# Research articles for the 2020-01-01

An Agnostic and Practically Useful Estimator of the Stochastic Discount Factor

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We propose an estimator for the stochastic discount factor (SDF) that does not require macroeconomic proxies or preference assumptions. It depends only on observed asset returns, yet is immune to the form of the multivariate return distribution, including the distributionâ€™s factor structure. Using US equity data, our estimator satisfies the Hansen/Jagannathan bounds.

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We propose an estimator for the stochastic discount factor (SDF) that does not require macroeconomic proxies or preference assumptions. It depends only on observed asset returns, yet is immune to the form of the multivariate return distribution, including the distributionâ€™s factor structure. Using US equity data, our estimator satisfies the Hansen/Jagannathan bounds.

An Axiomatic Approach to Credit Rating

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We propose an axiomatic framework for rating financial securities based on an axiom of self-consistency, which does not allow issuers to gain, by tranching financial securities, from investors who rely on the rating criterion. While the expected loss criterion used by Moody's satisfies the self-consistency axiom, the probability of default criterion used by S\&P does not. We find empirical evidences in the post-Dodd-Frank period (i.e., after July 2010) that the issuers may take advantage of the absence of self-consistency. We further propose an axiom of scenario-relevance which reflects practical evaluation procedures of potential losses from defaultable securities. Our main theoretical results show that a self-consistent rating measure admits a Choquet integral representation, and this representation becomes analytically tractable if one further takes economic scenarios into account. We also suggest new examples of self-consistent and scenario-based rating criteria, such as ones based on the VaR and the Expected Shortfall.

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We propose an axiomatic framework for rating financial securities based on an axiom of self-consistency, which does not allow issuers to gain, by tranching financial securities, from investors who rely on the rating criterion. While the expected loss criterion used by Moody's satisfies the self-consistency axiom, the probability of default criterion used by S\&P does not. We find empirical evidences in the post-Dodd-Frank period (i.e., after July 2010) that the issuers may take advantage of the absence of self-consistency. We further propose an axiom of scenario-relevance which reflects practical evaluation procedures of potential losses from defaultable securities. Our main theoretical results show that a self-consistent rating measure admits a Choquet integral representation, and this representation becomes analytically tractable if one further takes economic scenarios into account. We also suggest new examples of self-consistent and scenario-based rating criteria, such as ones based on the VaR and the Expected Shortfall.

Bank Herding and Systemic Risk

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This paper studies the relation between bank herding and financial system stability. I develop a set of bank-specific, time-varying measures of herding in asset, liability, and off-balance sheet (OBS) portfolios and empirically examine the relation between bank herding and systemic risk contribution. I find that for large banks, asset herding is associated with lower, liability herding is associated with higher, and OBS herding does not have a significant relation with systemic risk contribution. During crises, the relation of asset herding is stronger, the relation of liability herding is weaker, and the relation of OBS herding remains insignificant. I find that the â€œtoo-many-to-failâ€ effect contributes to the negative relation between bank herding and systemic risk contribution.

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This paper studies the relation between bank herding and financial system stability. I develop a set of bank-specific, time-varying measures of herding in asset, liability, and off-balance sheet (OBS) portfolios and empirically examine the relation between bank herding and systemic risk contribution. I find that for large banks, asset herding is associated with lower, liability herding is associated with higher, and OBS herding does not have a significant relation with systemic risk contribution. During crises, the relation of asset herding is stronger, the relation of liability herding is weaker, and the relation of OBS herding remains insignificant. I find that the â€œtoo-many-to-failâ€ effect contributes to the negative relation between bank herding and systemic risk contribution.

Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method

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This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method less errors are accumulated, and as a result of this the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

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This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method less errors are accumulated, and as a result of this the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

Design of Investment Options using Utility Functions: A Demonstration for â€˜MyRetirementâ€™ Products

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Utility functions can assist in designing a menu of investment options by encoding the objectives and preferences for various investor types with the aim of developing suitably tailored products. This paper demonstrates the process through the construction of an illustrative menu of Australian MyRetirement products. The demonstration shows how utility-based analysis can be combined with more traditional metrics to compare strategies and convey their implications; and provides direction on how product options might be presented to a retiring member. Central to the process is characterizing investor types by selected attributes. This both facilitates specifying utility functions for use in product development, and supports communication based around the type of investor for which a product is designed along with its key features and the outcomes it may deliver. Utility functions thus provide the mechanics that drive the analysis, without becoming an explicit component of investor engagement.

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Utility functions can assist in designing a menu of investment options by encoding the objectives and preferences for various investor types with the aim of developing suitably tailored products. This paper demonstrates the process through the construction of an illustrative menu of Australian MyRetirement products. The demonstration shows how utility-based analysis can be combined with more traditional metrics to compare strategies and convey their implications; and provides direction on how product options might be presented to a retiring member. Central to the process is characterizing investor types by selected attributes. This both facilitates specifying utility functions for use in product development, and supports communication based around the type of investor for which a product is designed along with its key features and the outcomes it may deliver. Utility functions thus provide the mechanics that drive the analysis, without becoming an explicit component of investor engagement.

Does Chief Investment Officer Pay Reflect Performance? Evidence from Non-profits

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This paper provides the first study of compensation and pay-for-performance for top executives at non-profit endowments. Using a detailed breakdown of compensation from IRS filings over the 2009-2017 period, we find that pay packages of Chief Investment Officers (CIOs) depend more heavily on bonuses than do those for other non-profit executives. As in the for-profit sector, compensation is highly correlated with the size of an organization. Even controlling for size, CIO compensation is significantly positively related to endowment performance. Both compensation levels and the sensitivity of pay to performance vary with a foundation's financial model, its location and governance policies.

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This paper provides the first study of compensation and pay-for-performance for top executives at non-profit endowments. Using a detailed breakdown of compensation from IRS filings over the 2009-2017 period, we find that pay packages of Chief Investment Officers (CIOs) depend more heavily on bonuses than do those for other non-profit executives. As in the for-profit sector, compensation is highly correlated with the size of an organization. Even controlling for size, CIO compensation is significantly positively related to endowment performance. Both compensation levels and the sensitivity of pay to performance vary with a foundation's financial model, its location and governance policies.

Drift Begone! Release Policies and Preannouncement Informed Trading

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In 2017 the UK Statistics Authority discontinued the early access of government officials to market-sensitive macroeconomic data. We examine the effect of this policy change on price adjustment in the foreign exchange futures market around major U.K. macroeconomic announcements. Three macroeconomic announcements (consumer price index, industrial production, and retail sales) show strong evidence of informed trading before their public releases until 2017. This preannouncement price drift weakens with the end of the prerelease access. Analogously, the market reaction to the announcements at the official release time has become stronger.

