Research articles for the 2020-11-29

Alpha Discovery Neural Network based on Prior Knowledge
Jie Fang,Shutao Xia,Jianwu Lin,Zhikang Xia,Xiang Liu,Yong Jiang

Genetic programming (GP) is the state-of-the-art in financial automated feature construction task. It employs reverse polish expression to represent features and then conducts the evolution process. However, with the development of deep learning, more powerful feature extraction tools are available. This paper proposes Alpha Discovery Neural Network (ADNN), a tailored neural network structure which can automatically construct diversified financial technical indicators based on prior knowledge. We mainly made three contributions. First, we use domain knowledge in quantitative trading to design the sampling rules and object function. Second, pre-training and model pruning has been used to replace genetic programming, because it can conduct more efficient evolution process. Third, the feature extractors in ADNN can be replaced by different feature extractors and produce different functions. The experiment results show that ADNN can construct more informative and diversified features than GP, which can effectively enriches the current factor pool. The fully-connected network and recurrent network are better at extracting information from the financial time series than the convolution neural network. In real practice, features constructed by ADNN can always improve multi-factor strategies' revenue, sharpe ratio, and max draw-down, compared with the investment strategies without these factors.

An Equilibrium Model for the Cross-Section of Liquidity Premia
Johannes Muhle-Karbe,Xiaofei Shi,Chen Yang

We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward-backward stochastic differential equations characterizing equilibrium asset prices and trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove the existence of a unique global solution and provide explicit asymptotic expansions that allow us to approximate the corresponding equilibrium for small transaction costs. These tractable approximation formulas make it feasible to calibrate the model to time series of prices and trading volume, and to study the cross-section of liquidity premia earned by assets with higher and lower trading costs. This is illustrated by an empirical case study.

Barriers to grid-connected battery systems: Evidence from the Spanish electricity market
Yu Hu,David Soler Soneira,María Jesús Sánchez

Electrical energy storage is considered essential for the future energy systems. Among all the energy storage technologies, battery systems may provide flexibility to the power grid in a more distributed and decentralized way. In countries with deregulated electricity markets, grid-connected battery systems should be operated under the specific market design of the country. In this work, using the Spanish electricity market as an example, the barriers to grid-connected battery systems are investigated using utilization analysis. The concept of "potentially profitable utilization time" is proposed and introduced to identify and evaluate future potential grid applications for battery systems. The numerical and empirical analysis suggests that the high cycle cost for battery systems is still the main barrier for grid-connected battery systems. In Spain, for energy arbitrage within the day-ahead market, it is required that the battery wear cost decreases to 15 Euro/MWh to make the potentially profitable utilization rate higher than 20%. Nevertheless, the potentially profitable utilization of batteries is much higher in the applications when higher flexibility is demanded. The minimum required battery wear cost corresponding to 20% potentially profitable utilization time increases to 35 Euro/MWh for energy arbitrage within the day-ahead market and ancillary services, and 50 Euro/MWh for upward secondary reserve. The results of this study contribute to the awareness of battery storage technology and its flexibility in grid applications. The findings also have significant implications for policy makers and market operators interested in promoting grid-connected battery storage under a deregulated power market.

Blockchain mechanism and distributional characteristics of cryptos
Min-Bin Lin,Kainat Khowaja,Cathy Yi-Hsuan Chen,Wolfgang Karl Härdle

We investigate the relationship between underlying blockchain mechanism of cryptocurrencies and its distributional characteristics. In addition to price, we emphasise on using actual block size and block time as the operational features of cryptos. We use distributional characteristics such as fourier power spectrum, moments, quantiles, global we optimums, as well as the measures for long term dependencies, risk and noise to summarise the information from crypto time series. With the hypothesis that the blockchain structure explains the distributional characteristics of cryptos, we use characteristic based spectral clustering to cluster the selected cryptos into five groups. We scrutinise these clusters and find that indeed, the clusters of cryptos share similar mechanism such as origin of fork, difficulty adjustment frequency, and the nature of block size. This paper provides crypto creators and users with a better understanding toward the connection between the blockchain protocol design and distributional characteristics of cryptos.

