Consumption Beta: Breeden's One-Factor Model That Should Have Replaced the CAPM

By the late 1970s asset pricing had a proliferation problem. Merton's intertemporal CAPM had shown that in a realistic world, where the investment opportunities available to you keep changing, a single market beta is not enough. You need extra factors, one for each thing that shifts your future opportunities: interest rates, expected returns, volatility, and so on. Theoretically satisfying, practically a mess. Nobody knew how many factors there were or what they were.

Douglas Breeden's 1979 paper is the moment somebody found the drain that all of them flow into. His result: all those state variables collapse into one number, the growth rate of aggregate consumption. One factor. One beta. Done.

The problem: too many factors, none of them observable

Merton's model was correct but open-ended. It said expected returns depend on market risk plus sensitivity to however many state variables happen to describe how the world's investment opportunities evolve. It did not say what those variables were, how many there were, or how to find them.

So finance had a choice between a model that was empirically usable but theoretically shaky (the CAPM) and one that was theoretically sound but empirically undefined (the ICAPM). That is not a happy place.

The key idea, via analogy

Think about how you would judge a person's overall well-being. You could try to list everything that affects it: their salary, their job security, their health, the interest rate on their mortgage, the price of groceries, their promotion prospects. That is a long, unruly list, and you will never be sure you have all of it.

Or you could just watch how much they actually spend on living well. Because a rational person's spending already reflects, in one number, everything they know and expect about all of those things. If they get news that their job is at risk, they cut back. If they get a raise they did not expect, they spend more. Their consumption is a sufficient statistic for the whole tangled list.

That is Breeden's insight, applied to the economy. Consumption is not just another factor sitting alongside interest rates and expected returns; it is the summary of all of them. A rational, forward-looking consumer sets their spending today by weighing everything they know about the future. So if you want to know how a piece of news about future investment opportunities affects marginal utility, you do not need to track the news. You just need to watch consumption move.

The pricing rule that comes out is beautifully simple, and it is called the Consumption CAPM:

An asset's expected return is determined by its consumption beta: how strongly its returns co-move with the growth rate of aggregate consumption. Assets that pay off well when consumption is falling, meaning when people are cutting back and every extra dollar counts, are valuable insurance and command low expected returns. Assets that pay off when consumption is already booming are near-useless and must offer high expected returns to get anyone to hold them.

That is it. One beta. Not against the stock market, but against the thing the stock market is supposed to be a proxy for: people's actual economic well-being. Breeden derived this in a continuous-time, multi-good setting, and even showed the zero-beta variant applies when no riskless asset exists.

Notice what this does to the CAPM. The market beta of the classic model is revealed to be a crude stand-in for consumption beta. It works only to the extent that the stock market happens to track consumption. When the two diverge, consumption is the one that is theoretically right.

Why it mattered

• It unified the field. The CAPM, the ICAPM, and the Lucas exchange economy all turn out to be facets of the same underlying object. Breeden collapsed a growing zoo into one principle.
• It said what "bad times" really means. Finance talks endlessly about assets that do badly in bad times. Breeden gives a precise, non-circular definition: bad times are times when consumption growth is low. That is a claim about people's lives, not about a stock index.
• It escapes Roll's critique, in principle. Roll had shown the market portfolio is unobservable. Consumption, at least, is something governments measure. The CCAPM offered a path to a testable model that did not depend on identifying every asset on earth.
• It is the theoretical backbone of modern macro-finance. Everything from habit formation models to long-run risk models is a modification of the consumption-based core Breeden set out.

The honest limitations

This is one of the great cases in economics of a theory that is more elegant than the world.

• It performs terribly in the data. Consumption beta explains the cross-section of stock returns poorly, and generally worse than plain old market beta. The single most beautiful result in asset pricing loses to the model it was supposed to replace.
• Consumption is measured badly. It is reported quarterly, revised repeatedly, aggregated across very different households, and much of it is imputed rather than observed. Durable goods and services muddy what "consumption this quarter" even means. A model whose central variable is this noisy is hard to test fairly.
• Aggregate consumption is far too smooth. Real consumption growth barely moves from year to year, while stock returns swing enormously. To reconcile the two, you need investors so risk averse that the numbers become absurd. This is precisely the equity premium puzzle that Mehra and Prescott would formalize six years later.
• Aggregation hides who is actually suffering. Average consumption may be fine while the people who actually hold stocks, or the people who just lost their jobs, are not. If risk is not shared smoothly across households, aggregate consumption is the wrong variable, and much subsequent research has chased exactly this idea.

The one-line takeaway

Breeden showed that every risk factor in asset pricing collapses into a single one, how an asset co-moves with what people actually consume, giving finance its most elegant model and, awkwardly, one that the data has never much liked.