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In 2017 the UK Statistics Authority discontinued the early access of government officials to market-sensitive macroeconomic data. We examine the effect of this policy change on price adjustment in the foreign exchange futures market around major U.K. macroeconomic announcements. Three macroeconomic announcements (consumer price index, industrial production, and retail sales) show strong evidence of informed trading before their public releases until 2017. This preannouncement price drift weakens with the end of the prerelease access. Analogously, the market reaction to the announcements at the official release time has become stronger.

Economic Policy Uncertainty and Cross-Border Lending

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During times of high economic policy uncertainty, domestic banks increase cross- border lending in the international syndicated loan market; credit migrates disproportionately to countries experiencing lower uncertainty. We control for credit demand by including time-varying borrower country fixed effects in our regressions. The migration effects are strongest for well-capitalized banks and banks with diverse income, and when banks face fiercer competition in the domestic banking sector. Additionally, using elections as a source of plausibly exogenous variation which positively affects political uncertainty, we provide causal evidence on the effect of political uncertainty on cross-border lending.

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During times of high economic policy uncertainty, domestic banks increase cross- border lending in the international syndicated loan market; credit migrates disproportionately to countries experiencing lower uncertainty. We control for credit demand by including time-varying borrower country fixed effects in our regressions. The migration effects are strongest for well-capitalized banks and banks with diverse income, and when banks face fiercer competition in the domestic banking sector. Additionally, using elections as a source of plausibly exogenous variation which positively affects political uncertainty, we provide causal evidence on the effect of political uncertainty on cross-border lending.

Economic Policy Uncertainty and Self-Control: Evidence from Unhealthy Choices

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We hypothesize that greater economic policy uncertainty (EPU) leads to increases in unhealthy behaviors by lowering individualsâ€™ impulse control. Based on 6.1 million interviews over 22 years, our analysis reveals a positive relation between EPU and the propensity to make poor lifestyle choices including higher rates of alcohol consumption, a larger number of drinks consumed, and greater binge drinking. EPU has long-lasting effects on drinking behavior, consistent with habit formation. Moreover the relation is stronger for younger individuals whose habits are more malleable. We find similar results when using smoking rates to measure unhealthy choices.

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We hypothesize that greater economic policy uncertainty (EPU) leads to increases in unhealthy behaviors by lowering individualsâ€™ impulse control. Based on 6.1 million interviews over 22 years, our analysis reveals a positive relation between EPU and the propensity to make poor lifestyle choices including higher rates of alcohol consumption, a larger number of drinks consumed, and greater binge drinking. EPU has long-lasting effects on drinking behavior, consistent with habit formation. Moreover the relation is stronger for younger individuals whose habits are more malleable. We find similar results when using smoking rates to measure unhealthy choices.

Financial Volatility and Economic Growth

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We investigate the impact of financial volatility on economic growth, using a panel spanning 150 years and 74 countries. A positive shock to volatility and persistent high volatility lead to a short-term decrease in growth. Persistent low volatility affects growth differently: Initially leading to higher growth, but with a reversal two years hence, consistent with theories of how continued low risk environment induces higher risk-taking. The impact is stronger when volatility is low globally, during the post Bretton Woods era, and for countries experiencing high credit growth. Furthermore, long-lasting global volatility has a significant impact on capital flows, investment, and lending quality.

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We investigate the impact of financial volatility on economic growth, using a panel spanning 150 years and 74 countries. A positive shock to volatility and persistent high volatility lead to a short-term decrease in growth. Persistent low volatility affects growth differently: Initially leading to higher growth, but with a reversal two years hence, consistent with theories of how continued low risk environment induces higher risk-taking. The impact is stronger when volatility is low globally, during the post Bretton Woods era, and for countries experiencing high credit growth. Furthermore, long-lasting global volatility has a significant impact on capital flows, investment, and lending quality.

How to Measure the Liquidity of Cryptocurrencies?

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We use data from cryptocurrency markets to analyze the accuracy of liquidity measures that are calculated from transactions data. We use benchmark measures calculated from high-frequency order book data to evaluate the performance of the transactions-based measures along three dimensions, the time-series correlation with the benchmark measures, the root mean squared and mean absolute error, and the liquidity ranking across three exchanges. The Abdi & Ranaldo (2017) estimator best captures the time series variation in liquidity. It also performs well in the cross-sectional dimension. When it comes to estimating the level of the benchmark measures the Kyle & Obizhaeva (2016) estimator and the Amihud (2002) illiquidity ratio perform best.

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We use data from cryptocurrency markets to analyze the accuracy of liquidity measures that are calculated from transactions data. We use benchmark measures calculated from high-frequency order book data to evaluate the performance of the transactions-based measures along three dimensions, the time-series correlation with the benchmark measures, the root mean squared and mean absolute error, and the liquidity ranking across three exchanges. The Abdi & Ranaldo (2017) estimator best captures the time series variation in liquidity. It also performs well in the cross-sectional dimension. When it comes to estimating the level of the benchmark measures the Kyle & Obizhaeva (2016) estimator and the Amihud (2002) illiquidity ratio perform best.

IPO Underpricing and Underwriting Spreads: Evidence for Dichotomy of Formation

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The formal theoretical model in this study explicitly establishes the following results. Suppose the distribution of IPO quality either is time invariant, or equivalently, that distributions for IPO underpricing and underwriting spreads are explicitly conditioned on realizations of IPO quality. Within this context, cross-sectional relations that subsist between IPO underpricing and underwriting spreads, which are shown to be negative, predominate. Suppose, on the contrary, that the distribution of IPO quality is time varying. In this context, time series relations between IPO underpricing and underwriting spreads, which are shown to be positive, tend to predominate. If time series relations exactly counterbalance cross-sectional relations, relations between IPO underpricing and underwriting spreads turn out statistically insignificant. Combined, study findings show the distribution of IPO underwriting spreads and underpricing cannot be induced by exactly the same economic agents. Given the distribution of underwriting spreads is shown, in context of a non-cooperative game theoretic rational expectations equilibrium, to be induced by underwriters, by default, the distribution of underpricing is predicted to be induced by investors. This prediction implies models of IPO underpricing within which equilibriums for underpricing are determined by underwriters cannot be deemed to be robust.

