We analyze 18 quadrillion models for the joint pricing of corporate bond and stock returns. Only a handful of factors, behavioural and nontradable, are robust sources of priced risk. Yet, the true latent stochastic discount factor is dense in the space of observable factors. A Bayesian Model Averaging Stochastic Discount Factor (BMA-SDF), combining the corporate bond and stock factor zoos, explains risk premia better than all existing models, both in- and out-of-sample. We show that multiple factors are noisy proxies for common underlying sources of risk, and the BMA-SDF aggregates them optimally, yielding a tradable portfolio with an out-of-sample annualized Sharpe ratio of 1.5 to 1.8. The SDF, as well as its conditional mean and volatility, are persistent, track the business cycle and times of heightened economic uncertainty, and predict future asset returns. Finally, we show that stock factors price the credit component of corporate bond excess returns well, while their Treasury component is priced almost exclusively by the bond factors.
Using a unique transaction-level dataset covering the UK bilateral repo market, we show that only 61% of the repos are backed by high-quality collateral, with banks intermediating liquidity across counterparties and using CCPs mainly for high-quality collateral and netting benefits. Haircuts reflect both collateral and borrower characteristics: larger, higher-rated, less levered, less sophisticated borrowers, and those with repeated relationships receive lower or even zero haircuts. Borrower attributes explain as much variation in haircuts as collateral quality, while lender liquidity and default risk play little role. We also document a pecking order in collateral use, with higher-quality assets pledged first.
Using information in returns we identify the stochastic process of consumption. We find that aggregate consumption reacts over multiple quarters to innovations spanned by financial markets, and this persistent component accounts for over a quarter of consumption variation. These shocks are cross-sectionally priced, drive most of the time series variation in stocks, and a small, yet significant, share of volatility of bonds. Nevertheless, we find no support for stochastic volatility of consumption driving time-varying risk premia. Finally, an otherwise standard recursive utility model based on our estimated process explains both equity premium and risk-free rate puzzles with low risk aversion.
Previously circulated as “Consumption Risk of Bonds and Stocks” and “Consumption” Winner of Oustanding Paper Award in Investment, Midwest Finance Association, 2016
We propose a novel approach to measure the cost of aggregate economic fluctuations, that does not require complete specification of investors’ risk preferences or their beliefs. With data on consumption and asset prices, an information-theoretic method is used to recover an information kernel (I-SDF). The I-SDF accurately prices broad cross-sections of assets, thereby offering a reliable candidate for the measurement of the welfare cost of business cycles. Our method enables the estimation of both the unconditional (or, average) cost of fluctuations as well as the cost conditional on each possible economic state. We find that the cost of fluctuations is strongly time-varying and countercyclical and that the cost of business cycle fluctuations is substantial, accounting for a quarter to a third of the cost of all consumption uncertainty.
We show that a non-parametric estimate of the pricing kernel, extracted using an information-theoretic approach, delivers smaller out-of-sample pricing errors and a better cross-sectional fit than leading multi factor models. The information SDF (I-SDF) identifies sources of risk not captured by standard factors, generating very large annual alphas (20%-37%) and Sharpe ratio (1.1). The I-SDF extracted from a wide cross-section of equity portfolios is highly positively skewed and leptokurtic, and implies that about a third of the observed risk premia represent a compensation for 2.5% tail events. The I-SDF offers a powerful benchmark relative to which competing theories and investment strategies can be evaluated.
We generalise a stochastic version of the workhorse SIR (Susceptible-Infectious- Removed) epidemiological model to account for spatial dynamics generated by network interactions. Using the London metropolitan area as a salient case study, we show that commuter network externalities account for about 42% of the propagation of COVID-19. We find that the UK lockdown measure reduced total propagation by 44%, with more than one third of the effect coming from the reduction in network externalities. Counterfactual analyses suggest that: i) the lockdown was somehow late, but further delay would have had more extreme consequences; ii) a targeted lockdown of a small number of highly connected geographic regions would have been equally effective, arguably with significantly lower economic costs; iii) targeted lockdowns based on threshold number of cases are not effective, since they fail to account for network externalities.
We propose a novel framework for analyzing linear asset pricing models: simple, robust, and applicable to high dimensional problems. For a (potentially misspecified) standalone model, it provides reliable price of risk estimates for both tradable and non-tradable factors, and detects those weakly identified. For competing factors and (possibly non-nested) models, the method automatically selects the best specification – if a dominant one exists – or provides a Bayesian model averaging (BMA-SDF), if there is no clear winner. We analyze 2.25 quadrillion models generated by a large set of factors, and find that the BMA-SDF outperforms existing models in- and out-of-sample
BayesianFactorZoo R CRAN package (user-friendly R package that implements all the methods in the paper, with extensive documentation and teaching examples) (extended) Presentation Slides An early video presentation by Svetlana Bryzgalova Full replication codes (including usage examples and posterior draws of the published version, 4.56GB) BMA-SDF (time series of BMA-SDF posterior mean for different SR values, based on factors of Table 3, csv format)
Using a structural model, we estimate the liquidity multiplier of an interbank network and banks’ contributions to systemic risk. To provide payment services, banks hold reserves. Their equilibrium holdings can be strategic complements or substitutes. The former arises when payment velocity is high and payments begets payments. The latter prevails when the opportunity cost of liquidity is large, incentivising banks to borrow neighbors’ reserves instead of holding their own. Consequently, the network can amplify or dampen individual shocks. Empirically, network topology explains cross-sectional heterogeneity in banks’ contribution to systemic risks while changes in the equilibrium type drive the time-series variation.
