# Research articles for the 2019-11-24

arXiv

Uniswap---and other constant product markets---appear to work well in practice despite their simplicity. In this paper, we give a simple formal analysis of constant product markets and their generalizations, showing that, under some common conditions, these markets must closely track the reference market price. We also show that Uniswap satisfies many other desirable properties and numerically demonstrate, via a large-scale agent-based simulation, that Uniswap is stable under a wide range of market conditions.

arXiv

We study asset price bubbles in market models with proportional transaction costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [48]. By following [27], we define the fundamental value $F$ of a risky asset $S$ as the price of a super-replicating portfolio for a position terminating in one unit of the asset and zero cash. We then obtain a dual representation for the fundamental value by using the super-replication theorem of [49]. We say that an asset price has a bubble if its fundamental value differs from the ask-price $(1+\lambda)S$. We investigate the impact of transaction costs on asset price bubbles and show that our model intrinsically includes the birth of a bubble.

SSRN

In this article we discuss whether commodities should be included as an asset class when establishing portfolios. By investigating second order stochastic dominance relations, we find that the stock and bond indices tend to dominate the individual commodities. We further study if we can find a combination of stocks, bonds and commodities that dominate others. Compared to a 60% stock and 40% bond portfolio mix, portfolios consisting of long positions in gold futures and two different actively managed indices are the only commodity investments to be included as long positions in a stock/bond portfolio. The results should be of interest for fund managers and traders that seek to improve their risk-return trade off compared to the traditional 60/40 portfolio.

arXiv

In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors.

We compute analytically the optimal investment-consumption strategy for a fund of $n$ identical investors with homogeneous Epstein--Zin preferences, investing in the Black--Scholes market in continuous time but consuming in discrete time. Our result holds for arbitrary mortality distributions.

We also compute the optimal strategy for an infinite fund of investors, and prove the convergence of the optimal strategy as $n\to \infty$. The proof of convergence shows that effective strategies for inhomogeneous funds can be obtained using the optimal strategies found in this paper for homogeneous funds, using the results of [2].

We find that a constant consumption strategy is suboptimal even for infinite collectives investing in markets where assets provide no return so long as investors are "satisfaction risk-averse." This suggests that annuities and defined benefit investments will always be suboptimal investments.

We present numerical results examining the importance of the fund size, $n$, and the market parameters.

arXiv

We adopt Deep Reinforcement Learning algorithms to design trading strategies for continuous futures contracts. Both discrete and continuous action spaces are considered and volatility scaling is incorporated to create reward functions which scale trade positions based on market volatility. We test our algorithms on the 50 most liquid futures contracts from 2011 to 2019, and investigate how performance varies across different asset classes including commodities, equity indices, fixed income and FX markets. We compare our algorithms against classical time series momentum strategies, and show that our method outperforms such baseline models, delivering positive profits despite heavy transaction costs. The experiments show that the proposed algorithms can follow large market trends without changing positions and can also scale down, or hold, through consolidation periods.

arXiv

We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from symbolic data analysis, we consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and develop a new class of dynamic models for quantile-function-valued (QF-valued) time series. In order to make statistical inferences and account for parameter uncertainty, we propose a method whereby a likelihood function can be constructed for QF-valued data, and develop an adaptive MCMC sampling algorithm for simulating from the posterior distribution. Compared to modelling realised measures, modelling the entire quantile functions of intra-daily returns allows one to gain more insight into the dynamic structure of price movements. Via simulations, we show that the proposed MCMC algorithm is effective in recovering the posterior distribution, and that the posterior means are reasonable point estimates of the model parameters. For empirical studies, the new model is applied to analysing one-minute returns of major international stock indices. Through quantile scaling, we further demonstrate the usefulness of our method by forecasting one-step-ahead the Value-at-Risk of daily returns.

