Revisiting The Capital Asset Pricing Model

by Jonathan Burton

Reprinted with permission from Dow Jones Asset Manager
May/June 1998, pp. 20-28

For pictures and captions, click here

Modern Portfolio Theory was not yet adolescent in 1960 when William F. Sharpe, a 26-year-old researcher at the RAND Corporation, a think tank in Los Angeles, introduced himself to a fellow economist named Harry Markowitz.. Neither of them knew it then, but that casual knock on Markowitz's office door would forever change how investors valued securities.

Sharpe, then a Ph.D. candidate at the University of California, Los Angeles, needed a doctoral dissertation topic. He had read "Portfolio Selection," Markowitz's seminal work on risk and return—first published in 1952 and updated in 1959—that presented a so-called efficient frontier of optimal investment. While advocating a diversified portfolio to reduce risk, Markowitz stopped short of developing a practical means to assess how various holdings operate together, or correlate, though the question had occurred to him.

Sharpe accepted Markowitz's suggestion that he investigate Portfolio Theory as a thesis project. By connecting a portfolio to a single risk factor, he greatly simplified Markowitz's work. Sharpe has committed himself ever since to making finance more accessible to both professionals and individuals.

From this research, Sharpe independently developed a heretical notion of investment risk and reward, a sophisticated reasoning that has become known as the Capital Asset Pricing Model, or the CAPM. The CAPM rattled investment professionals in the 1960s, and its commanding importance still reverberates today. In 1990, Sharpe's role in developing the CAPM was recognized by the Nobel Prize committee. Sharpe shared the Nobel Memorial Prize in Economic Sciences that year with Markowitz and Merton Miller, the University of Chicago economist.

Every investment carries two distinct risks, the CAPM explains. One is the risk of being in the market, which Sharpe called systematic risk. This risk, later dubbed "beta," cannot be diversified away. The other—unsystematic risk—is specific to a company's fortunes. Since this uncertainty can be mitigated through appropriate diversification, Sharpe figured that a portfolio's expected return hinges solely on its beta—its relationship to the overall market. The CAPM helps measure portfolio risk and the return an investor can expect for taking that risk.

More than three decades have passed since the CAPM's introduction, and Sharpe has not stood still. A professor of finance at the Stanford University Graduate School of Business since 1970, he has crafted several financial tools that portfolio managers and individuals use routinely to better comprehend investment risk, including returns-based style analysis, which assists investors in determining whether a portfolio manager is sticking to his stated investment objective. The Sharpe ratio evaluates the level of risk a fund accepts vs. the return it delivers.

Sharpe's latest project is characteristically ambitious, combining his desire to educate a mass audience about risk with his longtime love of computers. Technology is democratizing finance, and Sharpe is helping to push this powerful revolution forward. Through Financial Engines, Sharpe and his partners will bring professional investment advice and analysis to individuals over the Internet.

What do you think of the talk that beta is dead?

The CAPM is not dead. Anyone who believes markets are so screwy that expected returns are not related to the risk of having a bad time, which is what beta represents, must have a very harsh view of reality.

"Is beta dead?" is really focused on whether or not individual stocks have higher expected returns if they have higher betas relative to the market. It would be irresponsible to assume that is not true. That doesn't mean we can confirm the data. We don't see expected returns; we see realized returns. We don't see ex-ante measures of beta; we see realized beta. What makes investments interesting and exciting is that you have lots of noise in the data. So it's hard to definitively answer these questions.

Would you approach a study of market risk differently today than you did back in the early 1960s?

It's funny how people tend to misunderstand the CAPM's academic, theoretical and scientific process. The CAPM was a very simple, very strong set of assumptions that got a nice, clean, pretty result. And then almost immediately, we all said, let's bring more complexity into it to try to get closer to the real world. People went on—myself and others—to what I call "extended" capital asset pricing models, in which expected return is a function of beta, taxes, liquidity, dividend yield, and other things people might care about.

Did the CAPM evolve? Of course. Are the results more complicated shall just expected return is a linear function of beta relative to the Standard & Poor's 500-Stock Index? Of course. But the fundamental idea remains that there's no reason to expect reward just for bearing risk. Otherwise, you'd make a lot of money in Las Vegas. If there's reward for risk, it's got to be special. There's got to be some economics behind it or else the world is a very crazy place. I don't think differently about those basic ideas at all.

What about Harry Markowitz's contribution to all of this?