We consider asset pricing models in which the SDF can be factorized into an observable component and a potentially unobservable one. Using a relative entropy minimization approach, we nonparametrically estimate the SDF and its components. Empirically, we find that the SDF has a business-cycle pattern and significant correlations with market crashes and the Fama-French factors. Moreover, we derive novel bounds for the SDF that are tighter and have higher information content than existing ones. We show that commonly used consumption-based SDFs correlate poorly with the estimated one, require high risk aversion to satisfy the bounds and understate market crash risk.
We study the implications of human capital hedging for international portfolio choice. First, we document that, at the household level, the degree of home country bias in equity holdings is increasing in the labor income to financial wealth ratio. Second, we show that a heterogeneous agent model in which households face short selling constraints and labor income risk, calibrated to match both micro and macro labor income and asset returns data, can both rationalize this finding and generate a large aggregate home country bias in portfolio holdings. Third, the empirical evidence supporting the belief that the human capital hedging motive should skew domestic portfolios toward foreign assets, is driven by an econometric misspecification rejected by the data.
Note: This paper is based upon, and replaces, two companion papers: “The International Diversification Puzzle is not Worse Than You Think” and “Human Capital and International Portfolio Choice.”
Probably not. First, allowing the probabilities of the states of the economy to differ from their sample frequencies, the Consumption-CAPM is still rejected in both U.S. and international data. Second, the recorded world disasters are too small to rationalize the puzzle unless one assumes that disasters occur every 6-10 years. Third, if the data were generated by the rare events distribution needed to rationalize the equity premium puzzle, the puzzle itself would be unlikely to arise. Fourth, the rare events hypothesis, by reducing the cross-sectional dispersion of consumption risk, worsens the ability of the Consumption-CAPM to explain the cross-section of returns.
A reduction in inflation can fuel run-ups in housing prices if people suffer from money illusion. For example, investors who decide whether to rent or buy a house by simply comparing monthly rent and mortgage payments do not take into account the fact that inflation lowers future real mortgage costs. We decompose the price-rent ratio into a rational component — meant to capture the “proxy effect” and risk premia — and an implied mispricing. We find that inflation and nominal interest rates explain a large share of the time-series variation of the mispricing, and that the tilt effect is very unlikely to rationalize this finding.
This paper evaluates the central insight of the consumption capital asset pricing model that an asset’s expected return is determined by its equilibrium risk to consumption. Rather than measure risk by the contemporaneous covariance of an asset’s return and consumption growth, we measure risk by the covariance of an asset’s return and consumption growth cumulated over many quarters following the return. While contemporaneous consumption risk explains little of the variation in average returns across the 25 Fama-French portfolios, our measure of ultimate consumption risk at a horizon of three years explains a large fraction of this variation.
Commonly used frequentist estimation methods for linear factor models of asset returns are invalidated by weak and spurious factors. The problem is amplified by omitted variables and model misspecification, and often calls for specialized non-standard estimation techniques. Conversely, the Bayesian analogue of the popular Fama and MacBeth (1973) two-pass regressions method provides reliable risk premia estimates for both tradable and nontradable factors, detects those weakly identified, delivers valid credible intervals for all objects of interest, and is intuitive, fast and simple to implement. In other words, weak and spurious factors are not a problem for the Bayesian estimation of Fama-MacBeth regressions.
We provide a novel priced Wold representation theorem that sharply identifies shocks common to financial markets and the macroeconomy, their propagation, and the term structure of macro risk premia. Our identification leverages the fact that, in equilibrium models, asset prices are jump variables that reveal priced risks in large cross-sections of returns (N → ∞). We find that macro factors’ risk premia are strongly time-varying and countercyclical, with sharply increasing unconditional term structures. This pattern is driven by the slow propagation of a priced common shock, distinct from TFP, that captures most of the persistence in macroeconomic variables. Macro risk premia are negligible in the short run, yet grow to match equity risk premia at the business cycle horizon. This finding is not a mechanical byproduct of persistence: while GDP, consumption, industrial production, and employment exhibit upward-sloping term structures, other similarly persistent factors—e.g., VIX or intermediary-based variables—display downward-sloping or flat ones.
