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.

The Bayesian Fama-MacBeth (OLS) estimator is available as part of the Bayesian Factor Zoo package

A Python package implementing the method in full generality (OLS, GLS and with omitted variables) is independently maintained by Gustavo Amarante

We develop a unified framework to study the term structure of risk premia of nontradable factors. Our method delivers level and time variation of risk premia, uncovers their propagation mechanism, is robust to misspecification and weak identification, and allows for segmented markets. Most macroeconomic factors are weakly identified at quarterly frequency, but have increasing (unconditional) term structures with large risk premia at business cycle horizons. Moreover, the slopes of their term structures are strongly procyclical. Most macroeconomic and intermediary-based factors command similar risk premia in equity and corporate bond markets, while we find strong evidence of segmentation for other factors.

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 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. 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 the Treasury component is priced almost exclusively by the bond factors.

Replication data available at: Open Source Bond Asset Pricing

Award financial support by INQUIRE Europe, grant 2023-10-03

Estimations performed using the the BayesianFactorZoo R CRAN package

An earlier version of the paper circulated under the title “The Corporate Bond Factor Zoo”

We analyse the structure of the UK repo market using a regulatory dataset that covers about 70% of this market. We examine the maturity structure, collateral types and different counterparty types that engage in this market and try to estimate the extent of collateral rehypothecation by the banks. We try to address the question of what variables determine haircuts using transaction-level data. We find that collateral rating and transaction maturity have first order importance in setting haircuts. Hedge funds, as borrowers, receive a significantly higher haircut even after controlling for measures of counterparty risk. We find that larger borrowers with higher ratings receive lower haircuts, but this effect can be overshadowed by collateral quality, because weaker borrowers try to use higher quality collateral to receive a lower haircut. Lender characteristics appear to matter for haircuts, but the results are less stable. Finally we examine the structure and attributes of the repo market network and assess if the network structure has an influence over haircuts. We do not find a significant effect in that respect.

Information asymmetries and trading costs, in a financial market with dynamic information, generate a self-exciting equilibrium price process with stochastic volatility, even if news have constant volatility. Intuitively, new information is released to the market at trading times that, due to traders’ strategic choices, differ from calendar times. This generates an endogenous stochastic time change between trading and calendar times, and stochastic volatility of the price process in calendar time. In equilibrium: price volatility is autocorrelated and is a non-linear function of number and volume of trades; the relative informativeness of number and volume of trades depends on the data sam- pling frequency; volatility, price quotes, tightness, depth, resilience, and trading activity, are jointly determined by information asymmetries and trading costs. Our closed form solutions rationalize a large set of empirical evidence and provide a natural laboratory for analyzing the equilibrium effects of a financial transaction tax. 

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.

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.