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The formal theoretical model in this study explicitly establishes the following results. Suppose the distribution of IPO quality either is time invariant, or equivalently, that distributions for IPO underpricing and underwriting spreads are explicitly conditioned on realizations of IPO quality. Within this context, cross-sectional relations that subsist between IPO underpricing and underwriting spreads, which are shown to be negative, predominate. Suppose, on the contrary, that the distribution of IPO quality is time varying. In this context, time series relations between IPO underpricing and underwriting spreads, which are shown to be positive, tend to predominate. If time series relations exactly counterbalance cross-sectional relations, relations between IPO underpricing and underwriting spreads turn out statistically insignificant. Combined, study findings show the distribution of IPO underwriting spreads and underpricing cannot be induced by exactly the same economic agents. Given the distribution of underwriting spreads is shown, in context of a non-cooperative game theoretic rational expectations equilibrium, to be induced by underwriters, by default, the distribution of underpricing is predicted to be induced by investors. This prediction implies models of IPO underpricing within which equilibriums for underpricing are determined by underwriters cannot be deemed to be robust.

Information Spillover through Private Lender Reports

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This paper examines private information spillover from the lending market to markets for public securities. We find that information from private monthly reports to institutional lenders gradually spills over to the public equity market. We observe positive abnormal stock returns after firms provide favorable private reports. After unfavorable private reports, we find negative abnormal returns, as well as increased short interest. This private information leakage is striking and previously undocumented. We demonstrate how traders benefit from private information, as we show that they do not trade immediately upon receiving the private information. Instead, they time their trades to manage both the price impact and the risk of additional information arrival before the scheduled public release of their private information.

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This paper examines private information spillover from the lending market to markets for public securities. We find that information from private monthly reports to institutional lenders gradually spills over to the public equity market. We observe positive abnormal stock returns after firms provide favorable private reports. After unfavorable private reports, we find negative abnormal returns, as well as increased short interest. This private information leakage is striking and previously undocumented. We demonstrate how traders benefit from private information, as we show that they do not trade immediately upon receiving the private information. Instead, they time their trades to manage both the price impact and the risk of additional information arrival before the scheduled public release of their private information.

Informed Bank Debt and Stock Returns

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We document that private debt contains value-relevant nonpublic information with significant economic value. Abnormal loan spreads significantly predict firms' future operating performance and uncertainty measures. Equity analysts and investors are not privy to banks' private information. Firms with higher abnormal loan spreads experience more negative earnings surprises over the next several quarters. Their stocks underperform on average by about 0.5% per month with no reversals in longer horizons. This result is concentrated among loans associated with better borrower-lender relationship, indicating that relationship banking facilitates valuable information acquisition. The abnormal loan spreads also negatively predict stock returns of borrowers' peer firms.

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We document that private debt contains value-relevant nonpublic information with significant economic value. Abnormal loan spreads significantly predict firms' future operating performance and uncertainty measures. Equity analysts and investors are not privy to banks' private information. Firms with higher abnormal loan spreads experience more negative earnings surprises over the next several quarters. Their stocks underperform on average by about 0.5% per month with no reversals in longer horizons. This result is concentrated among loans associated with better borrower-lender relationship, indicating that relationship banking facilitates valuable information acquisition. The abnormal loan spreads also negatively predict stock returns of borrowers' peer firms.

Integrating Time Series and Cross-Sectional Signals for Optimal Commodity Portfolios

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We study the optimal combination of different commodity signals in a dynamic portfolio theoretic framework. Following Brandt et al. (2006, 2009) we parameterize the portfolio weights of a risk-averse mean-variance investor to integrate information from time series predictors and cross-sectional characteristics of commodity assets. We show that the long end of the futures curve as well as open interest have significant timing power, whereas the short end of the futures curve and past returns are relevant characteristics for tilting commodities. Combining timing and tilting strategies outperforms all factor benchmarks out-of-sample and after transaction costs. Moreover, the optimal commodity allocation is not priced by common risk factors, such as commodity carry or momentum.

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We study the optimal combination of different commodity signals in a dynamic portfolio theoretic framework. Following Brandt et al. (2006, 2009) we parameterize the portfolio weights of a risk-averse mean-variance investor to integrate information from time series predictors and cross-sectional characteristics of commodity assets. We show that the long end of the futures curve as well as open interest have significant timing power, whereas the short end of the futures curve and past returns are relevant characteristics for tilting commodities. Combining timing and tilting strategies outperforms all factor benchmarks out-of-sample and after transaction costs. Moreover, the optimal commodity allocation is not priced by common risk factors, such as commodity carry or momentum.

Inversion of Convex Ordering in the VIX Market

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We investigate conditions for the existence of a continuous model on the S&P 500 index (SPX) that jointly calibrates to a full surface of SPX implied volatilities and to the VIX smiles. We present a novel approach based on the SPX smile calibration condition (the fact that the conditional expectation of the instantaneous variance given the spot equals the market local variance). In the limiting case of instantaneous VIX, a novel application of martingale transport to finance shows that such model exists if and only if, for each time t, the local variance is smaller than the instantaneous variance in convex order. The real case of a 30 day VIX is more involved, as averaging over 30 days and projecting onto a filtration can undo convex ordering.We show that in usual market conditions, and for reasonable smile extrapolations, the distribution of the VIX squared in the market local volatility model is larger than the market-implied distribution of the VIX squared in convex order for short maturities T, and that the two distributions are not rankable in convex order for intermediate maturities. In particular, a necessary condition for continuous models to jointly calibrate to the SPX and VIX markets is the inversion of convex ordering property: the fact that, even though associated local variances are smaller than instantaneous variances in convex order, the VIX squared is larger in convex order in the associated local volatility model than in the original model for short maturities. We argue and numerically demonstrate that, when the (typically negative) spot-vol correlation is large enough in absolute value, (a) traditional stochastic volatility models with large mean reversion, and (b) rough volatility models with small Hurst exponent, satisfy the inversion of convex ordering property, and more generally can reproduce the market term-structure of convex ordering of the local and stochastic squared VIX.

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We investigate conditions for the existence of a continuous model on the S&P 500 index (SPX) that jointly calibrates to a full surface of SPX implied volatilities and to the VIX smiles. We present a novel approach based on the SPX smile calibration condition (the fact that the conditional expectation of the instantaneous variance given the spot equals the market local variance). In the limiting case of instantaneous VIX, a novel application of martingale transport to finance shows that such model exists if and only if, for each time t, the local variance is smaller than the instantaneous variance in convex order. The real case of a 30 day VIX is more involved, as averaging over 30 days and projecting onto a filtration can undo convex ordering.We show that in usual market conditions, and for reasonable smile extrapolations, the distribution of the VIX squared in the market local volatility model is larger than the market-implied distribution of the VIX squared in convex order for short maturities T, and that the two distributions are not rankable in convex order for intermediate maturities. In particular, a necessary condition for continuous models to jointly calibrate to the SPX and VIX markets is the inversion of convex ordering property: the fact that, even though associated local variances are smaller than instantaneous variances in convex order, the VIX squared is larger in convex order in the associated local volatility model than in the original model for short maturities. We argue and numerically demonstrate that, when the (typically negative) spot-vol correlation is large enough in absolute value, (a) traditional stochastic volatility models with large mean reversion, and (b) rough volatility models with small Hurst exponent, satisfy the inversion of convex ordering property, and more generally can reproduce the market term-structure of convex ordering of the local and stochastic squared VIX.