SSRN

With recourse to archival, printed primary, and secondary sources, this paper reconstructs global real interest rates on an annual basis going back to the 14th century, covering 78% of advanced economy GDP over time. I show that across successive monetary and fiscal regimes, and a variety of asset classes, real interest rates have not been â€œstableâ€, and that since the major monetary upheavals of the late middle ages, a trend decline between 0.6-1.8bps p.a. has prevailed. A consistent increase in real negative-yielding rates in advanced economies over the same horizon is identified, despite important temporary reversals such as the 17th Century Crisis. Against their long-term context, currently depressed sovereign real rates are in fact converging â€œback to historical trendâ€ â€" a trend that makes narratives about a â€œsecular stagnationâ€ environment entirely misleading, and suggests that â€" irrespective of particular monetary and fiscal responses â€" real rates could soon enter permanently negative territory. I also posit that the return data here reflects a substantial share of â€œnonhuman wealthâ€ over time: the resulting R-G series derived from this data show a downward trend over the same timeframe: suggestions about the â€œvirtual stabilityâ€ of capital returns, and the policy implications advanced by Piketty (2014) are in consequence equally unsubstantiated by the historical record.

arXiv

In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical characteristic function method for the estimation of GARCH parameters with symmetric stable noise. Further, we show the efficiency, accuracy, and simplicity of our methods through Monte-Carlo simulation. Finally, we apply our proposed methods to model financial data.

arXiv

In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known law of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. A substantial part of our study is devoted to the problem of estimating fair risk allocations for expected shortfall. We study this problem under normality as well as in a nonparametric setup. We derive several estimators, and prove their fairness and/or asymptotic fairness. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. The paper closes with a substantial numerical study of the subject.

arXiv

In the area of credit risk analytics, current Bankruptcy Prediction Models (BPMs) struggle with (a) the availability of comprehensive and real-world data sets and (b) the presence of extreme class imbalance in the data (i.e., very few samples for the minority class) that degrades the performance of the prediction model. Moreover, little research has compared the relative performance of well-known BPM's on public datasets addressing the class imbalance problem. In this work, we apply eight classes of well-known BPMs, as suggested by a review of decades of literature, on a new public dataset named Freddie Mac Single-Family Loan-Level Dataset with resampling (i.e., adding synthetic minority samples) of the minority class to tackle class imbalance. Additionally, we apply some recent AI techniques (e.g., tree-based ensemble techniques) that demonstrate potentially better results on models trained with resampled data. In addition, from the analysis of 19 years (1999-2017) of data, we discover that models behave differently when presented with sudden changes in the economy (e.g., a global financial crisis) resulting in abrupt fluctuations in the national default rate. In summary, this study should aid practitioners/researchers in determining the appropriate model with respect to data that contains a class imbalance and various economic stages.

arXiv

How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as extreme cases the classical Heston model (when n = 1), and the rough Heston model (when n goes to infinity). We show that the lifted model enjoys the best of both worlds: Markovianity and satisfactory fits of implied volatility smiles for short maturities with very few parameters. Further, our approach speeds up the calibration time and opens the door to time-efficient simulation schemes.

SSRN

Landlords appear to use stale information when setting rents. Among over 43,000 California rental houses in 2018-2019, those last purchased during 2005-2007 (the peak) rent for 2-3% more than those purchased during 2008-2010 (bust). Neither house nor landlord characteristics explain this â€œpeak-bust rental spread.â€ To clarify the mechanism, we test cross-sectional predictions from a simple theory of rent-setting. We find empirical support for both anchoring and prospect theory. In the first, past sales prices distort landlordsâ€™ current estimates of house values/rents. In the second, monthly payments establish (recurring) reference points, against which gains or losses are measured.

