Research articles for the 2020-04-09

A Note on New Valuation Measures for Standard & Poor Composite Index Returns
Taran Grove,Michael Reyes,Andrey Sarantsev

Financial theory tells that long-run total real returns of the stock market are approximately equal to long-run earnings growth plus average dividend yield. Thus the total real returns minus real earnings growth must be stable in the long run. If this difference is abnormally high in the last few years, then we consider the market to be overheated and headed for a crash. A measure of such heat is (detrended) cumulative sum of differences. We regress future total real returns upon current heat measure. To make sure all residuals are normal i.i.d., we move in three-year steps. We use Bayesian inference with a non-informative prior. After verifying goodness-of-fit, we simulate future returns for horizons of 9, 15, 30 years, starting from current market conditions. We verify the conventional wisdom that future long-run stock market returns are likely to be lower than the historical averages.

Applications of the Coase Theorem
Tatyana Deryugina,Frances Moore,Richard S.J. Tol

The Coase Theorem has a central place in the theory of environmental economics and regulation. But its applicability for solving real-world externality problems remains debated. In this paper, we first place this seminal contribution in its historical context. We then survey the experimental literature that has tested the importance of the many, often tacit assumptions in the Coase Theorem in the laboratory. We discuss a selection of applications of the Coase Theorem to actual environmental problems, distinguishing between situations in which the polluter or the pollutee pays. While limited in scope, Coasian bargaining over externalities offers a pragmatic solution to problems that are difficult to solve in any other way.

Classifying economics for the common good: Connecting sustainable development goals to JEL codes
Jussi T. S. Heikkilä

How does economics research help in solving societal challenges? This brief note sheds additional light on this question by providing ways to connect Journal of Economic Literature (JEL) codes and Sustainable Development Goals (SDGs) of the United Nations. These simple linkages illustrate that the themes of SDGs have corresponding JEL classification codes. As the mappings presented here are necessarily imperfect and incomplete, there is plenty of room for improvements. In an ideal world, there would be a JEL classification system for SDGs, a separate JEL code for each of the 17 SDGs.

Deep Deterministic Portfolio Optimization
Ayman Chaouki,Stephen Hardiman,Christian Schmidt,Emmanuel Sérié,Joachim de Lataillade

Can deep reinforcement learning algorithms be exploited as solvers for optimal trading strategies? The aim of this work is to test reinforcement learning algorithms on conceptually simple, but mathematically non-trivial, trading environments. The environments are chosen such that an optimal or close-to-optimal trading strategy is known. We study the deep deterministic policy gradient algorithm and show that such a reinforcement learning agent can successfully recover the essential features of the optimal trading strategies and achieve close-to-optimal rewards.

Desperate times call for desperate measures: government spending multipliers in hard times
Sokbae Lee,Yuan Liao,Myung Hwan Seo,Youngki Shin

We investigate state-dependent effects of fiscal multipliers and allow for endogenous sample splitting to determine whether the US economy is in a slack state. When the endogenized slack state is estimated as the period of the unemployment rate higher than about 12 percent, the estimated cumulative multipliers are significantly larger during slack periods than non-slack periods and are above unity. We also examine the possibility of time-varying regimes of slackness and find that our empirical results are robust under a more flexible framework. Our estimation results points out the importance of the heterogenous effects of fiscal policy and shed light on the prospect of fiscal policy in response to economic shocks of the current coronavirus pandemic.

On Game-Theoretic Risk Management (Part Two) -- Algorithms to Compute Nash-Equilibria in Games with Distributions as Payoffs
Stefan Rass

The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our approach is "data driven" in the sense that we assume empirical data (measurements, simulation, etc.) to be available that can be compiled into distribution models, which are suitable for efficient decisions about preferences, and setting up and solving games using these as payoffs. While preferences among distributions turn out to be quite simple if nonparametric methods (kernel density estimates) are used, computing Nash-equilibria in games using such models is discovered as inefficient (if not impossible). In fact, we give a counterexample in which fictitious play fails to converge for the (specifically unfortunate) choice of payoff distributions in the game, and introduce a suitable tail approximation of the payoff densities to tackle the issue. The overall procedure is essentially a modified version of fictitious play, and is herein described for standard and multicriteria games, to iteratively deliver an (approximate) Nash-equilibrium. An exact method using linear programming is also given.

Quantification of Risk in Classical Models of Finance
Alois Pichler,Ruben Schlotter

This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical models in finance and characterize existence of the risk-averse limit. As a result we demonstrate that the nested limit is unique, irrespective of the initially chosen risk measure. Within the classical models risk aversion gives rise to a stream of risk premiums, comparable to dividend payments. In this context, we connect coherent risk measures with the Sharpe ratio from modern portfolio theory and extract the Z-spread - a widely accepted quantity in economics to hedge risk. By involving the Z-spread we demonstrate that risk-averse problems are conceptually equivalent to the risk-neutral problem.

The results for European option pricing are then extended to risk-averse American options, where we study the impact of risk on the price as well as the optimal time to exercise the option.

We also extend Merton's optimal consumption problem to the risk-averse setting.

Rank-Based Capital Asset Pricing Model
Kwame Boamah-Addo,Brandon Flores,Jakob Lovato,Andrey Sarantsev

A rank-based model of competing Brownian particles, introduced in (Banner, Fernholz, Karatzas, 2005), captures the dependence of stock dynamics on size: Small stocks have higher growth rate but higher volatility than large stocks, on average. However, in this model, geometric returns of stocks have Gaussian tails. We modify this model using Capital Asset Pricing Model: The market exposure depends on the rank, and the benchmark moves as a general L\'evy process. We show that this model fits real market data. We discuss stability and long-term convergence.

SABR smiles for RFR caplets
Sander Willems

We present a natural extension of the SABR model to price both backward and forward-looking RFR caplets in a post-Libor world. Forward-looking RFR caplets can be priced using the market standard approximations of Hagan et al. (2002). We provide closed-form effective SABR parameters for pricing backward-looking RFR caplets. These results are useful for smile interpolation and for analyzing backward and forward-looking smiles in normalized units.

The Politics of News Personalization
Lin Hu,Anqi Li,Ilya Segal

We study how news personalization affects policy polarization. In a two-candidate electoral competition model, an attention-maximizing infomediary aggregates information about candidate valence into news. Voters decide whether to consume news, trading off the expected utility gain from improved expressive voting against the attention cost. Broadcast news serves a broad and balanced audience with a symmetric signal. Personalized news serves extreme voters with skewed signals featuring own-party bias and occasional big surprise. Rational news aggregation generates policy polarization even between office-motivated candidates. Personalization makes extreme voters the disciplining entity for policy polarization and increases policy polarization mainly through occasional big surprise.

The cost of Bitcoin mining has never really increased
Yo-Der Song,Tomaso Aste

The Bitcoin network is burning a large amount of energy for mining. In this paper we estimate the lower bound for the global energy cost for a period of ten years from 2010 to 2020, taking into account changing oil costs, improvements in hashing technologies and hashing activity. Despite a ten-billion-fold increase in hashing activity and a ten-million-fold increase in total energy consumption, we find the mining cost relative to the volume of transactions has not increased nor decreased since 2010. This is consistent with the perspective that the proof of work must cost a sizable fraction of the value that can be transferred through the network in order to keep the Blockchain system secure from double spending attacks. We estimate that in the Bitcoin network this fraction is of the order of 1%.