When we use our survey-based framework to study consumption growth, we find no evidence that investors view this canonical risk factor as relevant to their portfolio decisions. This section aims to put this finding into the appropriate context. Researchers interpret factor models in different ways. We start by discussing what researchers can learn from our framework under these various interpretations. Next, we talk about concerns posed by equilibrium effects. We then describe how our results connect to existing literature in crosssectional asset pricing and macrofinance. Finally, we outline how researchers can use our approach to guide model development going forward. Our discussion relates to a model’s ability to explain and predict assetpricing data, but clearly, there are other important uses of models. For example, models can be used to make normative statements about what investors should be attending to in their investments even if they are not currently doing so. While such insights would not be relevant for understanding how asset prices move (if people are not actually engaging in such behavior), they can be important for building future financial products or emphasizing issues for investor education.
How survey evidence relates to testing asset pricing models depends on the interpretation of why these models are written and how they are used. When a researcher claims that exposure to a risk factor explains the data, he could mean a variety of different things. This section discusses the distinct interpretations of these models and the implications of survey-based evidence under each.

The first interpretation we discuss, and the one we largely focus on in this paper, is that these asset-pricing models are meant to accurately reflect the economic problem that investors are deliberately trying to solve. We focus on this interpretation because this is the one favored by the literature. Understanding the economic mechanism behind why prices move is important in its own right. Further, a model that reflects the problem that investors are actually trying to solve is more likely to make accurate predictions in novel asyet- unseen market environments.26 To summarize the purpose of asset-pricing models, in a recent review article, Cochrane (2017) writes that “the challenge is not one of telling stories or ‘explaining’ facts…ex post” but rather one of finding “explicit measures of fearful outcomes…that quantitatively account for asset pricing facts.”

In addition to such explicit statements, much of the discussion, motivation, and interpretation of results from these models is only coherent if the models capture the economic problem being solved by agents. For example, perhaps, the most common description of the equity premium puzzle (Mehra and Prescott (1985)) is that the risk aversion needed to match the data is implausibly high relative to evidence on how humans respond to risk. However, if assetpricing models are not meant to reflect actual human behavior, then there is no need for researchers to choose a model’s risk-aversion parameter based on estimates of how humans actually behave.28 Models in this literature are often motivated based on human psychology, including examples such as human beings wanting to “keep up with the Joneses” (Abel (1990)) or hedge-fund managers stating that they would “sooner die than fly commercial again” (Campbell and Cochrane (1999)). These motivations only make sense if models are meant to capture human behavior.

Before seeing our results, it would be reasonable to think that factor models capture the economic problem that investors are deliberately trying to solve. Examples in other settings show that people use financial markets to hedge a given risk, and in these situations, investors are typically able to provide evidence that they are implementing a strategy to do so. For example, investors trading oil futures know that they are doing so as insurance against future changes to oil prices and that today’s price is influenced by exposure to future oil shocks. When the CEO of Southwest airlines was asked about why they were active in the oil-futures market, he stated that the company “loaded up years ago on hedges against higher fuel prices.” This risk is commonly understood, which is why it is priced.

However, the fact that some asset markets operate like insurance markets does not imply that all markets operate on the same principles or that all insurance goes through asset markets. While investors could attempt to use their portfolio for auto insurance, most investors purchase this product elsewhere. Further, just because there is a risk that a theoretical investor would want to insure against, this does not mean that actual investors are doing so. Under the standard interpretation, investors should be able to describe which risk factors they are trying to insure against. This paper therefore provides evidence against using a broad class of asset-pricing models under this interpretation.

It is possible that a specific survey, such as the one in this paper, may be flawed, leading to erroneous conclusions.We have discussed why we think that our design is consistent with best practices and is a good test of these models. If there is a better survey design, we encourage future researchers to construct it and illustrate why the results of the current study are flawed. Doing so would not only provide a better test, but would also likely illustrate mechanisms not currently understood, and thus missed by this paper. Providing such survey evidence would lead to new insights that future models could build upon.

An alternative interpretation is that factors models do not capture the motives of individuals. Instead, they assume that the data arise from the collective actions of individuals behaving as if they were governed by the underlying mechanism (Friedman (1953)). Individuals could be doing anything, but as long as assets with more consumption-risk exposure also have higher average returns in the data, we would say that consumption growth is a relevant risk factor under this interpretation.

For some research questions, simply estimating this empirical relation and matching the data is illuminating. Indeed, there are literatures that examine purely empirical representations of the stochastic discount factor (SDF) and that study latent factor models without making any claim as to what these factors represent (e.g., Ang et al. (2006), Engle (1982), Fama and French (1993), Kozak, Nagel, and Santosh (2018), Kelly, Pruitt, and Su (2019)).With that said, this is not the typical justification for using consumption-based asset-pricing models.

