Cash-flow Betas Research Articles

Securities Markets in Which Some Investors Receive Information About Cash Flow Betas

We analyze a single-factor setting in which there is private information regarding cash flows as well as their betas. Private information about betas, together with market makers’ risk aversion and mean betas’ nonnegativity, implies a nonlinear price schedule whose stochastic slope covaries positively with order flow when the expected factor payoff is positive and vice versa. We predict a negative relation between the covariance and expected returns and an attenuation of the beta anomaly in asset returns after accounting for this relation. Empirical tests confirm these predictions. This paper was accepted by Lukas Schmid, finance. Funding: L. Yang acknowledges the Social Sciences and Humanities Research Council of Canada [Grant 435-2021-0040] and Bank of Canada Fellowship for financial support. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.02061 .

Betting against low nominal prices: Evidence from China

We offer evidence of a positive low-nominal-price return premium in China’s stock markets. We explain this by using Campbell and Vuolteenaho’s (2004) cash-flow and discount-rate betas. Low-priced stocks have high cash-flow that delivers high expected returns. The negative low-nominal-price return premium is negative in US markets and this discrepancy is attributed to reverse ranking of cash-flow betas for low-priced stocks. We find that high cash-flow risk for low-priced (high-priced) stocks in China (US) is associated with low price informativeness and analyst attention; the discrepancy of cash-flow betas in US and China is driven by book-to-market ratios and idiosyncratic volatility.

When is the Price of Dispersion Risk Positive?

We provide robust evidence that the price of analysts' dispersion risk in the cross-section of stock returns changes sign over time, and in particular, turns positive (negative) in periods of high (low) analysts' dispersion. Our result holds for a set of portfolios that are double-sorted on their betas and their coefficients on aggregate dispersion, as well as 36 different sets of test portfolios created by Kenneth French. We construct a general equilibrium model in which analysts of different types have heterogeneous beliefs about aggregate earnings growth. The consumer does not trust either analyst fully, and dynamically adjusts the weight given to each analyst, given the history of their past forecast performance. In equilibrium, each asset's risk premium depends on its exposure to three factors: (i) the market portfolio, (ii) the macroeconomic factor, and, (iii) a ``flight-to-safety'' factor. The first term decreases with dispersion, while the third term increases. These changes occurs because investors shift into assets with lower cash flow betas during periods of high dispersion. We find strong support for such a flight-to-safety in the data.

Are cash-flow betas really bad? Evidence from the Greater Chinese stock markets

This study evaluates the relative importance of cash-flow news and discount-rate news using the log-linear model for the Greater Chinese stock markets (i.e., China, Hong Kong, and Taiwan). Although they belong to the same cultural region, these countries have different capital market regulations and practices. In this context, we find that only the discount-rate beta is priced in Hong Kong; thus, the discount-rate beta is labeled as a ‘bad beta’ in Hong Kong. However, the cash-flow beta is ‘bad’ in China and both betas are ‘bad’ in Taiwan. These findings are consistent with each market's ownership structure, dividend policy, and tax system. However, as in the United States, risk premiums are significantly higher in down markets than in up markets.

Conditional Risk

Using a new and powerful conditional-risk factor, we document a global effect of time-varying market betas on stock returns. Across 23 developed countries, the major equity risk factors all load on the conditional-risk factor, which means their alpha can partly be explained by time-varying market betas. The conditional-risk factor explains 50% more alpha than traditional methods that use rolling betas to capture conditional risk. Studying the economic driver of the conditional risk, we find evidence that it arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.

Time Variation in Cash Flows and Discount Rates

The relative contributions of cash flow and discount rate news to the conditional variance of market returns exhibit significant variation over time. We identify lagged changes in PPI inflation as the main macroeconomic determinant of this time variation. Cash flow betas of value stocks increase following an increase in inflation, suggesting that investors should either tilt their portfolios away from high cash-flow-risk stocks or hedge this risk after observing increasing inflation.

Valuation: Accounting for Risk and the Expected Return

Under accounting principles, the recognition of earnings is path dependent and the path depends on risk resolution: Under the so-called realization principle, earnings are not booked until uncertainty is resolved. In asset pricing terms, the principle means that earnings cannot be recognized until the firm can book a low-beta asset such as cash or a near-cash discounted receivable. If the risk to which this accounting responds is priced risk, the accounting indicates the expected return. This paper connects accounting under this principle to risk and return, summarizes the supporting empirical evidence, and examines the implications for research on the implied cost of capital, cash-flow betas, asset pricing models that imbed accounting numbers, and papers that assume an autoregressive model for the earnings path to infer the expected return. The accounting that captures risk and its resolution also has implications for the unsolved issue of specifying the appropriate accounting for accounting-based valuation models and, indeed, for financial accounting standards.