Jump-Only Momentum and Reversal in Currency Markets

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This paper investigates the momentum and reversal signals in exchange rate jumps in currency markets. Following exchange rate jumps, currencies from emerging markets appreciate, but currencies from developed economies depreciate. Stepwise multiple testing confirms non-jump exchange rate changes signal neither momentum nor reversal. I construct strategies based on exchange rate jumps only, which perform better than pure momentum or reversal strategies with Sharpe ratios exceeding one. Returns of such strategies are robust out-of-sample and after transaction costs. A panel regression of aggregated jump sizes on macroeconomic factors suggests that exchange rate jumps in emerging markets are related to the country's GDP, while those in developed countries are explained by trade with the US.

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This paper investigates the momentum and reversal signals in exchange rate jumps in currency markets. Following exchange rate jumps, currencies from emerging markets appreciate, but currencies from developed economies depreciate. Stepwise multiple testing confirms non-jump exchange rate changes signal neither momentum nor reversal. I construct strategies based on exchange rate jumps only, which perform better than pure momentum or reversal strategies with Sharpe ratios exceeding one. Returns of such strategies are robust out-of-sample and after transaction costs. A panel regression of aggregated jump sizes on macroeconomic factors suggests that exchange rate jumps in emerging markets are related to the country's GDP, while those in developed countries are explained by trade with the US.

Keeping Them Honest: The Long-term Effects of Protestant Missionaries on Honesty and Corporate Tax Avoidance in Modern China

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Can Protestantism make people more honest? If yes, what does this mean for corporate behaviors and economic performance? Marshalling large and unique datasets on the 1920 Protestant diffusion in China, and the financial reports of about 125,000 Chinese industrial firms from 1999 to 2007, we find significant effects of historical Protestant activities on current corporate tax avoidance. We use disaster frequency as the instrumental variable to establish causality. Using data from the China Family Panel Studies and a peer-to-peer lending dataset containing the credit scores of over one million Chinese borrowers, we further find that individual honesty is the key social capital fostered by Protestantism in reducing tax avoidance. Our empirical results show that people from cities with more intense Protestant activities historically tend to have higher credit scores and trust others more. Our analyses suggest that religion may play a significant role in shaping individual and corporate behaviors, and that such effects tend to persist.

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Can Protestantism make people more honest? If yes, what does this mean for corporate behaviors and economic performance? Marshalling large and unique datasets on the 1920 Protestant diffusion in China, and the financial reports of about 125,000 Chinese industrial firms from 1999 to 2007, we find significant effects of historical Protestant activities on current corporate tax avoidance. We use disaster frequency as the instrumental variable to establish causality. Using data from the China Family Panel Studies and a peer-to-peer lending dataset containing the credit scores of over one million Chinese borrowers, we further find that individual honesty is the key social capital fostered by Protestantism in reducing tax avoidance. Our empirical results show that people from cities with more intense Protestant activities historically tend to have higher credit scores and trust others more. Our analyses suggest that religion may play a significant role in shaping individual and corporate behaviors, and that such effects tend to persist.

Managerial Protections, Capital Structure, and Investment: Theory and Evidence

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We introduce a model to illustrate three channels by which managerial protections affect how managers choose a firmâ€™s capital structure and level of investment. First, protections can intensify the incentive for managers to increase their equity share, resulting in excessive debt financing. Second, protections reinforce the incentive for managers to avoid liquidation, leading to reduced investment. Third, an important policy implication of the model is that policies that constrain firm debt ratios, such as stress testing for bank holding companies, can counterintuitively stimulate investment for firms with protections. We find that these results are consistent with patterns in the data.

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We introduce a model to illustrate three channels by which managerial protections affect how managers choose a firmâ€™s capital structure and level of investment. First, protections can intensify the incentive for managers to increase their equity share, resulting in excessive debt financing. Second, protections reinforce the incentive for managers to avoid liquidation, leading to reduced investment. Third, an important policy implication of the model is that policies that constrain firm debt ratios, such as stress testing for bank holding companies, can counterintuitively stimulate investment for firms with protections. We find that these results are consistent with patterns in the data.

Mind the Gap: Inequality and Diversification

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Understanding the origins of wealth inequality is critical in the debate over what, if anything, to do about it. In this note, we propose a simple model which is still rich enough to reproduce observed patterns of wealth inequality. We call it the Concentrated Asset Betting (CAB) model. A key element of CAB is a phenomenon known in the gambling world as â€œover-betting the edge.â€ The model we propose is based on the observation that a high fraction of investors have experienced sub-par growth in their savings, after allowing for consumption and philanthropy, relative to the tremendous long-term growth in the public stock market. Some of the reasons put forward to explain the shortfall in investor returns include investment fees, commissions and taxes. Our model suggests there may be something even larger and more insidious at work â€" pervasive and systematically poor money management.

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Understanding the origins of wealth inequality is critical in the debate over what, if anything, to do about it. In this note, we propose a simple model which is still rich enough to reproduce observed patterns of wealth inequality. We call it the Concentrated Asset Betting (CAB) model. A key element of CAB is a phenomenon known in the gambling world as â€œover-betting the edge.â€ The model we propose is based on the observation that a high fraction of investors have experienced sub-par growth in their savings, after allowing for consumption and philanthropy, relative to the tremendous long-term growth in the public stock market. Some of the reasons put forward to explain the shortfall in investor returns include investment fees, commissions and taxes. Our model suggests there may be something even larger and more insidious at work â€" pervasive and systematically poor money management.

Mortgage Choice and Expenditure Over the Lifecycle: Evidence From Expiring Interest-Only Loans

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We study how homeownersâ€™ consumption responds to a negative and anticipated disposable income shock: the beginning of the amortisation period on interest-only mortgages. We identify spending behavior through an event study approach, by matching loan-level data that covers the universe of Danish mortgages to detailed administrative registries on borrowers. In response to an average increase in installments worth 9 percent of income, consumption drops by 3 percent of income, in the year when amortisation begins. The reduction in expenditure is persistent. Borrowers who fail to smooth consumption are highly leveraged, hand-to-mouth consumers, likely to be unable to obtain a new interest-only loan.

