Putting the CAPM on Trial: Black, Jensen and Scholes Test the Theory

By 1972 the CAPM had been derived three times by three different people and was rapidly becoming the organizing idea of finance. What nobody had done properly was check whether it was true.

Fischer Black, Michael Jensen and Myron Scholes did that check. The paper is famous for two things: its conclusion, which was awkward for the theory, and its method, which turned out to be more influential than the conclusion. The way this paper organizes data is, without exaggeration, the way essentially all empirical asset pricing has been done ever since.

The problem: testing a theory about single stocks is a statistical nightmare

The CAPM makes a claim about individual stocks: a stock's expected return should rise in a straight line with its beta. So you might think the test is easy. Estimate each stock's beta, plot beta against average return, check for a straight line.

This fails, badly, for two reasons.

Individual stock returns are almost pure noise. A single stock's average return over even a long sample is so wildly uncertain that the true signal is buried. You are trying to detect a modest slope inside a hurricane of randomness.

Estimated betas are wrong in a way that biases the answer. Beta has to be estimated from data, so it comes with error. Stocks that look like they have very high beta are disproportionately stocks whose beta was overestimated by luck, and vice versa. When you then use those noisy betas as the x-axis of a regression, the classic errors-in-variables problem kicks in and pushes the estimated slope toward zero. You would find a flat line even if the theory were perfectly true. Any naive test is rigged to fail.

The key idea, via analogy

If you want to know whether taller basketball players score more, you do not compare individual players, because individual scoring is dominated by team, position, minutes played, and luck. You sort players into height groups and compare group averages. Individual noise cancels within each group, and the pattern across groups becomes visible.

Black, Jensen and Scholes did exactly this for stocks, and were careful about one trap. Their procedure:

1. Estimate each stock's beta using data from an earlier period.
2. Sort stocks by that beta and bundle them into ten portfolios, from lowest-beta to highest-beta.
3. Track how those portfolios perform over the following period, and re-estimate everything as time rolls forward.

Two things make this work. Averaging inside a portfolio cancels most of the idiosyncratic noise, so you can actually see the relationship. And using past beta to form the group, then measuring future returns, means that the luck that made a stock look high-beta does not automatically follow it into the test period. The bias that would have flattened the line is largely defused.

This is the portfolio sorting methodology. Decile portfolios, formation period, holding period, rolling re-estimation. Every factor paper you have ever read, including Fama-French, is a descendant of this design.

What they found

The good news for the theory: the relationship between beta and average return was real, positive, and roughly linear. Higher beta portfolios genuinely earned more. The CAPM was not nonsense.

The bad news: the line was in the wrong place. It was too flat. Low-beta portfolios earned consistently more than the CAPM said they should, and high-beta portfolios earned consistently less. In the language of the model, low-beta stocks had positive alpha and high-beta stocks had negative alpha, in a systematic pattern that repeated across sub-periods rather than looking like noise.

This is the finding that Black's zero-beta model was built to explain, and it is the empirical seed of everything now marketed as low-volatility or betting-against-beta investing. Fifty years later, that flat line is still there.

Why it mattered

• It created the standard toolkit. Sorting stocks into portfolios on a characteristic, then measuring subsequent returns, is the single most-used research design in quantitative finance. This paper is where it becomes rigorous.
• It taught the field to fear estimation error. The errors-in-variables argument here is a permanent lesson: if your sorting variable is measured with noise, your test is biased before you start. Modern quants meet this bug constantly and this is the canonical treatment.
• It documented the low-beta anomaly. The finding was not a footnote; it was the model's most durable empirical failure and it launched an entire strand of research and a real product category.
• It supported the two-factor, zero-beta version. Their results fit Black's restricted-borrowing model considerably better than the textbook CAPM, which is why the two papers are usually read together.

The honest limitations

• Roll's critique applies in full. They used a stock index as the market portfolio. Five years later Roll would argue that this makes the entire exercise a test of the index, not of the theory. Nothing in this paper escapes that.
• The market proxy is US stocks only. No bonds, no property, no human capital, no international assets. If the true market portfolio looks different, so do all the betas.
• Sorting on beta bundles other things with it. High-beta portfolios tend to also be smaller, more cyclical, and more leveraged. The paper cannot fully separate "beta" from the characteristics that travel with it, a problem the factor literature has been fighting ever since.
• Betas move. The method assumes a portfolio's beta is stable enough between the formation period and the test period. Betas drift, and that drift injects error the design can dampen but not eliminate.

The one-line takeaway

Black, Jensen and Scholes invented the portfolio-sorting method that all of empirical finance now runs on, and used it to show that the CAPM's risk-return line is real but persistently too flat, with safe stocks beating the theory and racy stocks falling short.