The Public Market Equivalent and Private Equity Performance

The authors show that the public market equivalent approach is equivalent to assessing the performance of private equity (PE) investments using Rubinstein’s dynamic version of the CAPM. They developed two insights: (1) one need not compute betas of PE investments, and any changes in PE cash flow betas due to changes in financial leverage, operating leverage, or the nature of the business are automatically taken into account; (2) the public market index used in evaluations should be the one that best approximates the wealth portfolio of the investor considering the PE investment opportunity.We provide the theoretical foundation for the use of the public market equivalent (PME) measure, which is often used to evaluate private equity (PE) performance. We show that the PME is equivalent to valuing cash flows using Rubinstein’s dynamic capital asset pricing model. Establishing this link enables us to show that the Kaplan and Schoar PME measure is surprisingly robust. The PME gives an estimate of the risk-adjusted performance of PE funds without having to calculate any betas, even if the betas of the cash flows vary over the life of the investments, for example, owing to changes in financial leverage, operating leverage, or the nature of the businesses. Further, a PE fund cannot artificially increase its PME by increasing its leverage. The discount rate used to calculate the PME should approximate the return on the investor’s overall wealth portfolio, and it may vary across investors, even for the same fund. Unlike the standard CAPM, the PME does not evaluate performance relative to the market returns of other investments with similar risks. Instead, the PME evaluates investment performance as an integrated part of the investor’s overall portfolio. Because the PME is derived from a formal asset-pricing model, it does not suffer from the problems of the internal rate of return (IRR), which is an alternative performance measure that is often used to evaluate PE performance. Unlike the IRR, the PME always exists, and it is always unique. Because the PME is equivalent to a present value (PV) calculation, it cannot be manipulated, for example, by PE funds’ deliberately choosing the timing and magnitudes of their investments, unlike the IRR. Compared with the standard CAPM, the PME also has several advantages: it is easier to calculate, it does not require any betas—which are typically estimated from the market risks of comparable traded companies—and it doesn’t require any assumptions about the expected market risk premium. Overall, the PME appears to be an attractive, robust, and easily applicable method for evaluating PE funds’ past performance or the performance of other alternative assets for which regularly quoted market prices and returns are unavailable.

Explaining the default risk anomaly by the two-beta model

This study attempts to explain the anomaly that firms with high-default risk earn low average realized returns. We measure default risk according to Ohlson's (1980) O-score and Campbell, Hilscher, and Szilagyi's (2008) failure probability and further implement Duffie, Saita, and Wang's (2007) doubly-stochastic intensity model to estimate default probabilities that incorporate the dynamics of the changes in covariates. We then employ Campbell and Vuolteenaho's (2004) two-beta model to estimate firms' cash-flow and discount-rate betas according to the default risk. The default risk anomaly persists when using Duffie el al.'s (2007) method. We show that cash-flow and discount-rate betas, respectively, earn a high and low premium and find that high-default firms tend to have relatively high discount-rate and low cash-flow betas. Hence, high-default firms deliver low expected returns. Importantly, 25.5% of the default risk anomaly can be explained by the two-beta model and that, on average, also accounts for 49.2% of the cross-sectional variation across the portfolios formed on default risk. This result implies that investors believe that high-default firms are unlikely to generate significantly extra cash flows when market-wide profitable opportunities improve.

A State-Space Model Approach to the Return Decomposition

We test the implications of the return decomposition of Campbell (1991), in which the unexpected market return is decomposed into cash-flow and discount-rate news. Unlike most of the previous literature, which uses VAR models to implement the return decomposition, we propose a state-space model with parameter restrictions, which is a more systematic and direct than the VAR approach on two aspects. First, the state-space model approach simultaneously models returns, cash-flow news, and discount-rate news, whereas the VAR approach models discount-rate news and uses the return decomposition to back out cash flow news. Second, the state-space model allows us to use information directly related to market and portfolio returns to study the return decomposition, whereas the VAR approach utilizes different predictive variables. We find that discount-rate news has larger variance than does cash-flow news and that the two types of news are nearly perfectly correlated, which can be economically intuitive. We also find that small stocks have higher cash-flow betas than do large stocks, but do not find that value stocks have higher ashflow betas than do growth stocks.