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We study how homeownersâ€™ consumption responds to a negative and anticipated disposable income shock: the beginning of the amortisation period on interest-only mortgages. We identify spending behavior through an event study approach, by matching loan-level data that covers the universe of Danish mortgages to detailed administrative registries on borrowers. In response to an average increase in installments worth 9 percent of income, consumption drops by 3 percent of income, in the year when amortisation begins. The reduction in expenditure is persistent. Borrowers who fail to smooth consumption are highly leveraged, hand-to-mouth consumers, likely to be unable to obtain a new interest-only loan.

Myopic Management Theory and R&D Investment Decisions

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This study attempts to asses firmsâ€™ financial conditions to explain why they use myopic R&D cuts. Contrary to prior literature, this study shows that the current financial indicators of firms are also significant determinants of R&D myopic management along with stock market. Financial indicators such as Leverage, cash holding, earned-to-capital ratio, market-to-book ratio, sales growth, dividend, tangibility, age, and size of firms significantly influence the probability of being myopic firms and R&D investment decisions. Further, we show that U-shaped and inverted U-shaped relationship of different determinants of R&D investments provide a better description for mix results of prior literature.

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This study attempts to asses firmsâ€™ financial conditions to explain why they use myopic R&D cuts. Contrary to prior literature, this study shows that the current financial indicators of firms are also significant determinants of R&D myopic management along with stock market. Financial indicators such as Leverage, cash holding, earned-to-capital ratio, market-to-book ratio, sales growth, dividend, tangibility, age, and size of firms significantly influence the probability of being myopic firms and R&D investment decisions. Further, we show that U-shaped and inverted U-shaped relationship of different determinants of R&D investments provide a better description for mix results of prior literature.

Negative Interest Rates and the Perpetuity Paradox

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With 30% of the world's investment grade sovereign bonds trading at sub-zero yields, there is a growing acceptance that negative interest rates are the 'new normal.' Even very low probabilities of sustained negative interest rates in the future leads to incredibly high Expected Values for ultra-long-term bonds. In this paper, we'll explain and offer one solution to what we call the 'Perpetuity Paradox', which provides an extreme example of the care that's needed in deciding how much to invest in an attractive opportunity.

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With 30% of the world's investment grade sovereign bonds trading at sub-zero yields, there is a growing acceptance that negative interest rates are the 'new normal.' Even very low probabilities of sustained negative interest rates in the future leads to incredibly high Expected Values for ultra-long-term bonds. In this paper, we'll explain and offer one solution to what we call the 'Perpetuity Paradox', which provides an extreme example of the care that's needed in deciding how much to invest in an attractive opportunity.

Objectives and Challenges for Stress Testing

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Stress testing proved to be an effective crisis fighting tool in the Great Financial Crisis and has since become widely used by regulators and financial institutions to test resilience to financial and economic shocks. This served two objectives: (1) to identify and remediate banks with a capital shortfall, and (2) to restore confidence in the core of the banking system by requiring that banks eliminate any regulatory capital shortfall promptly either by raising capital in private markets or, if unable, from a government backstop fund. The objectives of a stress test will determine six fundamental choices in structuring the exercise: (1) the design of stress scenarios; (2) the risk exposures to be stressed; (3) the range of institutions to be tested, the length of the scenario and the intervals over which shocks are measured; (4) the development of models to map shocks into outcomes and impact on individual bank financials and on the banking system; (5) the choice of criteria to determine whether banks pass or fail the stress test; (6) the decision about what to disclose to the public. But stress tests are no panacea. We discuss a range of challenges to improving the effectiveness of stress tests, such as incorporating nonfinancial risks like cyber, taking into account second-round effects of shocks, broadening the scope beyond just banks, and resisting a tendency to disaster myopia as memories of the financial crisis recede into the past.

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Stress testing proved to be an effective crisis fighting tool in the Great Financial Crisis and has since become widely used by regulators and financial institutions to test resilience to financial and economic shocks. This served two objectives: (1) to identify and remediate banks with a capital shortfall, and (2) to restore confidence in the core of the banking system by requiring that banks eliminate any regulatory capital shortfall promptly either by raising capital in private markets or, if unable, from a government backstop fund. The objectives of a stress test will determine six fundamental choices in structuring the exercise: (1) the design of stress scenarios; (2) the risk exposures to be stressed; (3) the range of institutions to be tested, the length of the scenario and the intervals over which shocks are measured; (4) the development of models to map shocks into outcomes and impact on individual bank financials and on the banking system; (5) the choice of criteria to determine whether banks pass or fail the stress test; (6) the decision about what to disclose to the public. But stress tests are no panacea. We discuss a range of challenges to improving the effectiveness of stress tests, such as incorporating nonfinancial risks like cyber, taking into account second-round effects of shocks, broadening the scope beyond just banks, and resisting a tendency to disaster myopia as memories of the financial crisis recede into the past.

On the Fast Track: Information Acquisition Costs and Information Production

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Using the introduction of high-speed rail as exogenous shocks to costs of information acquisition, we show that reductions in information-acquisition costs lead to a significant increase in information production and improvement in output quality, evidenced by higher frequency of analysts visiting portfolio firms, and higher forecast accuracy. We further find that information production represents the channel through which acquisition costs affect output quality. We corroborate these findings using a large-scale survey of financial analysts. More information production is also associated with improved price efficiency. Finally, both the empirical and survey results highlight the importance of soft information in analystsâ€™ information production.

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Using the introduction of high-speed rail as exogenous shocks to costs of information acquisition, we show that reductions in information-acquisition costs lead to a significant increase in information production and improvement in output quality, evidenced by higher frequency of analysts visiting portfolio firms, and higher forecast accuracy. We further find that information production represents the channel through which acquisition costs affect output quality. We corroborate these findings using a large-scale survey of financial analysts. More information production is also associated with improved price efficiency. Finally, both the empirical and survey results highlight the importance of soft information in analystsâ€™ information production.

On the Optimal Transparency in the Financial System

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Bouvard, Chaigneau, and Motta (2015) (hereafter, BCM) show that a regulator (he) optimally increases transparency of the financial system when fundamentals deteriorate, but his limited commitment power may lead to excess opacity and increases the likelihood of systemic runs. Their results crucially depend on the specific form of the signal observed by investors. I consider two different but commonly-used information technologies, then show that the optimal disclosure policy may not be monotonic in the strength of the economy, and either the regulator can implement an ex-ante optimal policy or lack of commitment power indeed leads to excess transparency.

