This paper successfully replicates all the main results in Kelly and Pruitt (2013) for the return on the market - and provides some evidence of market premium predictability - based on their original empirical choices in the 1930-2010 sample (and, to some extent, based on other empirical choices). However, the evidence of market premium predictability, in particular, essentially disappears by making any one of the following changes: (i) Updating the sample to June 1926 - December 2019; (ii) not taking logs of the book-to-markets used as regressors; (iii) not dividing book-to-markets by their time-series standard deviations; or (iv) not taking one extra book-to-market lag (for monthly forecasts). In summary, I find no evidence that the procedure generates a valid forecasting model of market premiums with persistently positive out-of-sample R2, especially since the Oil Shock (or early 2000) in the full sample.
This paper unifies macro-finance and multifactor asset pricing theories to show that, in sample and out of sample: (i) Larger cross-sectional book-to-market medians and spreads - price of risk proxies - predict larger market (in sample), size, value, and investment premiums; (ii) the investment and profitability spreads - factor risk (quantity) proxies - only forecast the investment and profitability premiums, respectively, especially when conditioned on the price of risk. This predictability generates "factor timing" strategies with substantial economic gains, supports the hypothesis of time-varying price of risk in macro-finance theories, and contradicts the hypothesis that the investment and profitability "factors" have constant risks.
Dollar carry trade risk premiums - unlike dollar-neutral or foreign exchange carry risk premiums - are positively correlated with firm-level dispersions in investment, profitability, and book-to-market in addition to the Treasury-bill rate, long term bond yield, term spread, and default spread. This predictability is also statistically and economically significant out of sample: It generates Sharpe ratios as large as 1.37 (compared to 0.44 unconditionally), for example. Indeed, several forecasting models pin down the few periods responsible for the entire premium. Finally, any detailed narrative (typically based on untestable claims) in which the variables above are proxies for the latent (quantity of) risk and price of risk states - and the business cycle - in the U.S. explains the results in the present paper. However, I avoid making this type of less scientific claims as much as possible and focus on the evidence, instead.
This paper empirically describes how the risk premiums of size portfolios vary with macro-economic fluctuations in the price of risk at the portfolio formation dates, thereby explaining the lack of robustness involving the unconditional size premium: Only portfolios formed in "bad" states - with price of risk among the largest 30% - earn significantly positive premiums (7.5% per year on average). Inevitably, the subsample in which the premium is absent dominates and easily distorts the unconditional evidence that supports the size premium literature. Conditional tests contradict the (unconditional) conclusions that the size premium is consistent with the ICAPM or recently non-existent.
I derive two valid forecasting models of the equity premium in monthly frequency, based on little more than no-arbitrage: A "predictability timing" version of partial least squares, given that predictability is theoretically time-varying; and a least squares model with realized market premiums in monthly frequency as the regressor, since realized returns are theoretically correlated to risk and to the price of risk. This evidence is consistent with the instability inherent to monthly equity premium forecasts based on standard partial least squares and disaggregated book-to-markets as regressors, and with the fact that taking one extra lag of book-to-markets in predictive return regressions improves the estimates.
This paper is the second in a series of critiques of the assumption that stable economic relations exist between certain "firm characteristics" and expected returns. The paper explains why this is not the case for past returns and provides theoretical, empirical, and simulated evidence that the stylized facts involving momentum are consistent with traditional risk-based asset pricing, thereby solving the apparent theoretical puzzle. For example, riskier assets tend to be in the loser portfolio after (large) increases in the price of risk: The time-varying correlation between past returns and risk, which determines the risk of momentum portfolios, decreases with the price of risk. Hence, their premiums are approximately negative quadratic functions of the price of risk, theoretically truncated at zero. The best linear (CAPM) function describing this relation unconditionally has the negative slope and positive intercept documented empirically and considered the main momentum puzzle.
This paper fixes the value investment strategy by following the simple, correct, but unpopular theoretical explanation of the value premium: X-value normalizes stock prices by the recursive out-of-sample expectation of each firm's net income, estimated by industry from its financials, while ignoring book equity. The resulting X-value factor is unspanned by the five Fama/French factors individually or in different combinations, and spans the value and investment factors. Its Sharpe ratio of 0.57 is the largest among the five factors, compared to 0.39 for value. However, the citation-oriented (as opposed to scientific-oriented) incentives in academia imply that academic popularity requires adherence to narratives that agree with the preferences of influential academics, regardless of scientific accuracy. Hence, this small example in the area of investments also illustrates a general tale of past - and a systematic prediction of future - failures of academic "truths" when faced with reality.