Continuous time mean-variance-utility portfolio problem and its equilibrium strategy
Ben-Zhang Yang,Xin-Jiang He,Song-Ping Zhu

In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective optimization problem is firstly transformed into a single-objective one by introducing the concept of overall "happiness" of an investor defined as the aggregation of the terminal wealth under the mean-variance criterion and the expected accumulated utility, and then solved under a game theoretic framework. We have managed to maintain analytical tractability; the closed-form solutions found for a set of special utility functions enable us to discuss some interesting optimal investment strategies that have not been revealed before in literature.

Decreasing market value of variable renewables is a result of policy, not variability
T. Brown,L. Reichenberg

Although recent studies have shown that electricity systems with shares of wind and solar above 80% can be affordable, economists have raised concerns about market integration. Correlated generation from variable renewable sources depresses market prices, which can cause wind and solar to cannibalize their own revenues and prevent them from covering their costs from the market. This cannibalization appears to set limits on the integration of wind and solar, and thus contradicts studies that show that high shares are cost effective. Here we show from theory and with numerical examples how market incentives interact with prices, revenue and costs for renewable electricity systems. The decline in average revenue seen in some recent literature is due to an implicit policy assumption that technologies are forced into the system, whether it be with subsidies or quotas. If instead the driving policy is a carbon dioxide cap or tax, wind and solar shares can rise without cannibalising their own market revenue, even at penetrations of wind and solar above 80%. The policy of subsidy is thus the primary factor driving lower market values, and this decline happens even for dispatchable low-emission technologies; the variability of wind and solar is only a secondary factor that accelerates the decline if they are subsidised. The strong dependence of market value on the policy regime means that market value needs to be used with caution as a measure of market integration.

Detecting p-hacking
Graham Elliott,Nikolay Kudrin,Kaspar Wuthrich

We theoretically analyze the problem of testing for $p$-hacking based on distributions of $p$-values across multiple studies. We provide general results for when such distributions have testable restrictions (are non-increasing) under the null of no $p$-hacking. We find novel additional testable restrictions for $p$-values based on $t$-tests. Specifically, the shape of the power functions results in both complete monotonicity as well as bounds on the distribution of $p$-values. These testable restrictions result in more powerful tests for the null hypothesis of no $p$-hacking. A reanalysis of two prominent datasets shows the usefulness of our new tests.

Endogenous Representation of Asset Returns
Zhipu Zhou,Alexander Shkolnik,Sang-Yun Oh

Factor modeling of asset returns has been a dominant practice in investment science since the introduction of the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). The factors, which account for the systematic risk, are either specified or interpreted to be exogenous. They explain a significant portion of the risk in large portfolios. We propose a framework that asks how much of the risk, that we see in equity markets, may be explained by the asset returns themselves. To answer this question, we decompose the asset returns into an endogenous component and the remainder, and analyze the properties of the resulting risk decomposition. Statistical methods to estimate this decomposition from data are provided along with empirical tests. Our results point to the possibility that most of the risk in equity markets may be explained by a sparse network of interacting assets (or their issuing firms). This sparse network can give the appearance of a set exogenous factors where, in fact, there may be none. We illustrate our results with several case studies.

Fat Tailed Factors
Jan Rosenzweig

Standard, PCA-based factor analysis suffers from a number of well known problems due to the random nature of pairwise correlations of asset returns. We analyse an alternative based on ICA, where factors are identified based on their non-Gaussianity, instead of their variance. Generalizations of portfolio construction to the ICA framework leads to two semi-optimal portfolio construction methods: a fat-tailed portfolio, which maximises return per unit of non-Gaussianity, and the hybrid portfolio, which asymptotically reduces variance and non-Gaussianity in parallel. For fat-tailed portfolios, the portfolio weights scale like performance to the power of $1/3$, as opposed to linear scaling of Kelly portfolios; such portfolio construction significantly reduces portfolio concentration, and the winner-takes-all problem inherent in Kelly portfolios. For hybrid portfolios, the variance is diversified at the same rate as Kelly PCA-based portfolios, but excess kurtosis is diversified much faster than in Kelly, at the rate of $n^{-2}$ compared to Kelly portfolios' $n^{-1}$ for increasing number of components $n$.

