Session 3: Macro Finance and Computation

We directly optimize the objectives of portfolio management via reinforcement learning—an alternative to conventional supervised-learning-based paradigms that entail first-step estimations of return distributions, pricing kernels, or risk premia. Building upon breakthroughs in AI, we develop multi-sequence neural-network models tailored to the distinguishing features of financial data, while allowing training without labels and potential market interactions. Our AlphaPortfolio yields stellar out-of-sample performances (e.g., Sharpe ratio above two and over 13% risk-adjusted alpha with monthly re-balancing) that are robust under various economic restrictions and market conditions (e.g., exclusion of small stocks and short-selling). Moreover, we project AlphaPortfolio onto simpler modeling spaces (e.g., using polynomial-feature-sensitivity) to uncover key drivers of investment performance, including their rotation and nonlinearity. More generally, we highlight the utility of deep reinforcement learning in finance and “economic distillation” for model interpretation.

We develop an asset-pricing model with heterogeneous investors and search frictions. Trade is intermediated by risk-neutral dealers subject to capacity constraints. Risk-averse investors can direct their search towards dealers based on price and execution speed. Order flows affect the risk premium, volatility, and equilibrium interest rate. We propose a new solution method to characterize the equilibrium analytically. We assess the quantitative implications of the model in response to a large adverse shock. Consistent with the empirical evidence from the COVID-19 crisis, we find an increase in the risk premium and market illiquidity, and a decline in interest rates.

This empirical paper deals with the impacts of sentiment about the future, short-run risk, and long-run risk in a dynamic economic model of optimal consumption decisions with recursive preferences. The empirical strategy combines both a latent factor method and a democratic orthogonalization technique. The latent factor method is applied to a large database of macroeconomic indicators and a democratic orthogonalization technique is used to separate the relative importance of sentiment about the future and long-run risk channels in shaping optimal consumption decisions. This offers the opportunity to exploit a data rich informationbase in assessing uncertainty shocks and changes in the dynamics of the state of the economy over time. The empirical results suggest that consumers with recursive preferences are not indifferent to long-run uncertainty shocks to future consumption prospects. Endogenous consumption variations are driven by a multi-component mechanism, where on average the sentiment component accounts for 15.33%, the short-run risk accounts for 16.89%, and the long-run risk pertains to 34.51%. This suggests that channels of economic decisions relating to sentiment about the future and broader attitudes towards short-run and long-run risks are important features to be considered in analyzing dynamic stochastic economic models with recursive utility.

We apply a new methodology for identifying pervasive and discrete changes (“breaks”) in cross-sectional risk premia and find empirical evidence that these are economically important for understanding returns on US stocks. Size, value, and investment risk premia have fallen off to the point where they are insignificantly different from zero at the end of the sample. The market risk premium has also declined systematically over time but remains significant and positive as do the momentum and profitability risk premia. We construct a new instability risk factor from cross-sectional differences in individual stocks’ exposure to time-varying risk premia and show that this factor earns a premium comparable to that of commonly used risk factors. Using industry- and characteristics-sorted portfolios, we show that some breaks to the return premium process are broad-based, affecting all stocks regardless of industry- or firm characteristics, while others are limited to stocks with specific style characteristics. Moreover, we identify distinct lead-lag patterns in how breaks to the risk premium process impact stocks in different industries and with different style characteristics.

We identify a shock that explains the bulk of fluctuations in equity risk premia, and show that the shock also explains a large fraction of the business-cycle comovements of output, consumption, employment, and investment. Recessions induced by the shock are associated with reallocation away from full-time permanent positions, towards part-time and flexible contract workers. A flexible-price model with labor market frictions and fluctuations in risk appetite can explain all of these facts, both qualitatively and quantitatively. The size of risk-driven fluctuations depends on the relationship between the riskiness and productivity of different stores of value: if safe savings vehicles have relatively low marginal products, then a flight to safety will drive a larger aggregate contraction.

Ten trillion dollars are allocated to illiquid vehicles for which investors commit ex-ante to transferring capital on demand – most of which are Private Equity (PE) funds. We design a dynamic portfolio allocation model in which investors commit capital to PE. The effects of commitment risk on investors’ portfolios and welfare are large. Investors are under-allocated to PE, and willing to pay a premium to update their PE allocation when capital is called, which is more than twice the one to eliminate standard liquidity frictions induced by the limited tradability of PE. In contrast, investors are not willing to pay to remove the uncertainty over the timing of capital call.

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including long-run risk models and (time-varying) rare-disaster risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro-finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross-equation restrictions. For empirical application, we apply the proposed conditional specification test to evaluate a time-varying rare-disaster risk model and construct data-driven robust model uncertainty sets.

We propose the Corporate Bond Market Distress Index (CMDI) to quantify corporate bond market dislocations in real time. The index takes a preponderance-of-metrics perspective to combine a broad set of measures of market functioning from primary and secondary markets but not driven by any one statistic. We document that the index correctly identifies periods of dislocations and predicts future realizations of commonly-used measures of market distress, while the converse is not the case. Moreover, theCMDI is an economically and statistically significant predictor of future economic activity, even after controlling for standard predictors, including credit spreads.