Using an equilibrium network model and a large international panel of cross-border trade, we analyse empirically the drivers of foreign currency invoicing. First, we find strong evidence of strategic complementarity in currency invoicing across countries: Exporting countries tend to invoice more in a given currency when their main trade partners invoice in that same currency. This in turn leads to an amplification of domestic shocks through the trade network. Second, key players for a given currency are not only countries that invoice most of their exports in that foreign currency (e.g., China, South Korea, and Russia), but also countries that are central in the international trade network (e.g., Japan, Germany, and Canada). Third, at the country-level, we find evidence of strategic complementarity, or natural hedging, between the choices of export and import currencies. Fourth, in counterfactual analysis we find that, due to the large network externalities that we identify, the position of the USD as dominant trade currency is inherently fragile with respect to the currency invoicing choices of EU and BRICS countries.
We develop a generalization of the Glosten and Milgrom (1985) sequential trading model that delivers a fully endogenous, multi-time-scale, agent-based equilibrium theory of price dynamics, volatility, liquidity, and trading activity. Starting from an axiomatization of the Glosten-Milgrom model, we characterize the tick-by-tick equilibrium in closed form and establish its scaling limits as traders’ arrival or trading rates increase. The resulting lower-frequencies price and trade processes are obtained through a novel probabilistic machinery: (i) a continuous (in the Skorokhod topology) mapping from the shadow-valuation process—a branching Brownian motion—to all equilibrium quantities; (ii) a new probabilistic result on the most recent common ancestor; (iii) a mixingale convergence theorem for equilibrium price functionals defined through state-dependent hitting times; and (iv) a central limit theorem for irregularly spaced renewal-reward sequences, which yields the low- and ultra-low-frequency diffusion limits. These results show that stochastic volatility arises endogenously as a linear functional of the equilibrium number-of-trades process. Our closed-form solutions rationalize a large body of empirical evidence and provide a natural laboratory for analyzing the equilibrium effects of a financial transaction tax.
Most households’ portfolios are extremely close to the efficient frontier once we explicitly take into account no short-selling constraints, while the null hypothesis of efficiency is rejected for all portfolios if we don’t consider these constraints.
Work in Progress
Speculative Trading and Derivative Market Imbalances, with A. Danilova and Y. Stoev
We consider an economy in which some agents do not continuously hedge their position in derivative assets using the underlying assets market – i.e. we study the effects of an imbalanced derivate market. We show that, even in the presence of complete markets, the imbalance significantly alters the equilibrium price process of the underlying assets: risk premia and volatility become stochastically time varying, hence option implied volatility is characterized by smile and smirk patterns, momentum-like price dynamics arise as well as price spillovers across underlying assets. Moreover, the derivative imbalance generates self-fulfilling equilibria, e.g. if the imbalance takes the form of a bet on an increase in asset volatility, then the equilibrium volatility does increase. Finally, since our formulation is extremely general, our results also apply to segmented markets where some investments are achievable only via financial intermediation.
Social Networks and Loan Repayments, with K. Yuan, and Y. Yuan
This paper shows that social networks have significant effects on loan repayments. In the loan records of a peer-to-peer lending platform, we proxy social networks based on the contact persons that borrowers provide at loan applications. We estimate the effect of the propensity to pay of a borrower on the propensity to pay of their contact persons using a Spatial Autoregressive Probit model. If the probability to repay of a borrower’s contact persons increases by 10%, the repayment probability of the linked borrower increases by 0.8%, which increases the lender’s profit on average by 360 RMB (i.e. $52). In contrast, a borrower’s propensity to pay does not significantly affect the propensity to pay of other borrowers from the same home or work address. We interpret the results as evidence that social networks affect loan repayment decisions beyond common borrower characteristics and financial situations.
We study the implications of human capital hedging for international portfolio diversification. First, we show that given the degree of international economic integration observed in the data, very small domestic redistributive shocks can lead to home country bias in portfolio holdings. Second, we find that the seminal empirical result of Baxter and Jermann (1997) – that the international diversification puzzle is worsened if we consider the human capital hedging motive – is driven by an econometric misspecification that restricts the countries considered in their study to be economically not integrated. Moreover, once this misspecification is corrected, considering the human capital risk does not unequivocally worsen the puzzle, and in some cases helps explaining it. Third, we document that the substantial statistical uncertainty on measuring returns to the aggregate capital stock can rationalize the disagreements in the previous literature. Fourth, we find sharp evidence that if the set of assets that can be used to hedge aggregate human capital is restricted to publicly traded stocks, the human capital hedging motive has a negligible impact on optimal portfolio choice. This last finding is driven by the extremely small correlation between stock market returns and returns to human capital.
This paper shows that in a non-representative agent model in which households face short selling constraints and labor income risk, in the form of both uninsurable shocks and a common aggregate component, small differences in the correlation between aggregate labor income shocks and domestic and foreign stock market returns lead to a very large home bias in asset holdings. Calibrating this buffer-stock saving model to match both microeconomic and macroeconomic U.S. labor income data, I demonstrate that, consistent with the empirical literature, a) investors that enter the stock market will initially specialize in domestic assets, b) individual portfolios become more internationally diversified, adding foreign stocks one at a time, as the level of asset wealth increases, and c) most importantly, the implied aggregate portfolio of U.S. investors shows a large degree of home bias consistent with observed levels.