Dividend Growth, Cash Flow, and Discount Rate News

AbstractUsing a new variable based on a model of dividend smoothing, we find that dividend growth is highly predictable and that cash flow news contributes importantly to return variability. Cash flow betas derived from this predictability are central to explaining the size effect in the cross section of returns. However, they do not explain the value effect; this is explained by noise betas. We also find that the relative importance of cash flow news in explaining recent stock price run-ups and subsequent declines increases when cash flow news is estimated directly.

The cross-section of equity returns and assets’ fundamental cash-flow risk

The decomposition of consumption beta into a component driven by assets’ cash-flow news and one related to assets’ discount-rate news reveals that macroeconomic risks embodied in cash flows largely account for the cross-sectional dynamics of average stock returns. Empirically, we find that differences in expected excess returns between low book-to-market and high book-to-market portfolios are associated with differences in their cash-flow betas, and thus reflect macroeconomic, especially consumption-related risks. This result holds true for a broad set of consumption-based asset pricing models. In addition, the results indicate that the risk premium on equity markets is primarily driven by the exposure of assets’ cash-flow components to the cyclical variability of durable consumption goods.

Consumption, Dividends, and the Cross Section of Equity Returns

ABSTRACTWe show that aggregate consumption risks embodied in cash flows can account for the puzzling differences in risk premia across book‐to‐market, momentum, and size‐sorted portfolios. The dynamics of aggregate consumption and cash flow growth rates, modeled as a vector autoregression, are used to measure the consumption beta of discounted cash flows. Differences in these cash flow betas account for more than 60% of the cross‐sectional variation in risk premia. The market price for risk in cash flows is highly significant. We argue that cash flow risk is important for interpreting differences in risk compensation across assets.

The Price Is (Almost) Right

Most previous research tests market efficiency and asset pricing models using average abnormal trading profits on dynamic trading strategies, and typically rejects the joint hypothesis. In contrast, we measure the ability of a simple risk model and the efficient-market hypothesis to explain the level of stock prices. First, we find that cash-flow betas (measured by regressing firms' earnings on the market's earnings) explain the prices of value and growth stocks well, with a plausible premium. Second, we use a present-value model to decompose the cross-sectional variance of firms' price-to-book ratios into two components due to riskadjusted fundamental value and mispricing. When we allow the discount rates to vary with cash-flow betas, the variance share of mispricing is negligible.

Bad Beta, Good Beta

This paper explains the size and value “anomalies” in stock returns using an economically motivated two-beta model. We break the beta of a stock with the market portfolio into two components, one reflecting news about the market's future cash flows and one reflecting news about the market's discount rates. Intertemporal asset pricing theory suggests that the former should have a higher price of risk; thus beta, like cholesterol, comes in “bad” and “good” varieties. Empirically, we find that value stocks and small stocks have considerably higher cash-flow betas than growth stocks and large stocks, and this can explain their higher average returns. The poor performance of the capital asset pricing model (CAPM) since 1963 is explained by the fact that growth stocks and high-past-beta stocks have predominantly good betas with low risk prices.

Does Risk or Mispricing Explain the Cross-Section of Stock Prices

Most previous research evaluates market efficiency and asset pricing models using average abnormal trading profits on dynamic trading strategies. We measure the ability of the capital asset pricing model (CAPM) and the efficient-market hypothesis to explain the level of stock prices. First, we find that cash-flow betas (measured by regressing firms' earnings on the market's earnings) explain the prices of value and growth stocks well, with a plausible premium. Second, we use a present-value model to decompose the cross-sectional variance of firms' price-to-book ratios into two components due to risk-adjusted fundamental value and mispricing. When we allow the discount rates to vary as predicted by the CAPM, the variance share of mispricing is negligible.

Bad Beta, Good Beta

This paper explains the size and value anomalies in stock returns using an economically motivated two-beta model. We break the CAPMbeta of a stock with the market portfolio into two components, one reflecting news about the market's future cash flows and one reflecting news about the market's discount rates. Intertemporal asset pricing theory suggests that the former should have a higher price of risk; thus beta, like cholesterol, comes in bad and varieties. Empirically, we find that value stocks and small stocks have considerably higher cash-flow betas than growth stocks and large stocks, and this can explain their higher average returns. The poor performance of the CAPMsince 1963 is explained by the fact that growth stocks and high-past-beta stocks have predominantly good betas with low risk prices.