Research articles for the 2020-10-15

A Deep Learning Framework for Predicting Digital Asset Price Movement from Trade-by-trade Data
Qi Zhao
arXiv

This paper presents a deep learning framework based on Long Short-term Memory Network(LSTM) that predicts price movement of cryptocurrencies from trade-by-trade data. The main focus of this study is on predicting short-term price changes in a fixed time horizon from a looking back period. By carefully designing features and detailed searching for best hyper-parameters, the model is trained to achieve high performance on nearly a year of trade-by-trade data. The optimal model delivers stable high performance(over 60% accuracy) on out-of-sample test periods. In a realistic trading simulation setting, the prediction made by the model could be easily monetized. Moreover, this study shows that the LSTM model could extract universal features from trade-by-trade data, as the learned parameters well maintain their high performance on other cryptocurrency instruments that were not included in training data. This study exceeds existing researches in term of the scale and precision of data used, as well as the high prediction accuracy achieved.



A Horserace of Volatility Models for Cryptocurrency: Evidence from Bitcoin Spot and Option Markets
Yeguang Chi,Wenyan Hao
arXiv

We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform much better than other models. Moreover, the EGARCH model's asymmetric term is positive and insignificant, which suggests that Bitcoin prices lack the asymmetric volatility response to past returns. Finally, we formulate an option trading strategy by exploiting the volatility spread between the GARCH volatility forecast and the option's implied volatility. We show that a simple volatility-spread trading strategy with delta-hedging can yield robust profits.



Asymmetric Loan Loss Provision Models
Basu, Sudipta,Vitanza, Justin,Wang, Wei
SSRN
Large net loan charge-offs are frequently associated with large decreases in nonperforming loans and large increases in loan loss provisions, inducing a V-shaped relation between loan loss provisions and nonperforming loan changes. Failure to model the asymmetry attributable to net loan charge-offs can change inferences about the presence of earnings management and the effects of delayed loan loss recognition in prior papers that assumed linearity. Future researchers should either include net loan charge-offs in linear models of loan loss provisions or explicitly model the asymmetry induced by omitting net loan charge-offs.

Bank Lending during the COVID-19 Pandemic
Hasan, Iftekhar,Politsidis, Panagiotis N.,Sharma, Zenu
SSRN
This paper examines the pricing of global syndicated loans during the COVID-19 pandemic. We find that loan spreads rise by over 11 basis points in response to a one standard deviation increase the lender’s exposure to COVID-19 and over 5 basis points for an equivalent increase in the borrower’s exposure. This renders firms subject to a burden of about USD 5.16 million and USD 2.37 million respectively in additional interest expense for a loan of average size and duration. The aggravating effect of the pandemic is exacerbated with the level of government restrictions to tackle the virus’s spread, with firms’ financial constraints and reliance on debt financing, whereas it is mitigated for relationship borrowers, borrowers listed in multiple exchanges or headquartered in countries that can attract institutional investors.

Choosing News Topics to Explain Stock Market Returns
Paul Glasserman,Kriste Krstovski,Paul Laliberte,Harry Mamaysky
arXiv

We analyze methods for selecting topics in news articles to explain stock returns. We find, through empirical and theoretical results, that supervised Latent Dirichlet Allocation (sLDA) implemented through Gibbs sampling in a stochastic EM algorithm will often overfit returns to the detriment of the topic model. We obtain better out-of-sample performance through a random search of plain LDA models. A branching procedure that reinforces effective topic assignments often performs best. We test methods on an archive of over 90,000 news articles about S&P 500 firms.



Creditor Protection, Ease of Repossession, and the Cost of Equity Capital: Evidence from Quasi-natural Experiments
Ni, Xiaoran,Yin, David
SSRN
Exploiting the staggered adoption of anti-recharacterization laws across various U.S. states as quasi-exogenous shocks to secured lenders’ ability to repossess assets in bankruptcy, we find that the strengthening of creditor rights is associated with a significant decrease in the cost of equity capital. This effect is more pronounced among firms that are more financially constrained and weakly governed. We further find that the adoption of such laws is associated with lower information asymmetry and lower firm risk. Our overall findings indicate that strengthened creditor protection can lead to a better alignment of the interests of shareholders and creditors through improved financing capacity and creditor monitoring.

