world.

His latest book, "Investors and Markets: Portfolio Choices, Asset Prices and Investment Advice," may send investors and academics scurrying. Published this month by Princeton Univer- sity Press, the book eschews mean-variance analysis — the mathematically complex formula that relates rewards to risks of securities or portfolios — in favor of a "state/preference" approach that relies on an easy-to-understand simulation. The state/preference approach is based on a model closer to that used in financial engineering than in the ivory tower.

"I think of it as ‘beyond mean-variance,'" Mr. Sharpe said in an interview.

Whether that approach will work in the real world is unknown. Mr. Sharpe says he is just starting work on applying it to asset allocation. If the approach proves successful, it could result in a shift away from the traditional mean-variance optimizer used in establishing asset mixes and managing securities portfolios.

Mr. Sharpe gets high marks for his willingness to reassess the validity of his earlier thinking.

"I like many things about Bill Sharpe," said Meir Statman, Glenn Klimek Professor of Finance at Santa Clara University's Leavey School of Business, Santa Clara, Calif. "One of them is that he's not busy protecting things that he's done as a young man. Because what this is, is a new approach to asset pricing that undermines the CAPM. ‘Well,' (Mr. Sharpe) says, ‘so be it.'"

There are numerous reasons for finding a substitute for a mean-variance approach. For one thing, it is ill-suited for considering extraordinary economic events such as bubbles, depressions, hyperinflation or terrorist attacks. These types of "tail risk" are ignored by mean-variance analysis, which distributes expected returns on a normally shaped bell curve and then measures the likelihood of a scenario occurring in terms of standard deviations from the mean.

"We've come to thinking about risk as standard deviation," Mr. Statman said. "What people want is protection when the economy tanks."

Another problem is that mean-variance analysis assumes that all investors have the same beliefs about the market and the relationship among different assets. That's like saying Warren Buffett and Jennifer Lopez have the same market outlook.

In addition, mean-variance analysis ignores taxes, transaction costs and illiquidity. The analysis also assumes all investors can borrow at the risk-free rate — a major flaw requiring repair, in Mr. Markowitz's view.

CAPM was a revolutionary concept when Mr. Sharpe developed it in 1964. (Separately, academics Jan Mossin and John Lintner also came up with the theory, but Mr. Sharpe was the first to publish.)

In CAPM, Mr. Sharpe found the most efficient portfolio was the entire market. Mr. Sharpe also related the riskiness of an individual security to the entire market, which was termed "beta."

Mr. Sharpe concluded that most of a stock's risk stemmed from the market. The idea of an index fund — passively tracking the entire market — came directly out of CAPM and the "efficient market hypothesis" unveiled a year later by Eugene F. Fama in his doctoratal dissertation at the University of Chicago's Graduate School of Business.

In developing the CAPM, Mr. Sharpe relied on mean-variance analysis, suggested by Mr. Markowitz, which Mr. Sharpe simplified in constructing his model. That oversimplification now requires a new methodology, he believes.

In contrast to mean-variance analysis, the state/preference approach does not rely on a normal distribution, and the mathematics are far simpler than in mean-variance analysis.

"The elegance of (the state/preference model) is that you can understand the elements of the various moving parts of the optimization," said Gifford Fong, editor of the Journal of Investment Management and president of Gifford Fong Associates, a Lafayette, Calif.-based consultant on fixed income and derivatives.

Taken from research done in the 1950s by Nobel Laureate Kenneth Arrow, an economics professor emeritus at Stanford University, and Gerard Debreu, the late economist, state/preference theory says there are many possible future states of the world, but only one of them will actually occur.

Investors can assign probabilities of any given state occurring. In a complete market, an investor can buy or sell a security for every possible outcome. These contingent claims are like insurance policies. In fact, this methodology is used in pricing options, Mr. Sharpe explains.

Many economists don't like state/preference theory because it is not provable, instead relying on a simulator. Some experts also note it involves a massive amount of calculations.

"I find (the state/preference approach uses) a very general set of assumptions out of which very little specific can be deduced," said Mr. Markowitz. Messrs. Markowitz and Sharpe will debate their differing views on Oct. 16 at the Q Group's 40th anniversary conference in Santa Barbara, Calif.

Mr. Sharpe's new book shows that a simulator based on the state/preference model can mimic market behavior and can be used where mean-variance analysis won't work.

Using a couple of fishermen as his basic example — Mario from Monterey and Hue from Half Moon Bay, two towns about 100 miles apart on the Northern California coast — Mr. Sharpe runs through a series of scenarios where each fisherman's risk appetite, market outlook and even behavioral biases are built into a simulation model.

With every scenario, Mr. Sharpe's fishermen — whose numbers eventually are expanded in number — trade stocks and bonds until everyone is satisfied and equilibrium prices are set.

What's more, Mr. Sharpe's simulator works even when markets are "incomplete" — meaning there isn't a contingent claim for every possibility — and when investors have outside sources of income.

Unlike a mean-variance analysis, however, the simulator finds that it does make sense for some investors to take non-market risk. For example, someone living in Silicon Valley might want to underweight technology stocks to reduce risk, Mr. Sharpe explained.

Laurence B. Siegel, director of research at the $10.7 billion Ford Foundation's investment division, New York, praised Mr. Sharpe's new work for validating classical finance theory. He said some managers are willing to discard CAPM because of its flaws, but Mr. Sharpe's new work shows equilibrium prices can be set without using a mean-variance analysis.

H. Russell Fogler, principal at Fogler Management and Research, Gainesville, Fla., and a former finance academician, said Mr. Sharpe's work represents an important step in helping finance students understand how prices are set in a market with different types of investors.

While he thinks the state/preference approach will help investors deal with major unexpected events such as inflation or depression, Mr. Fogler doesn't think it will cause a radical change in practice because most optimizers are constrained to reflect investors' views and preferences.

The book, which retails for $39.95, will hit stores this month. "I think what Sharpe is giving us is an asset that is positively skewed with absolutely no downside for $39," Mr. Fogler said. "How can an MBA lose?"