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Bouvard, Chaigneau, and Motta (2015) (hereafter, BCM) show that a regulator (he) optimally increases transparency of the financial system when fundamentals deteriorate, but his limited commitment power may lead to excess opacity and increases the likelihood of systemic runs. Their results crucially depend on the specific form of the signal observed by investors. I consider two different but commonly-used information technologies, then show that the optimal disclosure policy may not be monotonic in the strength of the economy, and either the regulator can implement an ex-ante optimal policy or lack of commitment power indeed leads to excess transparency.

On the Origins of the Market for Corporate Law

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I study the origins of the market for corporate charters and the emergence of Delaware as the leader of this market. Specifically, I assemble new data on 19th and 20th-century corporations to evaluate two widely-held beliefs: (1) the U.S. Supreme Court is responsible for enabling a national market for corporate charters in the 19th century and (2) Delaware became the leader in this market only because New Jersey (the initial leader) repealed its extremely liberal corporate laws in 1913. I argue that both claims are false: The Supreme Court always opposed a national market for corporate charters, and New Jerseyâ€™s decline began a decade before its 1913 repeal. It is more likely that the market for corporate charters emerged as a collateral consequence of interstate commerce and that New Jersey declined because Delaware and other states simply copied its laws.

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I study the origins of the market for corporate charters and the emergence of Delaware as the leader of this market. Specifically, I assemble new data on 19th and 20th-century corporations to evaluate two widely-held beliefs: (1) the U.S. Supreme Court is responsible for enabling a national market for corporate charters in the 19th century and (2) Delaware became the leader in this market only because New Jersey (the initial leader) repealed its extremely liberal corporate laws in 1913. I argue that both claims are false: The Supreme Court always opposed a national market for corporate charters, and New Jerseyâ€™s decline began a decade before its 1913 repeal. It is more likely that the market for corporate charters emerged as a collateral consequence of interstate commerce and that New Jersey declined because Delaware and other states simply copied its laws.

Optimal Value-at-Risk Disclosure

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Abstract In 1995, the Basel Accords introduced an alternative method to compute the market risk charge through the use of a risk model developed internally by the financial institution. These internal models, based on the Value-at-Risk (VaR), follow certain rules that are defined under the Basel Accords. From this moment on, risk analysts and financial academics focused their attentions on how to accurately estimate the VaR in order to reduce the regulatory capital. However, considering the market risk framework defined in the Basel Accords, the best strategy to optimize the regulatory capital may not lie in truthfully disclosing an accurate VaR estimation. In this study, we propose to solve, through dynamic programming, for the optimal policy function for disclosing the reported VaR based on the estimated value that minimizes the daily capital charge. This policy function will provide the optimal percentage of the estimated 1-day VaR that should be disclosed, taking into account the impact that this disclosure decision will have in future capital charges, by managing the rules defined in the Basel Accords. Our goal is to prove that truthful disclosure of an accurately estimated VaR is suboptimal. The main results from our investigation show that using the optimal reporting strategy leads to an average daily reduction in the capital requirements of 4.32% in a simulated environment, compared with a normal strategy of always truthfully disclosing the estimated 1-day VaR, and leads to an average daily saving of 7.22% when applied to our S&P500 test portfolio.

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Abstract In 1995, the Basel Accords introduced an alternative method to compute the market risk charge through the use of a risk model developed internally by the financial institution. These internal models, based on the Value-at-Risk (VaR), follow certain rules that are defined under the Basel Accords. From this moment on, risk analysts and financial academics focused their attentions on how to accurately estimate the VaR in order to reduce the regulatory capital. However, considering the market risk framework defined in the Basel Accords, the best strategy to optimize the regulatory capital may not lie in truthfully disclosing an accurate VaR estimation. In this study, we propose to solve, through dynamic programming, for the optimal policy function for disclosing the reported VaR based on the estimated value that minimizes the daily capital charge. This policy function will provide the optimal percentage of the estimated 1-day VaR that should be disclosed, taking into account the impact that this disclosure decision will have in future capital charges, by managing the rules defined in the Basel Accords. Our goal is to prove that truthful disclosure of an accurately estimated VaR is suboptimal. The main results from our investigation show that using the optimal reporting strategy leads to an average daily reduction in the capital requirements of 4.32% in a simulated environment, compared with a normal strategy of always truthfully disclosing the estimated 1-day VaR, and leads to an average daily saving of 7.22% when applied to our S&P500 test portfolio.

Risk Management Practices of Central Counterparties: European vs. Third-Country CCPs

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Relying on recent CPMI-IOSCO public quantitative disclosure (PQD) data provided by 35 central counterparties (CCPs) over the 2015-2018 period, this paper empirically explores the risk management practices of central counterparties. We examine whether European CCPs are more prudent relative to their third-country peers. Our results indicate that EU CCPs request from their clearing members initial margins and default fund contributions that are of higher quality compared to those requested by non-EU CCPs. Omnibus and individual client segregation is more common in EU CCPs, suggesting a higher level of asset protection for clearing members. Regarding investment risk management, EU CCPs prefer to deposit cash at central banks, while non-EU CCPs rather have cash deposits at commercial banks. European CCPs have almost three times as many liquid resources than non-EU CCPs and rely more on cash deposited at central banks of issue. Their non-EU peers prefer unsecured cash deposits at commercial banks and unsecured committed lines of credit as liquidity resources.

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Relying on recent CPMI-IOSCO public quantitative disclosure (PQD) data provided by 35 central counterparties (CCPs) over the 2015-2018 period, this paper empirically explores the risk management practices of central counterparties. We examine whether European CCPs are more prudent relative to their third-country peers. Our results indicate that EU CCPs request from their clearing members initial margins and default fund contributions that are of higher quality compared to those requested by non-EU CCPs. Omnibus and individual client segregation is more common in EU CCPs, suggesting a higher level of asset protection for clearing members. Regarding investment risk management, EU CCPs prefer to deposit cash at central banks, while non-EU CCPs rather have cash deposits at commercial banks. European CCPs have almost three times as many liquid resources than non-EU CCPs and rely more on cash deposited at central banks of issue. Their non-EU peers prefer unsecured cash deposits at commercial banks and unsecured committed lines of credit as liquidity resources.