DeFi Protocols for Loanable Funds: Interest Rates, Liquidity and Market Efficiency
Lewis Gudgeon,Sam M. Werner,Daniel Perez,William J. Knottenbelt
arXiv

We coin the term *Protocols for Loanable Funds (PLFs)* to refer to protocols which establish distributed ledger-based markets for loanable funds. PLFs are emerging as one of the main applications within Decentralized Finance (DeFi), and use smart contract code to facilitate the intermediation of loanable funds. In doing so, these protocols allow agents to borrow and save programmatically. Within these protocols, interest rate mechanisms seek to equilibrate the supply and demand for funds. In this paper, we review the methodologies used to set interest rates on three prominent DeFi PLFs, namely Compound, Aave and dYdX. We provide an empirical examination of how these interest rate rules have behaved since their inception in response to differing degrees of liquidity. We then investigate the market efficiency and inter-connectedness between multiple protocols, examining first whether Uncovered Interest Parity holds within a particular protocol and second whether the interest rates for a particular token market show dependence across protocols, developing a Vector Error Correction Model for the dynamics.



Efficient Risk Measures Calculations for Generalized CreditRisk+ Models
Kwok, Yue Kuen
SSRN
Numerical calculations of risk measures in credit risk models amount to evaluation of various forms of tail expectations of portfolio loss distribution. Though the moment generating function of the loss distribution in CreditRisk+ model is available in analytic closed form, efficient, accurate and reliable computation of risk measures (VaR and Expected Shortfall) and risk contributions for the CreditRisk+ model pose technical challenge. We propose various numerical algorithms for risk measures and risk contributions calculations of the enhanced CreditRisk+ model under the common background vector framework using the Johnson curve fitting method, saddle-point approximation method, curve fitting method, importance sampling in Monte Carlo simulation and check function formulation. Our numerical studies on stylized credit portfolios and benchmark industrial credit portfolios reveal that the Johnson curve fitting approach works very well for credit portfolios with a large number of obligors, demonstrating high level of numerical reliability and computational efficiency. The importance sampling in Monte Carlo simulation methods are easy to implement, but they compete less favorably in accuracy and reliability with other numerical algorithms. The less commonly used check function formulation is limited to risk measures calculations. It competes favorably in accuracy and reliability, but an external industrial optimization software is required.

Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate
Foad Shokrollahi,Marcin Marcin Magdziarz
arXiv

In this paper we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze equity warrant in a fractional Brownian motion environment, when the short rate follows the subdiffusive fractional Black-Scholes model. We obtain the pricing formula for zero-coupon bond in the introduced model and derive the partial differential equation with appropriate boundary conditions for the valuation of equity warrant. Finally, the pricing formula for equity warrant is provided under subdiffusive fractional Brownian motion model of the short rate.



FRTB and Fat Tails
Roos, Thomas
SSRN
We calculate the probability of returns exceeding a multiple of Expected Shortfall for fat-tailed portfolios. Our results show that, taken in isolation, the Basel 3 FRTB Market Risk capital requirements are insufficient to prevent a large number of insolvencies. The impact of applying a cutoff to the tail distribution is also examined.

Firm-Specific Shocks and Contagion: Are Banks Special?
Engljähringer, Hannah Katharina,Stracca, Livio
SSRN
This paper builds a database of idiosyncratic shocks (events) in global banks and car manufacturers (as representative of non-financial firms), and focuses on how these influence a number of macroeconomic and firm-specific variables in the short- and medium-term. We find that these shocks spawn large and persistent effects on the firms’ own market valuation in terms of their equity prices, CDS spreads and expected default probabilities, while contagion across firms in both sectors is generally small. Surprisingly, we find that spill-overs of bank-related events are not significantly different from the car sector, suggesting that, at least from this perspective, banks are not special. We also investigate whether our events are “granular”, i.e. influencing aggregate variables such as the VIX, equity indexes and key exchange rates, with mixed results.

