Naming the Factors: Chen, Roll and Ross Connect Stocks to the Economy

Six years earlier, Roll and Ross had tested the Arbitrage Pricing Theory by letting a statistical algorithm dig unnamed factors out of stock returns. It worked, in the sense that they found factors that were priced. It also left everyone unsatisfied, because factor analysis hands you abstractions, not explanations. "Factor two is priced" is a sentence with almost no economic content.

So in 1986, Chen, Roll and Ross came back and did it the other way around. Instead of extracting factors from stock prices, they started with the economy and asked which parts of it stocks are compensated for being exposed to.

The problem: statistical factors are uninterpretable and possibly circular

There is something a bit troubling about deriving your risk factors from the very returns you are trying to explain. It smells of circularity, and it certainly does not tell you why investors demand a premium for anything.

The whole logic of risk premia says people are paid to bear risks they genuinely dislike, meaning risks tied to their real economic lives: losing their job, inflation eating their savings, a recession hitting their income. If that story is right, then the priced factors ought to be recognizable macroeconomic forces, not mathematical abstractions.

So: go find the macroeconomic forces, and check whether the market pays you to hold assets exposed to them.

The key idea, via analogy

Suppose you want to know which weather conditions farmers fear most. The statistical approach is to look at crop yields across thousands of farms, find the common patterns, and label them "pattern one" and "pattern two." Useful, but you still do not know what they are.

The direct approach is to go get the actual weather data, rainfall, temperature, frost days, and ask: which of these actually moves crop yields, and which do farmers pay real money to insure against?

Chen, Roll and Ross did the direct version for stocks. They picked a set of macroeconomic variables with a plausible claim to mattering, and the important subtlety is that they used surprises, not levels. This is crucial and easy to miss. Known, expected inflation is already in the price. It cannot move markets, because everybody already knew it. What moves markets is the part of the news that was not anticipated. So they carefully constructed innovation series: the unexpected component of each variable.

The macroeconomic forces they examined included:

• Industrial production growth, standing in for the real health of the economy, whether factories are busy and the economy is actually producing.
• Unexpected inflation, and changes in expected inflation, because inflation surprises redistribute wealth and erode the value of nominal cash flows.
• The credit spread, the gap between yields on low-grade and high-grade corporate bonds. This is a wonderfully intuitive variable: when the market gets frightened about defaults and the economy, this spread widens. It is essentially a real-time market-based fear gauge.
• The term spread, the gap between long-term and short-term interest rates, which reflects shifts in how the market discounts distant cash flows.

Then they asked the APT question: do stocks with more exposure to these surprises earn higher average returns?

The answer was yes. These macroeconomic risks were significantly priced. Stocks that suffer most when industrial production disappoints, or when credit spreads blow out, do earn a premium for that exposure. The economy shows up in the cross-section of stock returns.

And they added a needle. Once you account for these macro exposures, the market index itself adds little or no explanatory power. That is a pointed result. It suggests the market portfolio, the sacred object of the CAPM, may itself be nothing more than a bundle of these underlying economic risks, and a somewhat redundant one at that.

Why it mattered

• It gave risk premia an economic story. For the first time, the abstract factors of the APT had names you could explain to a client: growth, inflation, credit, and the shape of the yield curve. That is a far more satisfying account of why a premium should exist.
• It is the template for macro factor models. The framework of pricing assets against a set of named macroeconomic innovations is now standard, and it underlies the risk-factor language used by pension funds, sovereign wealth funds, and multi-asset allocators everywhere, including the "risk factor" framing popularized in institutional portfolio construction.
• It elevated the credit spread. Making the default spread a first-class priced risk factor was prescient. It anticipates a large modern literature on credit risk as the common thread running through many asset classes, and the way credit spreads behaved in 2008 makes the choice look inspired.
• It challenged the market portfolio's primacy. Showing the index becomes redundant once macro risks are included is a direct assault on the CAPM's central object, from two of the people best equipped to make it.

The honest limitations

• The variable selection is discretionary. The macro variables were chosen by economists exercising judgment. Different plausible choices give different answers, and there is no theory that says these five and not some other five. The APT still does not name its own factors; here the humans did it.
• Measuring surprises is hard. To get the unexpected component of inflation or production, you need a model of what was expected. That model is itself an assumption, and the results depend on it.
• Macro data is slow, revised, and coarse. Industrial production is published monthly with a lag and then revised. Stocks trade continuously. Trying to link a high-frequency, forward-looking asset to a low-frequency, backward-looking statistic is inherently lossy.
• The results have not replicated cleanly. Later work over different samples and different countries has found the macro factors to be considerably less robust than the original paper suggested, and later research revisiting the same question has generally found weaker evidence. Meanwhile the characteristic-based factors of Fama and French, which have far less economic justification, have consistently worked better empirically. That is an uncomfortable trade: the models with the best economic stories are not the ones that fit the data best.
• Data mining is a live risk. With many candidate macro series and a fixed sample, finding some that price well is not hard by accident.

The one-line takeaway

Chen, Roll and Ross replaced the APT's anonymous statistical factors with real economic forces, growth, inflation surprises, credit spreads and the yield curve, and showed that investors are genuinely paid to bear them, giving factor investing an economic story rather than just a statistical one.