Within a standard risk-based asset pricing framework with rational expectations, realized returns have two components: Predictable risk premiums and unpredictable shocks. In bad times, the price of risk increases. Hence, the predictable fraction of returns - and predictability - increases. "Disagreement" (dispersion in analyst forecasts) also grows in bad times if (i) analysts report (close to) risk-neutral expectations weighted by state prices, which become more volatile, or (ii) dividend volatility changes with the price of risk, for example because consumption volatility changes. In both cases, individual analysts produce unbiased forecasts based on partial information.
Tests of the conditional CAPM are often based on the joint (internally inconsistent) hypothesis that the stock portfolio used in the tests is the theoretical, mean-variance efficient, market portfolio. I derive a new test based exclusively on the theory in the conditional CAPM. According to this test, the conditional CAPM explains asset pricing anomalies, such as the unconditional alphas and betas of momentum, value, and size portfolios. In contrast, the unconditional CAPM theory is rejected by portfolios with negative unconditional betas and positive unconditional alphas, under the same assumptions. Hence, relaxing this joint assumption does not render the CAPM untestable.
Riskier firms have lower prices - and higher book-to-market - exclusively due to the present value identity. For a small subset of firms, book equity is a good proxy for expected cash flows. This is why (i) the difference between the value and size premiums significantly decreases and becomes negative with the price of risk; (ii) among portfolios formed in low price of risk states, SMB returns explain none of the variation in HML returns; (iii) for the remaining portfolios, a strong factor structure exists; (iv) only among these portfolios, SMB returns span HML returns; and (v) the same SMB portfolios span the (stock) market portfolio. The hypothesis of (even indirect) stable economic relations between risk and market capitalization ("size") or book-to-market is theoretically inconsistent with the present value identity and inconsistent with the empirical evidence under fairly general conditions. There are no "missing factors" which size or book-to-market proxy for: Regressions that rely on size-related portfolios do not produce valid unconditional models of returns.
The equity premium–risk-free rate level and predictability puzzles in standard power utility consumption-based asset pricing models disappear once we remove the government-imposed component from the consumption expenditure series. I calibrate this component based on the growth rates of two proxies for government intervention, which I also show to forecast the short- and long-term equity premiums between 1974 (or 1981) and 2017. In summary, investors require large premiums to hold stocks because stocks deliver poor returns when government intervention (failure) increases, systematically reducing individual utility levels. Government failure is likely the key macro-finance variable linking asset prices and economic fluctuations.
This paper theoretically reconciliates the several types of value premiums observed in cross-section with the use of aggregate scaled-price ratios – including "value spreads" – as price of risk proxies in time series. Prices in scaled-price ratios reflect risk premiums (and the price of risk), while the scaling variables control for expected cash flows. They differ from risk proxies (without a price component) that only predict returns in cross-section. The ratios between each proxy's risk premium in cross section and the proxy's standard deviation in time series rank the proxies based on their theoretical correlations with the price of risk.
I use Financial Economics theory to derive a measure of model risk with clear and actionable implications. The resulting "Model Risk Price" is based on the covariance between the payoffs associated with the model and the Stochastic Discount Factor, setting it fundamentally apart from the model accuracy statistics that have been typically used as model risk measures. Given that it is measured in financial terms, the Model Risk Price and its associated hedging strategies can also be intuitively communicated to non-technical audiences, such as investors, CEOs, other C-suite executives, and risk managers. From a practical standpoint, the paper addresses one of the most critical questions posed to risk managers by the firm's investors: What is the precise impact of model risk on their investments, and what concrete actions can be taken to mitigate it. More broadly, the paper makes a seminal contribution to the literature by formally defining and economically measuring the risk of using a model, rather than simply estimating the uncertainty in its output as is currently done.
In this paper, I show how the presence of long-term investors using different return forecasting models and switching these models based on their past performance generates the price trends observed in the financial markets. I develop an asset pricing model in which agents have long horizon objectives, based on a stream of consumption. Each agent chooses a forecasting model and maximises a recursive utility function. The choice of the forecasting model in each period determines the agent type. Their types, however, change in time and the evolution is endogenous and based on the relative performance of the forecasting models. This happens because agents have an incentive to adopt the forecasting model with the best performance in the previous period to coordinate with the market. I estimate the asset pricing model using data on the international stock markets. I show that especially for very risk averse individuals, the results of the model change completely whether we consider the intertemporal demand for assets, or only its myopic component as it has been done so far in the literature on heterogeneous beliefs.
Discussion of "Disaggregated Sales and Stock Returns" by Sumit Agarwal, Wenlan Qian, and Xin Zou.
Discussion of "A non-parametric test for representative agent pricing" by Luca Pezzo.
Discussion of "Sentiment across asset markets" by Dashan Huang, Heikki Lehkonen, Kuntara Pukthuanthong, and Guofu Zhou.