Forecasting with Bayesian Grouped Random Effects in Panel Data
Zhang, Boyuan
SSRN
In this paper, we estimate and leverage latent constant group structure to generate the point, set, and density forecasts for short dynamic panel data. We implement a nonparametric Bayesian approach to simultaneously identify coefficients and group membership in the random effects which are heterogeneous across groups but fixed within a group. This method allows us to flexibly incorporate subjective prior knowledge on the group structure that potentially improves the predictive accuracy. In Monte Carlo experiments, we demonstrate that our Bayesian grouped random effects (BGRE) estimators produce accurate estimates and score predictive gains over standard panel data estimators. With a data-driven group structure, the BGRE estimators exhibit comparable accuracy of clustering with the Kmeans algorithm and outperform a two-step Bayesian grouped estimator whose group structure relies on Kmeans. In the empirical analysis, we apply our method to forecast the investment rate across a broad range of firms and illustrate that the estimated latent group structure facilitates forecasts relative to standard panel data estimators.

Hedge Fund Redemption Restrictions and Stock Price Fragility
Reynolds, Julia
SSRN
This paper explores the idea that the increasing concentration of institutional ownership in equity markets makes stock prices more "fragile," i.e., more exposed to liquidity shocks to institutional investors. I argue that institutional stockholders with stricter redemption policies, who are less likely to experience redemption-generated liquidity shocks, should expose stocks to lower levels of price fragility. An analysis of hedge fund characteristics confirms that hedge funds with strict redemption policies exhibit less portfolio turnover, and stocks held by high-restriction funds are less exposed to flow-induced liquidity trading. A hand-collected dataset of institutional block acquisitions reveals comparatively higher cumulative abnormal returns following block acquisitions by hedge funds with tighter redemption restrictions, confirming that the market places a value on strict redemption policies. Finally, a difference-in-differences regression reveals that stocks purchased by institutional blockholders with stricter redemption policies experience a significant decrease in volatility.

Impact of FOMC Cycle on Market Uncertainty: Evidence From Interest Rate Derivatives
Chatterjee, Indradeap,Di Giacinto, Marina,Tebaldi, Claudio
SSRN
This paper investigates how Federal Reserve (Fed) actions influence market uncertainty. We consider two kinds of Fed events: the day of the Federal Open Market Committee (FOMC) meeting -- which includes a policy statement, press conference and release of a Summary of Economic Projections -- and the day the minutes of the FOMC minutes are released -- which is typically set 3 weeks after the meeting. Unlike related papers focused on the issue, we measure market uncertainty by the implied volatility extracted from interest rate options, specifically swaptions. We use 1-month constant maturity volatility for swaptions over tenors ranging from one up to 30 years as they are reflective of how these volatilities are marked by dealers/market-makers and cover only one FOMC meeting/minutes release at a time. We use an event study approach along with extensive graphical analysis to evaluate the impact of Fed actions. The results show that 1-month constant maturity implied volatility increases marginally going into these events and falls much more significantly afterwards. Remarkably, the increase and reduction in uncertainty around a meeting is not reducing with increasing tenors, showing that the impact of information release has a similar impact over all horizons ranging from 1 to 30 years. If, on one side, this evidence witnesses the capacity of the central bank to control the long end of the curve, on the other it indicates the possibility that overreaction to news may generate the puzzling excess volatility which is observed in long term rates.

Introducing a Real Option Framework for EVA/MVA Analysis
Arnold, Tom,Crack, Timothy Falcon,Marshall, Cassandra D.,Schwartz, Adam
SSRN
For the first time, a framework is introduced that allows for a real options analysis to be performed in an EVA/MVA-embedded binomial tree. This framework enhances traditional EVA/MVA analysis so that it can capture the additional value generated through strategic decision making during a project’s life. The EVA calculation is separated into three parts: a variable component, a fixed component in regard to the cash flow, and a fixed component in regard to the cost of capital. A reconciliation of methods shows that the EVA/MVA framework produces the same real option valuation as an equivalent NPV-embedded binomial tree.

