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 times the infinite sum from ℓ=0 of φ^ℓ times 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 stochastic discount factor (SDF) is then given by log Mt+1 = log δ − γ times log Ct+1 − γ times 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 approximately equals γ times the covariance of log Ct+1 and Rt+1 plus γ times the covariance of log Xt+1 and 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 the 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 approximately equals (γ / Xt) times the covariance of log Ct+1 and 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.
We study the properties of optimal accounting rules in a setting where an impatient firm needs to sell shares to raise immediate cash. The firm possesses information that cannot be credibly conveyed to the outside investors, resulting in costly signaling via the percentage of shares retained by the firm. However, before observing any private information, the firm can choose to commit to an accounting rule that will provide the outside investors a noisy signal of the private information. We show that, so long as the disclosure cannot perfectly reveal the firm’s private information, the uniquely optimal accounting rule always consists of (1) disclosure of a lower bound of the expected firm value and (2) a moment of the posterior belief, which, together with the lower bound, completely determines the expected firm value conditional on the disclosure. This optimal accounting rule can be interpreted as being consistent with certain features of the accounting rules that guide firms in financial reporting. In particular, the disclosure of the lower bound is consistent with the conservatism principle embedded in the accounting rules. Our results provide support for conservatism, arguably one of the most important attributes of accounting, in a setting that is particularly relevant for accounting.
Our study is, to the best of our knowledge, the first study of the optimal qualitative properties of accounting information in a systematic way. Previous studies on accounting conservatism (e.g., Chen et al. (2007), Gigler et al. (2009) and Gao (2013a)) also model conservatism as a qualitative property of accounting information that changes the relative informativeness of favorable versus unfavorable signals. However, because of their focus on the particular attributes of conservatism, their papers do not address the qualitative properties of accounting information in a fairly general way, which is our focus.
In deriving the optimal qualitative properties of accounting information, we adopt the concept of information well established in the information theory. This choice exhibits the virtue of flexibility because it is free to choose any information structure so long as it is Bayes-plausible. As discussed in section 2, we believe that this feature makes it particularly appealing to study accounting rules. Our choice of mutual information also exhibits the virtue of comparability because different information structures can be measured using one number: the reduction of entropy. This measure ensures comparability between arbitrary information structures, which we subsequently use to study optimal accounting rules.
We believe our focus on the qualitative properties of information structure is especially relevant for financial reporting because accounting rules often must trade off between different qualitative properties of information with the impact on the quantitative properties being less straightforward. Conservatism versus aggressiveness is one example, while a principle-based accounting standard versus a rule-based accounting standard is another. From this point of view, our paper can be seen as a first step in a line of future research incorporating more institutional details to generate additional insights related to optimal accounting rules. Specifically, in our model, accounting disclosure is still modelled as a black box. Although we can show that the optimal accounting rule can be interpreted to be consistent with conservatism, we cannot show in more detail how the lower bounds are directly related to accounting conservatism applied to specific accounting measurements. To answer those questions, we need to open the black box of accounting measurement (Gao (2013b)). This seems to be the natural next step in examining the relationship between the accounting rules and the optimal qualitative properties of information systems.