Fragile, yet resilient: Adaptive decline in a collaboration network of firms
Frank Schweitzer,Giona Casiraghi,Mario V. Tomasello,David Garcia

The dynamics of collaboration networks of firms follow a life-cycle of growth and decline. That does not imply they also become less resilient. Instead, declining collaboration networks may still have the ability to mitigate shocks from firms leaving, and to recover from these losses by adapting to new partners. To demonstrate this, we analyze 21.500 R\&D collaborations of 14.500 firms in six different industrial sectors over 25 years. We calculate time-dependent probabilities of firms leaving the network and simulate drop-out cascades, to determine the expected dynamics of decline. We then show that deviations from these expectations result from the adaptivity of the network, which mitigates the decline. These deviations can be used as a measure of network resilience.

Generative Learning of Heterogeneous Tail Dependence
Xiangqian Sun,Xing Yan,Qi Wu

We propose a multivariate generative model to capture the complex dependence structure often encountered in business and financial data. Our model features heterogeneous and asymmetric tail dependence between all pairs of individual dimensions while also allowing heterogeneity and asymmetry in the tails of the marginals. A significant merit of our model structure is that it is not prone to error propagation in the parameter estimation process, hence very scalable, as the dimensions of datasets grow large. However, the likelihood methods are infeasible for parameter estimation in our case due to the lack of a closed-form density function. Instead, we devise a novel moment learning algorithm to learn the parameters. To demonstrate the effectiveness of the model and its estimator, we test them on simulated as well as real-world datasets. Results show that this framework gives better finite-sample performance compared to the copula-based benchmarks as well as recent similar models.

Modeling Skewness in Portfolio Choice
Le, Trung H.,Kourtis, Apostolos,Markellos, Raphael N.
Despite half a century of research, we still do not know the best way to model skewness of financial returns. We address this question by comparing the predictive ability and associated portfolio performance of several prominent skewness models in a sample of ten international equity market indices. Models that employ information from the option markets provide the best outcomes overall. We develop an option-based model that accounts for the skewness risk premium. The new model produces the most informative forecasts of future skewness, the lowest prediction errors and the best portfolio performance in most of our tests.

Modeling Univariate and Multivariate Stochastic Volatility in R with stochvol and factorstochvol
Darjus Hosszejni,Gregor Kastner

Stochastic volatility (SV) models are nonlinear state-space models that enjoy increasing popularity for fitting and predicting heteroskedastic time series. However, due to the large number of latent quantities, their efficient estimation is non-trivial and software that allows to easily fit SV models to data is rare. We aim to alleviate this issue by presenting novel implementations of four SV models delivered in two R packages. Several unique features are included and documented. As opposed to previous versions, stochvol is now capable of handling linear mean models, heavy-tailed SV, and SV with leverage. Moreover, we newly introduce factorstochvol which caters for multivariate SV. Both packages offer a user-friendly interface through the conventional R generics and a range of tailor-made methods. Computational efficiency is achieved via interfacing R to C++ and doing the heavy work in the latter. In the paper at hand, we provide a detailed discussion on Bayesian SV estimation and showcase the use of the new software through various examples.

Multi-asset Generalised Variance Swaps in Barndorff-Nielsen and Shephard model
Subhojit Biswas,Diganta Mukherjee,Indranil SenGupta

This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for Barndorff-Nielsen and Shephard model used in financial markets. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.

Nowcasting Networks
Marc Chataigner,Stephane Crepey,Jiang Pu

We devise a neural network based compression/completion methodology for financial nowcasting. The latter is meant in a broad sense encompassing completion of gridded values, interpolation, or outlier detection, in the context of financial time series of curves or surfaces (also applicable in higher dimensions, at least in theory). In particular, we introduce an original architecture amenable to the treatment of data defined at variable grid nodes (by far the most common situation in financial nowcasting applications, so that PCA or classical autoencoder methods are not applicable). This is illustrated by three case studies on real data sets. First, we introduce our approach on repo curves data (with moving time-to-maturity as calendar time passes). Second, we show that our approach outperforms elementary interpolation benchmarks on an equity derivative surfaces data set (with moving time-to-maturity again). We also obtain a satisfying performance for outlier detection and surface completion. Third, we benchmark our approach against PCA on at-the-money swaption surfaces redefined at constant expiry/tenor grid nodes. Our approach is then shown to perform as well as (even if not obviously better than) the PCA which, however, is not be applicable to the native, raw data defined on a moving time-to-expiry grid).