Friedman (1953) illustrates his thinking about “as if” assumptions using examples.  The most relevant one for our setting involves an expert billiard player who makes shots as if he understands the underlying mathematical formulas even though he does not. A formal model would assume that the billiards player makes his shots by optimizing complex mathematical formulas, while Friedman claims the player “just figures it out” and “rubs a rabbit foot.”

Even if a billiards player relies on an intuitive feel for the game and not on explicit mathematical formulas, there are still many aspects of his thought process that a researcher should be able to identify directly with a well-designed survey. The player should be able to state that he was playing billiards, the rules of the game, and the placement of the balls on the table. Based on these characteristics, he could be able to describe the strategy he was trying to implement and the desired outcome of his next shot. Thus, even an intuitive player should be able to describe the game he is playing, his goal in playing the game, the strategy he is using to achieve that goal, and the values of the relevant input variables to that strategy.

Our paper documents that people are not shown correlations, do not consider correlations when they are provided, do not respond to correlations when making investments, and do not state that insurance of any kind is a goal in a free response. This is akin to an expert billiards player who does not know the rules of the game, does not understand the strategy he is trying to implement, and does not know the position of the balls on the table. A situation where the goal, the strategy, and the relevant parameters are unknown decreases the plausibility that an alternative decision rule leading to “as if” outcomes exists.

If one argues for using factor models based on “as if” reasoning, it is important to recognize that there are fewer uses of models under this interpretation. If the goal in writing a model is to understand why a pattern exists in the data, such an understanding can only occur when a model accurately captures the economic behavior explaining why. The literature has argued that models can help guide empirical work, but this guidance is meaningful primarily when a model captures what real-world investors are trying to do.35 It is common for empirical researchers to use factor models to compute risk-adjusted returns, but interpreting such an analysis as controlling for risk only makes sense if investors are trying to insure against this risk when forming portfolios. Further, if the model is not meant to capture behavior, it does not make sense to motivate it in terms of human behavior. We therefore contribute to the literature by ruling out these common uses of factor models in the absence of direct evidence about a risk factor’s relevance.

In general equilibrium models, it is often possible to express the influence of certain variables without including the variable itself. For example, investors in Campbell and Viceira (1999) have an optimal demand rule that is a decreasing function of an asset’s correlation with consumption growth in partial equilibrium. However, in general equilibrium, the authors show that it is possible to express this optimal demand rule without any correlation parameters by substituting in the budget constraint. Thus, an investor in such a model would be able to describe outcomes related to their correlation-based demand rule, without having to cite correlations themselves.

A benefit of using surveys is that we are not restricted to equilibrium outcomes. By examining outcomes off the equilibrium path, this breaks such a variable-elimination argument. Put another way, Campbell and Viceira (1999) investors should jump at the opportunity to buy an asset with high average returns and a negative correlation with consumption growth. They will never encounter such assets in equilibrium, but the logic of the model dictates how they should react if they did. We surveyed investors about what they would do in such a situation. Unlike the theoretical investors in Campbell and Viceira (1999), we find no evidence that real-world investors desire such assets.

One of the richest sources of empirical success in asset pricing lies in explaining cross-sectional patterns in returns. One of the benefits of our framework is that it is simple to apply to almost any proposed risk factor. We demonstrate this by applying our framework to the three most commonly studied risk factors from the cross-sectional asset-pricing literature.