Markowitz came along, and there was light. Markowitz said a portfolio has expected return and risk. Expected return is related to the expected return of the securities, but risk is more complicated. Risk is related to the risks of the individual components as well as the correlations.

That makes risk a complicated feature, and one that human beings have trouble processing. You can put estimates of risk/return correlation into a computer and find efficient portfolios. In this way, you can get more return for a given risk and less risk for a given return, and that's efficiency a la Markowitz.

What stands out in your mind when you think about Markowitz's contribution?

I liked the parsimony, the beauty, of it. I was and am a computer nut. I loved the mathematics. It was simple but elegant. It had all of the aesthetic qualities that a model builder likes. Investment texts in the pre- Markowitz era were simplistic: Don't put all your eggs in one basket, or put them in a basket and watch it closely. There was little quantification.

To this day, people recommend a compartmentalized approach. You have one pot for your college fund, another for your retirement fund, another for your unemployment fund. People's tendencies when they deal with these issues often lead to suboptimal solutions because they don't take covariance into account. Correlation is important. You want to think about how things move together.

Tell us about your relationship with Markowitz.

Harry was my unofficial dissertation advisor. In 1960, he and I were both at the RAND Corporation. My official advisor at the University of California at Los Angeles suggested I work with Harry, but Harry wasn't on the UCLA faculty. I introduced myself to him and said I was a great fan of his work.

With Markowitz's encouragement, you delved into market correlation, streamlining Portfolio Theory with the use of a single-factor model. This became part of your dissertation, published in 1963 as "A Simplified Model of Portfolio Analysis."

I did my dissertation under a strongly simplified assumption that only one factor caused correlation. The result I got was in that setting, prices would adjust until expected returns were higher for securities that had higher betas, where beta was the coefficient with "the factor."

Portfolio Theory focused on the actions of a single investor with an optimal portfolio. You wondered what would happen to risk and return if everyone followed Markowitz and built efficient portfolios.

I said what if everyone was optimizing? They've all got their copies of Markowitz and they're doing what he says. Then some people decide they want to hold more IBM, but there aren't enough shares to satisfy demand. So they put price pressure on IBM and up it goes, at which point they have to change their estimates of risk and return, because now they're paying more for the stock. That process of upward and downward pressure on prices continues until prices reach an equilibrium and everyone collectively wants to hold what's available. At that point, what can you say about the relationship between risk and return? The answer is that expected return is proportionate to beta relative to the market portfolio.

In a paper I finished in 1962 that was published in 1964, I found you didn't have to assume only one factor. That basic result comes through in a much more general setting. There could be five factors, or 20 factors, or as many factors as there are securities. In a Markowitz framework, where people care about the expected return of their portfolios and the risk as measured by standard deviation the results held. That paper was called "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions Of Risk." Eugene Fama called it the Capital Asset Pricing Model. That's where the name came from.

The CAPM was and is a theory of equilibrium. Why should anyone expect to earn more by investing in one security as opposed to another? You need to be compensated for doing badly when times are bad. The security that is going to do badly just when you need money when times are bad is a security you have to hate, and there had better be some redeeming virtue or else who will hold it? That redeeming virtue has to be that in normal times you expect to do better. The key insight of the Capital Asset Pricing Model is that higher expected returns go with the greater risk of doing badly in bad times. Beta is a measure of that. Securities or asset classes with high betas tend to do worse in bad times than those with low betas.

Perhaps you never imagined that the CAPM would become a linchpin of investment theory, but did you believe it was something big?

I did. I didn't know how important it would be, but I figured it was probably more important than anything else I was likely to do. I had presented it at the University of Chicago in January 1962, and it had a good reaction there. They offered me a job. That was a good sign. I submitted the article to The Journal of Finance in 1962. It was rejected. Then I asked for another referee, and the journal changed editors. It was published in 1964. It came out and I figured OK, this is it. I'm waiting. I sat by the phone. The phone didn't ring. Weeks passed and months passed, and I thought, rats, this is almost certainly the best paper I'm ever going to write, and nobody cares. It was kind of disappointing. I just didn't realize how long it took people to read journals, so it was a while before reaction started coming in.

What does the CAPM owe to finance research that came immediately before?