Stock Compensation Expense, Cash Flows and Inflated Valuations

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This paper reviews the statement of cash flow implications of stock compensation expense and the effect it can have on valuations. The paper suggests that treating stock compensation as a non-cash item in the statement of cash flows can be misleading from internal decision making and external valuation perspectives. This is important in light of the increasing role of non-GAAP cash flow disclosures in financial reporting as well as their use internally by managers. It quantifies the potential size of the problem and suggests potential solutions including treating stock compensation expense as an operating cash outflow and a financing cash inflow and/or adding further descriptive disclosures to the financial statements.

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This paper reviews the statement of cash flow implications of stock compensation expense and the effect it can have on valuations. The paper suggests that treating stock compensation as a non-cash item in the statement of cash flows can be misleading from internal decision making and external valuation perspectives. This is important in light of the increasing role of non-GAAP cash flow disclosures in financial reporting as well as their use internally by managers. It quantifies the potential size of the problem and suggests potential solutions including treating stock compensation expense as an operating cash outflow and a financing cash inflow and/or adding further descriptive disclosures to the financial statements.

Systemic Risk, Economic Policy Uncertainty and Firm Bankruptcies: Evidence from Multivariate Causal Inference

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The paper investigates causal relationships between systemic risk, economic policy uncertainty and firm bankruptcies, conditional on global volatility proxied by the VIX index, in a sample of 15 advanced and major emerging market economies during January 2008-June 2018. We test for Granger causality in time and frequency domains as well as dissect multivariate causal linkages in the dynamic complex system framework by applying a novel technique â€" convergent cross mapping (Sugihara et al., 2012). Based on strictly coincident results from all the three approaches, we find that systemic risk causes firm exit in Spain, while in the UK and the Netherlands bankruptcies are triggered by economic policy uncertainty. In South Korea, the VIX index causes the firm shutdown. For the rest of the countries, the causality inference provides less robust evidence. We argue that the magnitude of deleveraging by banks with respect to the private nonfinancial sector, proxied by the volatility of credit-toGDP gaps, shapes the presence or absence of causal impact by systemic risk, economic policy uncertainty or the VIX index on bankruptcies.

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The paper investigates causal relationships between systemic risk, economic policy uncertainty and firm bankruptcies, conditional on global volatility proxied by the VIX index, in a sample of 15 advanced and major emerging market economies during January 2008-June 2018. We test for Granger causality in time and frequency domains as well as dissect multivariate causal linkages in the dynamic complex system framework by applying a novel technique â€" convergent cross mapping (Sugihara et al., 2012). Based on strictly coincident results from all the three approaches, we find that systemic risk causes firm exit in Spain, while in the UK and the Netherlands bankruptcies are triggered by economic policy uncertainty. In South Korea, the VIX index causes the firm shutdown. For the rest of the countries, the causality inference provides less robust evidence. We argue that the magnitude of deleveraging by banks with respect to the private nonfinancial sector, proxied by the volatility of credit-toGDP gaps, shapes the presence or absence of causal impact by systemic risk, economic policy uncertainty or the VIX index on bankruptcies.

The Gilded Bubble Buffer and Optimal Macroprudential Policy

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We provide a microfounded framework for the welfare analysis of macroprudential policy within a model of rational bubbles. For this we posit an overlapping generation model where productivity and credit supply are subject to random shocks. We find that when real interest rates are lower than the rate of growth, credit financed bubbles may be welfare improving because of their role as a buffer in channeling excessive credit supply and inefficient investment at the firms' level, but its sudden price decrease may cause a systemic crisis. Therefore a well designed macroprudential policy plays a key role in improving efficiency while preserving financial stability. Our theoretical framework allows us to compare the efficiency of alternative macroprudential policies. Contrarily to conventional wisdom, we show that (i) macroprudential policy may be efficient even in the absence of systemic risk, (ii) it has to be contingent on productivity shocks and (iii) it must be contingent upon the level of real interest rates.

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We provide a microfounded framework for the welfare analysis of macroprudential policy within a model of rational bubbles. For this we posit an overlapping generation model where productivity and credit supply are subject to random shocks. We find that when real interest rates are lower than the rate of growth, credit financed bubbles may be welfare improving because of their role as a buffer in channeling excessive credit supply and inefficient investment at the firms' level, but its sudden price decrease may cause a systemic crisis. Therefore a well designed macroprudential policy plays a key role in improving efficiency while preserving financial stability. Our theoretical framework allows us to compare the efficiency of alternative macroprudential policies. Contrarily to conventional wisdom, we show that (i) macroprudential policy may be efficient even in the absence of systemic risk, (ii) it has to be contingent on productivity shocks and (iii) it must be contingent upon the level of real interest rates.

The Memory of Beta

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Researchers and practitioners employ a variety of time-series processes to forecast betas, using either short-memory models or implicitly imposing infinite memory. We find that both approaches are inadequate: beta factors show consistent long-memory properties. For the vast majority of stocks, we reject both the short-memory and difference-stationary (random walk) alternatives. A pure long-memory model reliably provides superior beta forecasts compared to all alternatives. Finally, we document the relation of firm characteristics with the forecast error differentials that result from inadequately imposing short-memory or random walk instead of long-memory processes.

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Researchers and practitioners employ a variety of time-series processes to forecast betas, using either short-memory models or implicitly imposing infinite memory. We find that both approaches are inadequate: beta factors show consistent long-memory properties. For the vast majority of stocks, we reject both the short-memory and difference-stationary (random walk) alternatives. A pure long-memory model reliably provides superior beta forecasts compared to all alternatives. Finally, we document the relation of firm characteristics with the forecast error differentials that result from inadequately imposing short-memory or random walk instead of long-memory processes.

The Value of Academic Independent Directors

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This paper investigates the value of academic independent directorsâ€™ (ADsâ€™) services by exploring an unexpected policy shock that forces ADs to resign from Chinese listed firms. Empirical results show that around the announcement of this policy, the stock prices of firms with ADs drop by 2.2%, which can be translated to a 135M RMB loss. These results suggest a likely causal relation between AD presence and firm value. ADs with academic backgrounds related to the firmsâ€™ primary line of business, with connections to an industry association, and holding top positions in a prestigious university are more valuable to firms. For ADs with business backgrounds, their services are more valuable when sitting on some specific board subcommittees. Moreover, ADs are more hardworking as they miss fewer meetings. Consistent with the market reactions, firm fundamentals and the efficiency of independent director monitoring and advising deteriorate significantly after ADs actually resign.