Specifically, we focus on the excess return on the market, the return to a small-minus-big (SMB) size factor, and the return to a high-minus-low (HML) value factor Fama and French (1993). Labeling these sources of return predictability as risk factors implies that they represent nondiversifiable risks that investors would like to insure against. Thus, all else equal, an asset that is more correlated with one of these risk factors will offer worse insurance and investors should be less inclined to hold it.
To examine cross-sectional variation, we change our survey from asking about investing in the aggregate stock market to asking about investing in a generic mutual fund.We do so because it would be difficult to examine whether investors viewed the market as a risk factor if they could only invest in the market. Instead of economic growth, we present investors with monthly excess returns from one of the three factors from Ken French’s website. We tell participants that the mutual fund returns are simulated using different parameter values each period. We provide definitions for each, and outside of these changes rerun our experiment in a similar manner as in our baseline treatment.
Table XII reports results for the three Fama-French factors. Each column represents the estimated coefficients from regressing the fraction invested in themutual fund on the fund’s average returns, its return volatility, and the correlation between the fund’s returns and a particular Fama-French factor. For each factor, we ran a separate survey on a different population of MTurkers. Similar to our main results, participants strongly respond to changes in the mean and volatility of a mutual fund’s returns. The coefficients on meani,q and volatilityi,q are statistically significant, economically large, and directionally consistent with textbook models. However, we find no evidence of the negative coefficient on correlationi,q predicted by theory. We find similar results when we look at the economic-reasoning portion of our framework in Table XIII.
The idea that return predictability must represent compensation for risk is so ingrained in academic finance that empirical regularities are called risk factors almost without thought, even though there is evidence that at least some of this predictability seems consistent with mispricing (McLean and Pontiff (2016)). This semantic issue underscores the fact that academic finance tends to focus solely on the econometric relation when labeling cross-sectional return predictability a risk factor. We suggest using a more agnostic term, such as predictable returns, when a pattern is first discovered in the data. A strong empirical relation on its own should not be considered sufficient evidence for the risk factor label. Evidence needs to be provided, such as that from our framework, that investors view these returns as compensation for exposure to a risk factor before the risk factor label can be accurately applied.
The framework we develop in this paper can be used to evaluate the relevance of nearly any proposed risk factor. To demonstrate the framework, however, we had to select a specific risk factor for our case study. We chose consumption growth as our main variable of interest. Consumption growth is the sole state variable of the CCAPM, but this is not the main reason why we selected it. In this section, we discuss how results for this variable have implications for most modern asset-pricing models.
To address the empirical failings of the CCAPM, modern macrofinance models (e.g., habit formation (Campbell and Cochrane (1999)), long-run risks (Bansal and Yaron (2004)), rare disasters (Barro (2006), Rietz (1988)), and heterogeneous agents (Constantinides and Duffie (1996)), etc.) introduce new mechanisms that amplify the influence of consumption. The idea is that, if exposure to consumption growth cannot fully account for why markets fluctuate, then exposure to consumption growth interacted with an additional state variable can. According to Cochrane (2017), “each of them [the new models] boils down to a generalization of marginal utility or discount factor, most of the same form Mt+1 = δ · (Ct+1/Ct)^−γ · Xt+1,” where Xt+1 represents the new state variable of each model. Empirically, consumption growth is not very volatile, so in essence, these new state variables serve to amplify the core concern of consumption hedging to better match the data.
Before discussing the specific models, it is worth emphasizing that consumption-based models represent the current dominant paradigm of asset pricing. While opinions in the field vary as to whether this is warranted, such models represent the majority of asset-pricing papers currently being published and circulated at the most prestigious outlets. To provide empirical evidence of this, we examined all papers from recent NBER asset-pricing meetings (five meetings from 2019 to 2020) as well as those published in The Journal of Finance (six issues during 2020) to see if they included a model that implied consumption risk should be priced. For the NBER, we found that more than 80% of papers with models and more than 40% of all papers implied that consumption risk should be priced. For The Journal of Finance, we found that 60% of papers with asset-pricing models and more than 20% of all papers (including non-asset-pricing papers) did the same.
The Campbell and Cochrane (1999) model studies a representative investor with power utility, Ut defined as (Ct − Ht)^(1−γ)/(1 − γ), over consumption in excess of a slow-moving benchmark, Ht-that is, habit; the level of consumption investors have become accustomed to, log Ht defined as λ · Σ from ℓ=0 to ∞ of φ^ℓ · log Ct−ℓ where λ > 0, φ ∈ (0, 1). The idea is to make drops in consumption following booms more painful to investors. The key state variable in this model is investors’ surplus-consumption ratio, Xt defined as (Ct − Ht)/Ct. The SDF is then given by log Mt+1 = log δ − γ · log Ct+1 − γ · log Xt+1.
ICAPM logic suggests that average stock returns could be high either because they covary with consumption growth or because they covary with growth in the surplus-consumption ratio:
E[Rt+1] − Rf ≈ γ × Cov[log Ct+1, Rt+1] + γ × Cov[log Xt+1, Rt+1].
But either/or is not the right conjunction. The second term is not independent of the first. If investors are not trying to insure drops in consumption (if first term is zero), then they cannot be trying to insure drops in surplus consumption (second term must be zero). The surplus-consumption ratio is not a separate risk factor; it is a way of amplifying the effects of consumption risk. Expected returns in Campbell and Cochrane (1999) can be rewritten as