The CAPM comes out of two things: Markowitz, who showed how to create an efficient frontier, and James Tobin, who in a 1958 paper said if you hold risky securities and are able to borrow—buying stocks on margin—or lend—buying risk-free assets— and you do so at the same rate, then the efficient frontier is a single portfolio of risky securities plus borrowing and lending, and that dominates any other combination.

Tobin's Separation Theorem says you can separate the problem into first finding that optimal combination of risky securities and then deciding whether to lend or borrow, depending on your attitude toward risk. It then showed that if there's only one portfolio plus borrowing and lending, it's got to be the market.

Both the CAPM and index funds come from that. You can't beat the average; net of costs, the returns for the average active manager are going to be worse. You don't have to do that efficient frontier stuff. If markets were perfectly efficient, you'd buy the market and then use borrowing and lending to the extent you can. Once you get into different investment horizons, there are many complications. This is a very simple setting. You get a nice, clean result. The basic philosophical results carry through in the more complex settings, although the results aren't quite as simple.

The University of Chicago's Gene Fama and Yale University's Ken French came up with the Three- Factor Model, which states that beta matters less than either market capitalization or book-to-market value. Do Fama and French exaggerate?

All empiricists, myself included when I do empirical work, tend to exaggerate the importance of their particular empirical study. There are different time periods, different markets, different countries. You don't always get the same thing. Fama and French are looking at the question: Using historical manifestations of these ex-ante constructs, can we confirm that expected returns are related to beta and/or related to book-to-price and/or related to size? Given what they did and how they did it—using realized average returns, which are not expected returns—they found a stronger empirical correlation with book-to-price and with size than to their measure of historic beta.

The size effect and the value/growth effect had been written about before, so neither of these phenomena were new What was new was that Fama and French got that very strong result at least for the period they looked at—which, by the way, included the mid-1970s, a very good period for value stocks, which really drove up those results.

Fama and French's results were a product of the time period they examined?

There's a whole industry of turning out papers showing things "wrong" and "partially wrong" with the Fama- French study. I have not been part of that industry. I would only point out that during that period in the United States, value stocks did much better than growth. In the bear market of 1973 and 1974, people thought the world was coming to an end. It didn't come to an end. Surprise. The stocks that had been beaten down came back, and they came back a lot more than some of the growth stocks.

Maybe in an efficient market, small stocks would do better because they're illiquid, and people demand a premium for illiquidity That gets to be less compelling if you start thinking about mutual funds that package a bunch of small stocks and therefore make the illiquid liquid. As people figured that out, they'd put money into those funds, which would drive up the price of small stocks, and there goes the premium. For the value/growth effect, there's the behaviorist story that people overextrapolate. I have quite a bit of sympathy with that. I'm a bit of a fan of behavioral finance—the psychology of markets—so I don't dismiss that argument out of hand.

Since the studies about the size effect were published, small stocks have not done better than large stocks on average. Since the publicity about the value effect, value stocks haven't done as well as before around the world. So there's always the possibility that whatever these things were may have gone away, and that the publication of these studies may have helped them go away. It's too early to tell. It's a short data period. One would not want to infer too much, except that rushing to embrace those strategies has not turned out to be a very good idea, recently, certainly in the United States.

Empiricism is integral to investment theory. Do you discount such methodology?

I wouldn't discount it. I do it, and we all look carefully at the results. But it's been my experience that if you don't like the result of an empirical study, just wait until somebody uses a different period or a different country or a different part of the market. In the data it's hard to find a strong, statistically significant relationship between measured betas and average returns of individual stocks in a given market. On the other hand it's easy to build a model of a perfectly efficient market in which you could have just that trouble in any period. The noise could hide it.

The optimal situation involves theory that proceeds from sensible assumptions, is carefully and logically constructed, and is broadly consistent with the data. You want to avoid empirical results that have no basis in theory and blindly say, "It seemed to have worked in the past, so it will work in the future." That's especially true of anything that involves a way to get something for nothing. You're not likely to get something for nothing as long as you've got investors looking to get something for nothing.

Fama and French claim the Three Factor Model is an extension of the CAPM. Would you agree?

To the extent that the Fama-French study is a richer way of measuring the probability of doing badly in bad times, then there's nothing inconsistent with the Capital Asset Pricing Model. But there's a lot of confusion and inconsistency in how some people take the Fama-French results to market and advocate a big value tilt and a big small tilt in your portfolio. If those are just measures of an unrealized but future-looking beta, then you shouldn't have those tilts unless you happen to be one of those people who doesn't care how badly you do when times are bad. We do care when times are bad. Otherwise, there shouldn't be a risk premium for anything.