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This paper investigates the value of academic independent directorsâ€™ (ADsâ€™) services by exploring an unexpected policy shock that forces ADs to resign from Chinese listed firms. Empirical results show that around the announcement of this policy, the stock prices of firms with ADs drop by 2.2%, which can be translated to a 135M RMB loss. These results suggest a likely causal relation between AD presence and firm value. ADs with academic backgrounds related to the firmsâ€™ primary line of business, with connections to an industry association, and holding top positions in a prestigious university are more valuable to firms. For ADs with business backgrounds, their services are more valuable when sitting on some specific board subcommittees. Moreover, ADs are more hardworking as they miss fewer meetings. Consistent with the market reactions, firm fundamentals and the efficiency of independent director monitoring and advising deteriorate significantly after ADs actually resign.

Using Long Term Implied Volatilities to Assess Past and Present U.S. Stock Prices

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This paper empirically analyzes a model that relates earnings price ratios to long term risk free rates and implied volatilities. The two periods with sufficient available data are 1890-1933, and 2007-2019. I estimate that modern investors have relative risk aversion of 1.34 and a time preference discount of 2.77%,while their historical counterparts have a relative risk aversion of 1.50 and a 6.42% discount. The paper studies if prices were efficient in Black's (1986) sense, and finds that while an error correction model works well for the modern period, and for 1890 to 1927, coherence breaks down completely from 1928 to 1933.

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This paper empirically analyzes a model that relates earnings price ratios to long term risk free rates and implied volatilities. The two periods with sufficient available data are 1890-1933, and 2007-2019. I estimate that modern investors have relative risk aversion of 1.34 and a time preference discount of 2.77%,while their historical counterparts have a relative risk aversion of 1.50 and a 6.42% discount. The paper studies if prices were efficient in Black's (1986) sense, and finds that while an error correction model works well for the modern period, and for 1890 to 1927, coherence breaks down completely from 1928 to 1933.

Using a Cost of Capital Where One Really Shouldn't

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Myers (1974---`M74') derives the Cost of Capital (CC), including the corporate-tax subsidy on borrowing, for a one-period investment project. From Miles and Ezzell (1980), this CC remains valid in multiperiod projects provided that, during the project's life, debt is continuously re-aligned with \textit{ex post} GPVs. In contrast, when the debt schedule is static --- i.e. set to stabilise leverage {\it ex ante} only --- no CC works outside the Modigliani and Miller (1963---`MM63') perpetuities scenario; one generally needs a recursive Adjusted NPV (rANPV). Real-life leverage being neither fully static nor fully dynamic, two questions arise: (i) do M74's CC and rANPV produce very different valuations in a static/multiperiod problem?, and (ii) is it useful to heuristically adopt a non-linear interpolation between the M74 and MM63 polar CCs? We find, first, that M74's CC is is (mildly) conservative but vastly less biased and more precise than MM63's. Second, two of the heuristic compromise CCs are marginally more correct than even M74, but they remain biased upwards. Remembering that M74 also applies when debt is GPV-indexed ex post, M74 seems the safer procedure.Highlights: â€" With a â€˜staticâ€™ debt schedule set to stabilise leverage ex ante, a finite-life projectâ€™s risk cannot be constant, so no Cost of Capital (CC) can work perfectly.â€" When expressed as fractions of gross present value, minor-looking CC-based valuation errors largely reflect the low PV of the true tax shields rather than a precise assessment.â€" The Myers (1974) one-period cost of capital (CC) is mildly conservative and works very well for multiperiod NPV-ing even when debt is static.â€" The Miller-Modigliani CC for perpetuities, when applied in finite-life problems, is vastly overoptimistic and imprecise, especially when the CC takes into account growth.â€" We also propose four heuristic procedures that non-linearly interpolate between the above two CCs. The two that take into account the changing risk do succeed in beating Myersâ€™ CC, but the gains are small and the bias is upward rather than conservative.

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Myers (1974---`M74') derives the Cost of Capital (CC), including the corporate-tax subsidy on borrowing, for a one-period investment project. From Miles and Ezzell (1980), this CC remains valid in multiperiod projects provided that, during the project's life, debt is continuously re-aligned with \textit{ex post} GPVs. In contrast, when the debt schedule is static --- i.e. set to stabilise leverage {\it ex ante} only --- no CC works outside the Modigliani and Miller (1963---`MM63') perpetuities scenario; one generally needs a recursive Adjusted NPV (rANPV). Real-life leverage being neither fully static nor fully dynamic, two questions arise: (i) do M74's CC and rANPV produce very different valuations in a static/multiperiod problem?, and (ii) is it useful to heuristically adopt a non-linear interpolation between the M74 and MM63 polar CCs? We find, first, that M74's CC is is (mildly) conservative but vastly less biased and more precise than MM63's. Second, two of the heuristic compromise CCs are marginally more correct than even M74, but they remain biased upwards. Remembering that M74 also applies when debt is GPV-indexed ex post, M74 seems the safer procedure.Highlights: â€" With a â€˜staticâ€™ debt schedule set to stabilise leverage ex ante, a finite-life projectâ€™s risk cannot be constant, so no Cost of Capital (CC) can work perfectly.â€" When expressed as fractions of gross present value, minor-looking CC-based valuation errors largely reflect the low PV of the true tax shields rather than a precise assessment.â€" The Myers (1974) one-period cost of capital (CC) is mildly conservative and works very well for multiperiod NPV-ing even when debt is static.â€" The Miller-Modigliani CC for perpetuities, when applied in finite-life problems, is vastly overoptimistic and imprecise, especially when the CC takes into account growth.â€" We also propose four heuristic procedures that non-linearly interpolate between the above two CCs. The two that take into account the changing risk do succeed in beating Myersâ€™ CC, but the gains are small and the bias is upward rather than conservative.

Why Do Value Stocks Have More Consumption Risk?

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I build a production-based continuous-time equilibrium model with Markov regime switches. The model is solved in closed-form and endogenously generates the following previously documented patterns: (1) Value stocks yield larger returns than growth stocks that cannot be reconciled by CAPM; (2) The cash-flows of value stocks are more exposed to consumption risk than those of growth stocks; (3) The volatility of cash-flows of value stocks are more exposed to consumption volatility than that of growth stocks; (4) The returns of value stocks have larger beta on consumption volatility than growth stocks. Business cycle risk and costly reversibility provides a plausible explanation of those patterns.

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I build a production-based continuous-time equilibrium model with Markov regime switches. The model is solved in closed-form and endogenously generates the following previously documented patterns: (1) Value stocks yield larger returns than growth stocks that cannot be reconciled by CAPM; (2) The cash-flows of value stocks are more exposed to consumption risk than those of growth stocks; (3) The volatility of cash-flows of value stocks are more exposed to consumption volatility than that of growth stocks; (4) The returns of value stocks have larger beta on consumption volatility than growth stocks. Business cycle risk and costly reversibility provides a plausible explanation of those patterns.