Mass Flow Analysis of SARS-CoV-2 for quantified COVID-19 Risk Analysis
Gjalt Huppes,Ruben Huele
arXiv

How may exposure risks to SARS-CoV-2 be assessed quantitatively? The material metabolism approach of Industrial Ecology can be applied to the mass flows of these virions by their numbers, as a key step in the analysis of the current pandemic. Several transmission routes of SARS-2 from emission by a person to exposure of another person have been modelled and quantified. Start is a COVID-19 illness progression model specifying rising emissions by an infected person: the human virion factory. The first route covers closed spaces, with an emission, concentration, and decay model quantifying exposure. A next set of routes covers person-to-person contacts mostly in open spaces, modelling the spatial distribution of exhales towards inhalation. These models also cover incidental exposures, like coughs and sneezes, and exposure through objects. Routes through animal contacts, excrements, and food, have not been quantified. Potential exposures differ by six orders of magnitude. Closed rooms, even with reasonably (VR 2) to good (VR 5) ventilation, constitute the major exposure risks. Close person-to-person contacts of longer duration create two orders of magnitude lower exposure risks. Open spaces may create risks an order of magnitude lower again. Burst of larger droplets may cause a common cold but not viral pneumonia as the virions in such droplets cannot reach the alveoli. Fomites have not shown viable viruses in hospitals, let alone infections. Infection by animals might be possible, as by cats and ferrets kept as pets. These results indicate priority domains for individual and collective measures. The wide divergence in outcomes indicates robustness to most modelling and data improvements, hardly leading to major changes in relative exposure potentials. However, models and data can substantially be improved.



Monetary Policy and Bond Prices with Drifting Equilibrium Rates
Favero, Carlo A.,Melone, Alessandro,Tamoni, Andrea
SSRN
We propose a framework that reconciles drifting monetary policy and bond prices with stationary and predictable bond returns. Bond prices are drifting because they reflect the drift in average expected monetary policy rates over the life of the bonds. In our framework, deviations of bond prices from their drift should be stationary and can originate from term premia or temporary deviations from rational expectations in a behavioral framework. Empirically, modeling the drift in monetary policy rates using demographics and productivity trends, and expected long-term inflation, leads to stationary deviations of bond prices from their drift that predict future bond returns.

Monitoring Institutional Ownership and Corporate Innovation
Miller, Steve,Qiu, Bin,Wang, Bin,Yang, Tina
SSRN
In this study, we examine the role of monitoring institutional investors in firm innovation. Following Fich, Harford and Tran (2015), we define monitoring institutions as those whose holding value in a firm is among the top 10% of holdings in the institution’s portfolio. We document a positive effect of monitoring institutional ownership on firm innovation after controlling for traditional measures of institutional ownership. The positive effect is more pronounced when monitoring institutions are more diversified. We further find that monitoring institutions enhance firm innovation by: (1) increasing failure tolerance and CEO risk-taking incentives, and (2) reducing intense board monitoring, managerial career concerns, and diversion of corporate resources. Overall, the evidence shows that monitoring institutions are instrumental in promoting firm innovation.

Network Effects in Corporate Financial Policies
Grieser, William,Hadlock, Charles J.,LeSage, James P.,Zekhnini, Morad
SSRN
We study the role of peer effects in capital structure decisions by exploiting the heterogeneous and intransitive nature of product market networks combined with spatial econometric techniques that account for these features. In contrast to prior work, this approach allows us to provide economically meaningful estimates of the magnitude of the causal role of peer effects in capital structure decisions. Our estimates indicate an initial sensitivity of a firm's leverage choice to peer average leverage on the order of .20, indicating a substantive but moderate level of strategic complementarity in capital structure decisions. Our modeling allows peer effects to vary by a firm's location in the product market network, with more central firms having relatively larger aggregate effects on their set of network peers. Our evidence appears most likely to reflect strategic behavior. Extensions of our modeling framework to related finance questions are also briefly considered.

On the Theoretical Foundation of Corporate Finance
Chen, Jing
SSRN
Modigliani and Miller theory forms the theoretical foundation of corporate finance. Yet Modigliani and Miller theory was derived from a very special case of cash flows. Weighted Average Cost of Capital (WACC), which is part of the Modigliani and Miller theory, plays a fundamental role in capital structure decision and asset valuation. In practice, asset valuation calculated from cash flows discounted by WACC almost always differs from the sum of debt and equity values. We derive asset valuations for more general cashflows. Only when the debt equity ratio is constant over time, valuation by WACC is equal to the sum of debt and equity values.