Times of elevated aggregate uncertainty are associated with lower investment, but surprisingly, future capital growth does not drop and even increases in the data. To reconcile this novel evidence, we show that high uncertainty predicts lower utilization and depreciation of existing capital, which dominates the reduction in new investment. We construct and estimate a general-equilibrium model to explain the relation between uncertainty and capital accumulation. In the model, precautionary saving is achieved by lowering utilization, instead of increasing investment. Lower utilization persistently decreases depreciation, conserving capital for the future, and simultaneously, discourages new investment. This channel amplifies stock price exposure to uncertainty risks, especially for firms with more flexible utilization, which we confirm in the data. We further show the importance of our mechanism to generate a negative impact of uncertainty shocks in an extended New-Keynesian framework.

Using constrained optimization, we develop a simple, efficient approach (applicable in both unconstrained and constrained maximum-likelihood estimation problems) to computing profile-likelihood confidence intervals. In contrast to Wald-type or score-based inference, the likelihood ratio confidence intervals use all the information encoded in the likelihood function concerning the parameters, which leads to improved statistical properties. In addition, the method does not suffer from the computational burdens inherent in the bootstrap. Moreover, it allows the computation of confidence intervals for transformations of the parameters—including counter-factual model quantities—in a straightforward fashion. In an application to Rust’s (1987) bus-engine replacement problem, our approach does better than either the Wald or the bootstrap methods, delivering very accurate estimates of the confidence intervals quickly and efficiently. Furthermore, we demonstrate how to compute confidence bands for the model-implied demand curve for engine replacement. An extensive Monte Carlo study reveals that in small samples, only likelihood ratio confidence intervals yield reasonable coverage properties, while at the same time discriminating implausible values.

Recent findings on the term structure of equity and bond yields pose serious challenges to existing equilibrium asset pricing models. This paper presents a new equilibrium model to explain the joint historical dynamics of equity and bond yields (and their yield spreads). Equity/bond yields movements are mainly driven by subjective dividend/GDP growth expectation. Yields on short-term dividend claims are more volatile because short-term dividend growth expectation mean-reverts to its less volatile long-run counterpart. Procyclical slope of equity yields are due to counter-cyclical slope of dividend growth expectations. The correlation between equity return-s/yields and nominal bond returns/yields switched from positive to negative after the late 1990s, owing to (1) procyclical inflation and (2) stronger correlation between expectations of real GDP growth and of real dividend growth post-2000. Dividend strip returns are predictable and the predictive power decreases with maturity due to predictable forecast errors and revisions. The model is also consistent with the data in generating persistent and volatile price-dividend ratios, and excess return volatility.

Elevated government debt in the wake of unprecedented stimulus packages increasingly raise concerns about a looming return of inflation, as governments may be tempted to monetize debt. In this paper, we examine optimal debt management in the presence of inflation concerns in a setting where i) the government can issue long-term nominal and real (TIPS) bonds, ii) the monetary authority sets short-term interest rates according to a Taylor rule, and iii) inflation has real costs as prices are sticky. Nominal debt can be inflated away, but bond prices reflect elevated inflation expectations. Real bond prices are higher, but such debt constitutes a real commitment ex post. We show that the optimal government debt portfolio includes a substantial allocation to real bonds, which lowers inflation levels, inflation volatility, and inflation persistence in equilibrium. The associated lower inflation risk premia are reflected in welfare gains through real debt management. Quantitatively, our results are stronger i) the higher the initial debt level, and ii) the longer debt maturity. Our results hold up when accounting for frictions in the TIPS market, such as illiquidity. Our findings suggest that TIPS should be an important tool for debt management in the presence of looming inflation.

We develop a dynamic model of stablecoins and crypto shadow banking, where the stablecoin issuer transforms risky assets, including cryptocurrencies, into digital tokens of stable values. Both the stablecoin issuer’s reserve assets and users’ collateral back the stablecoin. However, even under over-collateralization, a pledge of one-to-one convertibility to a reference currency can be fragile. The distribution of states is bimodal: A fixed exchange rate may persist, but once the stablecoin breaks the buck, the recovery is slow. When negative shocks drain the issuer’s reserves, debasement allows the issuer to share risk with users, but it triggers a vicious cycle of depressed stablecoin demand, lower transaction volume and transaction fees, slow rebuild of reserves, and a persistent need for debasement. Stablecoin management requires the optimal combination of strategies commonly observed in practice, such as open market operations, dynamic requirement of users’ collateral, transaction fees or subsidies, re-pegging, and issuances of “secondary units” that function as the stablecoin issuer’s equity. Our model lends itself to an evaluation of regulatory proposals (e.g., capital requirement) and sheds light on the complex incentives behind the stablecoin initiatives led by the network companies (e.g., Facebook).

We use option prices and realized returns to decompose risk premia into different parts of the return state space. In the data, 8/10 of the average equity premium is attributable to monthly returns below -10%, but returns below -30% matter very little. In contrast, leading asset pricing models based on habits, long-run risks, rare disasters, undiversifiable idiosyncratic risk, and constrained intermediaries attribute the premium predominantly to returns above -10% or to the extreme left tail. We show that the discrepancy arises from an unrealistically small price of risk for stock market tail events.

The market for option contracts relies on the ability to freely trade option contracts, and that the options themselves do not create strategic interactions between the market participants. In this paper, I show that a sufficiently complex option contract can create the possibility of strategic interactions, which makes the option unpriceable without knowing the identity of the option holders. I also identify the features of a contract that prevent such strategic interactions, and the implications for option pricing.