SSRN

This paper examines the benefits and costs associated with rookie independent directors (RIDs) in Chinese public companies from 2008 to 2014. We find that RIDs attend more board meetings. Boards with more RIDs tunnel less to controlling shareholders, suggesting that RIDs are efficient monitors. However, in state-owned firms, the presence of RIDs is negatively associated with investment efficiency, suggesting a potential cost of appointing RIDs. Overall, firms with more RIDs have higher operating performance, especially when tunneling is a more common issue, when board experience is less important and when monitoring costs are relatively low.

arXiv

A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset as to maximize the expected utility of the round-trip profit net of transaction costs. The optimization problem is formulated as a sequential optimal stopping problem and we provide a complete characterization of the solution. Depending on the preference and market parameters as well as the initial price of the asset, the optimal strategy can be "buy and hold", "buy low sell high", "buy high sell higher" or "no trading". Transaction costs do not necessarily curb speculative trading. For example, while a large proportional transaction cost on sale can unambiguously suppress trading participation, introducing a fixed market entry fee will indeed encourage trading when the asset price level is high.

arXiv

We consider a sequential social-learning environment with rational agents and Gaussian private signals, focusing on how the observation network affects the speed of learning. Agents learn about a binary state and take turns choosing actions based on own signals and observations of network neighbors' behavior. The observation network generally presents an obstruction to the efficient rate of signal aggregation, as agents compromise between incorporating the signals of the observed neighbors and not over-counting the signals of the unobserved early movers. We show that on any network, equilibrium actions are a log-linear function of observations and each agent's accuracy admits a signal-counting interpretation. We then consider a network structure where agents move in generations and observe all members of the previous generation. The additional information aggregated by each generation is asymptotically equivalent to fewer than two independent signals, even when generations are arbitrarily large.

arXiv

This paper reexamines the validity of the natural resource curse hypothesis, using the database of mineral exporting countries. Our findings are as follows: (i) Resource-rich countries (RRCs) do not necessarily exhibit poor political, economic and social performance; (ii) RRCs that perform poorly have a low diversified exports portfolio; (iii) In contrast, RRCs with a low diversified exports portfolio do not necessarily perform poorly. Then, we develop a model of strategic interaction from a Bayesian game setup to study the role of leadership and governance in the management of natural resources. We show that an improvement in the leadership-governance binomial helps to discipline the behavior of lobby groups (theorem 1) and generate a Pareto improvement in the management of natural resources (theorem 2). Evidence from the World Bank Group's CPIA data confirms the later finding. Our results remain valid after some robustness checks.

arXiv

Artificial Intelligence (AI) has become an integral part of domains such as security, finance, healthcare, medicine, and criminal justice. Explaining the decisions of AI systems in human terms is a key challenge--due to the high complexity of the model, as well as the potential implications on human interests, rights, and lives . While Explainable AI is an emerging field of research, there is no consensus on the definition, quantification, and formalization of explainability. In fact, the quantification of explainability is an open challenge. In our previous work, we incorporated domain knowledge for better explainability, however, we were unable to quantify the extent of explainability. In this work, we (1) briefly analyze the definitions of explainability from the perspective of different disciplines (e.g., psychology, social science), properties of explanation, explanation methods, and human-friendly explanations; and (2) propose and formulate an approach to quantify the extent of explainability. Our experimental result suggests a reasonable and model-agnostic way to quantify explainability

SSRN

This paper examines international spillovers from unconventional monetary policy (UMP) between the US, the Euro area, the UK and Japan, exploiting the asynchronous timing of monetary policy normalization to shed light on the term structure implications of UMP divergence. Using high frequency futures data to identify monetary policy surprises and controlling for contemporaneous news, I find that spillovers increase during periods of unconventional monetary policy, and that these strengthen in the period of asynchronous policy normalization. Local projections suggest persistent spillovers from the Federal Reserve, whereas other spillovers fade quickly. Through the lens of a shadow rate term structure model (SRTSM), I find that these surprises elicit, domestically and internationally, revisions to both the expected path of short-term interest rates and required risk compensation, with the latter gaining importance at the effective lower bound of interest rates.