Optimal Insurance under Maxmin Expected Utility
Corina Birghila,Tim J. Boonen,Mario Ghossoub
arXiv

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the Maxmin-Expected Utility model of Gilboa and Schmeidler (1989), whereas the insurer is a (risk-averse or risk-neutral) Expected-Utility maximizer. We characterize optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, marginal utility of wealth, belief heterogeneity, as well as ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how the singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Renyi ambiguity set.



Putting Numbers on the Coins: The Pricing and Performance of Initial Coin Offerings
Momtaz, Paul P.
SSRN
This paper examines the performance of cryptocurrencies issued in initial coin offerings (ICOs) over a three-year period after the initial exchange listing. Average (median) ICO underpricing amounts to 15% (3%), even though 4 out of 10 ICOs destroy value on the first trading day. Liquidity, market capitalization, and high-low price ratios predict returns. Long-run buy-and-hold returns are positive for the mean and negative for the median. For holding periods between one and twenty-four months, the median ICO depreciates by 30%. Evidently, there is substantial positive skewness in the cryptocurrency market. Further, a size effect emerges from the data as an empirical regularity: Large ICOs are more often overpriced and underperform in the long run.

Risk Management and Policy Sales in Life Insurance Companies
Giambona, Erasmo,Kumar, Anil
SSRN
We study the effect of risk management on policy sales (life insurance and annuities) of life insurers. For identification, we exploit the staggered adoption of Section 711 of the Insurer Receivership Model Act, granting derivatives counterparties of insurers the right to terminate the contract and claim the collateral in case of default. We find that hedging by highly leveraged insurers (those that could default) increased sharply post Section 711, relative to unaffected companies. Importantly, policy sales and market share also increased for affected companies, and they are associated to lower policy prices and higher financial stability due to more hedging.

Securities Lending and Trading by Active and Passive Funds
Honkanen, Pekka
SSRN
I study the market for lending and borrowing securities in the United States. I find that by making securities available for borrowing, mutual funds acquire information about short selling, which they exploit for trading. Funds with discretion in their investment choices rebalance their portfolios away from borrowed stocks, avoiding capital losses on stocks with decreasing prices. Funds also trade more aggressively on stocks with stronger signals. Finally, active funds charge lower lending fees than passive funds, consistent with funds paying for the information with lower fees.

Shipping Markets in Turmoil: An Analysis of the COVID-19 Outbreak and Its Implications
Michail, Nektarios,Melas, Konstantinos (Kostis)
SSRN
In the current study, we examine, for the first time in the literature, the impact of exogenous effects in the shipping industry by employing data from the recent COVID-19 pandemic outbreak and explore the reactions of freight rates for dry bulk, clean, and dirty tankers. Our results, using both GARCH (1,1) and VAR specifications, suggest that such events are directly affecting the dry bulk and the dirty tanker segments. In addition, the results also suggest that second round effects, mostly via the decline in oil prices and, in some cases, third round effects via the impact from the stock market, also exist. Finally, by employing daily port calls a proxy variable for the demand for transportation services, we show that both the dry bulk and clean tankers are highly affected by the demand side of the economy, while vessels which transport crude oil do not register such a relationship.

Stock-Oil Comovement: Fundamentals or Financialization?
Melone, Alessandro,Randl, Otto,Sögner, Leopold,Zechner, Josef
SSRN
We investigate the sources of time-variation in the stock-oil correlation over the period 1986-2018. We first derive an oil futures return news decomposition following Campbell and Shiller (1988) and Campbell (1991). Then, for both stock and oil, we split unexpected returns into cash-flow news (which can be related to asset fundamentals because of its link to production) and discount-rate news (which can be driven by shocks to investors holding both assets) using a vector autoregressive (VAR) model. We find that about 75% of the time-varying correlation is related to the comovement of cash-flow news between the two assets. This result is robust to different specifications of the VAR model used to decompose returns. We provide supportive evidence that underlying changes in the structure of the real economy, such as the increased oil production in the U.S., are key drivers for the changing stock-oil comovement beyond the financialization of commodity market.