Persuasion Produces the (Diamond) Paradox
Mark Whitmeyer

This paper extends the sequential search model of Wolinsky (1986) by allowing firms to choose how much match value information to disclose to visiting consumers. This restores the Diamond paradox (Diamond 1971): there exist no symmetric equilibria in which consumers engage in active search, so consumers obtain zero surplus and firms obtain monopoly profits. Modifying the scenario to one in which prices are advertised, we discover that the no-active-search result persists, although the resulting symmetric equilibria are ones in which firms price at marginal cost.

Predicting S&P500 Index direction with Transfer Learning and a Causal Graph as main Input
Djoumbissie David Romain

We propose a unified multi-tasking framework to represent the complex and uncertain causal process of financial market dynamics, and then to predict the movement of any type of index with an application on the monthly direction of the S&P500 index. our solution is based on three main pillars: (i) the use of transfer learning to share knowledge and feature (representation, learning) between all financial markets, increase the size of the training sample and preserve the stability between training, validation and test sample. (ii) The combination of multidisciplinary knowledge (Financial economics, behavioral finance, market microstructure and portfolio construction theories) to represent a global top-down dynamics of any financial market, through a graph. (iii) The integration of forward looking unstructured data, different types of contexts (long, medium and short term) through latent variables/nodes and then, use a unique VAE network (parameter sharing) to learn simultaneously their distributional representation. We obtain Accuracy, F1-score, and Matthew Correlation of 74.3 %, 67 % and 0.42 above the industry and other benchmark on 12 years test period which include three unstable and difficult sub-period to predict.

Price of liquidity in the reinsurance of fund returns
David Saunders,Luis Seco,Markus Senn

This paper aims to extend downside protection to a hedge fund investment portfolio based on shared loss fee structures that have become increasing popular in the market. In particular, we consider a second tranche and suggest the purchase of an upfront reinsurance contract for any losses on the fund beyond the threshold covered by the first tranche, i.e. gaining full portfolio protection. We identify a fund's underlying liquidity as a key parameter and study the pricing of this additional reinsurance using two approaches: First, an analytic closed-form solution based on the Black-Scholes framework and second, a numerical simulation using a Markov-switching model. In addition, a simplified backtesting method is implemented to evaluate the practical application of the concept.

Prior knowledge distillation based on financial time series
Jie Fang,Jianwu Lin

One of the major characteristics of financial time series is that they contain a large amount of non-stationary noise, which is challenging for deep neural networks. People normally use various features to address this problem. However, the performance of these features depends on the choice of hyper-parameters. In this paper, we propose to use neural networks to represent these indicators and train a large network constructed of smaller networks as feature layers to fine-tune the prior knowledge represented by the indicators. During back propagation, prior knowledge is transferred from human logic to machine logic via gradient descent. Prior knowledge is the deep belief of neural network and teaches the network to not be affected by non-stationary noise. Moreover, co-distillation is applied to distill the structure into a much smaller size to reduce redundant features and the risk of overfitting. In addition, the decisions of the smaller networks in terms of gradient descent are more robust and cautious than those of large networks. In numerical experiments, we find that our algorithm is faster and more accurate than traditional methods on real financial datasets. We also conduct experiments to verify and comprehend the method.

Scalar multivariate risk measures with a single eligible asset
Zachary Feinstein,Birgit Rudloff

In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We will prove the equivalence of this weaker notion of time consistency and a certain type of backward recursion with respect to the underlying risk measure with a fixed consistent pricing process. Several examples are given, with special emphasis on the superhedging risk measure.