E[Rt+1] − Rf ≈ (γ / Xt) × Cov[log Ct+1, Rt+1].
This analytical result allows us to compute the increase in expected returns that investors should demand as compensation for an increase in consumption-growth correlations of ρ = 0.45 according to the model. Taking standard calibration parameters, the model suggests that expected returns on the stock market should increase by 8% in response to ρ = 0.45. The fact that participants in our study do not adjust their demand in response to such correlation changes is inconsistent with this model.
D.2. Long-Run Risk
The Bansal and Yaron (2004) long-run-risk model uses a different preference specification and state variable, but the result is the same. The effects of shocks to the new state variable on asset prices cannot exist if investors do not want to insure their exposure to consumption-growth shocks. One way to see this is to notice that the long-run-risk model is formally equivalent to a model where investors are ambiguity averse with respect to parameters of the consumption-growth process (Hansen and Sargent (2008), Epstein and Schneider (2010), Bidder and Dew-Becker (2016)).
Let Pt denote the current price of an asset whose payout is aggregate consumption in the following period, and let 1/α denote investors’ elasticity of intertemporal substitution (EIS). The long-run risk model says that the equity premium will be determined by
E[Rt+1] − Rf ≈ γ × Cov[log Ct+1, Rt+1] + f(γ, α) × Cov[log (P/C)t+1, Rt+1],
where f(γ, α) ≤ 0 comes from the Campbell and Shiller (1988) approximation of (P/C)t. Thus, ICAPM logic suggests that expected returns could be high either because stock returns covary with consumption growth or because they covary with the aggregate price-to-consumption ratio. But again either/or is not the right conjunction. The second term is not independent of the first. Taking standard calibrations, the 1ρ = 0.45 increase that we study in our survey-based framework would increase annual expected excess returns by about 20% in the long-run risk model. The fact that participants in our survey do not respond to such correlation changes is inconsistent with this model.
D.3. Rare Disasters
There is a class of models built on top of the CCAPM framework that our results do not directly speak to: rare-disaster models à la Rietz (1988), Barro (2006), and Gabaix (2012). We find that investors are not trying to insure normal-times variation in consumption growth, but we do not directly test whether investors want to insure themselves against extreme shocks to consumption. Researchers could use the survey-based framework we develop in this paper to more directly test whether investors follow the economic logic behind this model.
D.4. Heterogeneous Agents
Most of the discussion in our paper (and in the literature) relates to representative-agent models, but our paper also has implications for heterogeneous-agent models. For example, in the Constantinides and Duffie (1996) model, heterogeneous investors try to insure shocks to their own personal income. When this hedging demand is aggregated, the model predicts that aggregate consumption growth should look like a priced risk factor. We directly show in Tables IV and IX that participants are not trying to insure shocks to their own personal consumption, income, wealth, spending, or standard of living.
Investors likely differ along a variety of dimensions: preferences, wealth, expectations, etc. While researchers have proposed models that focus on these other dimensions, most heterogeneous-agent models still assume that investors are trying to insure risk factors, be they aggregate or personal. Our results suggest that this approach is unlikely to capture how investors actually allocate their portfolios.
E. Model Development
The results in this paper provide direction for researchers interested in writing new risk-based models. Surveys are an ideal tool for this purpose. While an investor can buy an asset that happens to provide insurance without knowing it, investors cannot all agree on the equilibrium price of this insurance unless it is commonly understood ahead of time. Home owners can typically explain what they are paying for when they buy fire insurance. Drivers can typically explain what they are paying for when they buy car insurance. If asset markets are “in reality big insurance markets (Cochrane (1999)),” a well-designed survey should be able to provide evidence that investors typically view their portfolio as a way to buy insurance and construct their investment strategy with an eye toward achieving this goal.
We find that investors’ desire to insure consumption shocks is unlikely to explain why asset prices move, so models that add complexity to this basic idea are similarly unlikely to be correct. However, suppose that our results had suggested otherwise. Specifically, suppose that participants had strongly responded to changes in the correlation between stock returns and consumption. Further suppose that participants had reported thinking about an asset’s correlation with consumption growth as suggested by the CCAPM. Such results would not have solved the CCAPM’s empirical shortcomings, but they would have supported the literature’s standard approach to dealing with these flaws. Such results would have implied that investors cared about consumption risk in a more complicated way than captured by the CCAPM. So, models that add complications to the CCAPM, such as habit formation (Campbell and Cochrane (1999)) and long-run risk (Bansal and Yaron (2004)), would have a strong foundation to build on. This is just not what we find.
That being said, investors are not necessarily irrational or wrong because they do not follow CCAPM logic. If deep-pocketed asset managers at an invite-only conference are not trying to insure consumption shocks when investing in the stock market, it does not mean that these investors are using the wrong strategy. It means that economists are using the wrong model. Our results strongly support the textbook assumption that investors view the mean and variance of returns as first-order important. And the open-ended framework we develop can be used to gain a deeper understanding of how investors are considering these variables and what else is influencing their decisions.