The Dark Side of the Bank Levy
Borsuk, Marcin,Kowalewski, Oskar,Qi, Jianping
SSRN
We examine the consequences of imposing a high tax levy on bank assets. Employing unique supervisory bank-level data, we exploit different channels through which the new tax may impair the stability of the banking sector. We find that following the introduction of the levy, banks increase the cost of loans and decrease their overall availability to the real economy. We also document that changes in banks’ loan portfolios are strongly related to bank-specific profitability and capital adequacy ratios. Furthermore, our evidence supports the view that banks engage in risk-shifting by increasing the risk level of their loan portfolios, attempting to recover from the lower return on equity as the tax reduces their overall profits.

The Economic Value of Equity Implied Volatility Forecasting with Machine Learning
Borochin, Paul,Zhao, Yanhui
SSRN
We evaluate the importance of nonlinear interactions in volatility forecasting by comparing the predictive power of decision tree ensemble models relative to classical ones for normalized at-the-money implied volatility innovations. We measure the economic significance of these predictions in cross-sectional and time series pricing tests of delta-hedged option returns. Classification tree ensembles outperform a multinomial logit classifier by 0.35% to 0.46% monthly abnormal returns in delta-hedged option portfolio sorts on volatility innovation forecast data, while regression tree ensembles outperform OLS and LASSO models by 0.03% to 0.14%. Since the predictive variables are the same across all models, these performance differences likely capture the value of nonlinear interactions in implied volatility forecasts. Our results are robust to look-ahead bias and model over-fitting.

The Term Structure of Default Probabilities
Blümke, Oliver
SSRN
Accounting standards require that financial institutions must measure default risk with respect to the full maturity of a financial instrument. This requires forecasting of future default probabilities. The forecast of future default probabilities concerns two aspects: forecasting macroeconomic scenarios and future average (with respect to the macro-economy) default probabilities. The present paper addresses the modelling of future average default probabilities. Due to the small number of defaults and observations this poses a difficult problem in the corporate area and requires a parsimonious model to deal with the sparse data situation. The degree of difficulty is made greater by the fact that default probabilities change for corporations via different patterns over time, with the pattern being depend on the initial rating grade. For initial investment-grade ratings the risk of a default increases, while for the bottom of the rating scale default probabilities decrease. To model these different patterns the paper proposes to extend the existing discrete-time survival model and to incorporate an additional time- and co-variate-dependent shape parameter into the hazard function. Using data from Standard & Poor's the paper shows that the shape parameter is able to reproduce the different patterns. The proposed model is bench-marked against a model which does not employ a shape parameter and the results show that the shape parameter improves in-sample and out-of-sample prediction.

The application of multivariate classification in evaluating the regional differentiation by population income in Russia
Natalia A. Sadovnikova,Olga A. Zolotareva
arXiv

The article presents the results of multivariate classification of Russian regions by the indicators characterizing the population income and their concentration. The clusterization was performed upon an author approach to selecting the characteristics which determines the academic novelty in the evaluation of regional differentiation by population income and the interconnected characteristics. The performed analysis was aimed at the evaluation of the real scale of disproportions in spatial development of the country territories by the considered characteristics. The clusterization results allowed to formulate the condition of a relatively "strong" position of a group of high-income regions (the changes in the array of regions constituting it is highly unlikely in the foreseeable future). Additionally there has been revealed a group of Russian regions that the population is struggling to live on quite low income. These so-called "poor" regions, within the crisis conditions caused by Covid-19 are in need of additional public support, without which their population will impoverish.



Who Supplies PPP Loans (And Does It Matter)? Banks, Relationships and the COVID Crisis
Li, Lei,Strahan, Philip E.
SSRN
We analyze bank supply of credit under the Paycheck Protection Program (PPP). The literature emphasizes relationships as a mean to improve lender information, which helps bank manage credit risk. Despite imposing no risk, however, PPP supply reflects traditional measures of relationship lending: decreasing in bank size; increasing in prior experience, in commitment lending, and in core deposits. Our results suggest a new benefit of bank relationships, as they help firms access government-subsidized lending. We then show that bank PPP supply, based on the size and structure of the local banking sector, alleviates increasing unemployment, although the economic magnitude is small.