What about the Arbitrage Pricing Theory, which was originally proposed by Steve Ross at Yale? Is the APT stronger than the CAPM?

Yes and No. The APT assumes that relatively few factors generate correlation, and says the expected return on a security or an asset class ought to be a function of its exposure to those relatively few factors. That's perfectly consistent with the Capital Asset Pricing Model. But the APT stops there and says the expected return you get for exposure to factor three could be anything. The CAPM says no if factor three does badly in bad times, the expected return for exposure to that factor ought to be high. If that factor is a random event that doesn't correlate with whether or not times are bad, then the expected return should be zero.

The APT is stronger in that it makes some very strong assumptions about the return-generating process, and it's weaker because it doesn't tell you very much about the expected return on those factors. The CAPM and its extended versions offer some notion of how people with preferences determine prices in the market. The CAPM tells you more. The CAPM does not require that there be three factors or five factors. There could be a million. Whatever number of factors there may be, the expected return of a security will be related to its exposure to those factors.

Ross has said the APT came from dissatisfaction with the CAPM's assumptions.

You can't actually build a portfolio if you stop at the APT. You've got to figure out the factors and what the returns are for exposure to each factor. Some advocates of the APT have said one should just estimate expected returns empirically. I have argued that's very dangerous because historic average returns can differ monumentally from expected returns. You need a factor model to reduce the dimensions, whether it's a three- factor model or a five-factor model or a 14 asset-class factor model, which is what I tend to use. The APT says if in fact, returns are generated by a factor model, then without making any strong assumptions in addition to the model—which is strong to begin with—you can't assign numeric values to the expected returns associated with the factors. The CAPM goes further, putting some discipline and consistency into the process of assigning those expected returns.

So the great factor debate rages on.

I'd be the last to argue that only one factor drives market correlation. There are not as many factors as some people think, but there's certainly more than one. To measure the state of the debate, look at textbooks. Textbooks still have the Capital Asset Pricing Model because that's a very fundamental economic argument.

You've devoted much of your career to the study and understanding of market risk. Are today's investors focused enough on the downside?

Investment decisions are moving to individuals who are ill-prepared to make them. These are complicated issues. To say, here are 8,000 mutual funds, or even here are 10, do what's right, is not very helpful. The software versions and some of the human versions of the advice that people are getting often seem to ignore risk. They're bookkeeping schemes in which you earn 9% every year like clockwork. You die right on schedule. There's no uncertainty at all. Making a decision as to stocks vs. bonds vs. cash and about how much to save, without even acknowledging uncertainty—let alone trying to estimate it—seems to me the height of folly.

You've acknowledged your fascination with computers. What about your latest venture, Financial Engines, which will be available over the Internet?

We're working to help people understand the downside possibilities of different strategies, as well as the upside. There are two dangers that arise when people are ill-informed. One is that they won't realize what they've done. So when times are bad, they'll be very disappointed.

If you just take somebody's current investments and project return without any notion of risk, you give them a wildly distorted view of what their future might hold. It may be the best point estimate if you've done it carefully, but they have no notion of how good it can get or how bad it can get. So when and if it gets bad, they're not only likely to be desperately disappointed if they're already retired, they're also likely to do the wrong thing if they haven't retired.

In classrooms for decades, we've presented investments as a risk/return tradeoff.. Now, people are being presented investments as a return/return trade-off. There ought to be a law against that. Instead, we can help people understand the range of outcomes associated with different investments and help them find combinations of investments that are optimal.

How will the Internet impact the financial advisory business?

I don't think the Internet is the death knell for financial planning, but it certainly will affect it. There may be a migration to higher-net-worth individuals, or advisors will charge less and service more clients be cause they have better tools. At Financial Engines, we are focusing on investors who don't get any good advice. They get tips from their supervisor or relatives. These people really can't afford a financial advisor. The Internet is going to be potent and powerful for them. But that's not displacing advisors; it's bringing good advice to those who don't have it.

An upper level will always have human financial planners because, as a percentage of their assets, planners aren't very expensive. Even at that level, software is going to be increasingly important. The real issue is what happens in the middle. Almost everyone will get more computer and Internet input. There's going to be more of that and less of human beings in the mix. You can't afford to pay 3% of your money every year for advice, no matter how good it is.