This is a short note, which contains a simple dynamic factor model: Total (including dividends) real (inflation-adjusted) annual returns of Standard \& Poor Composite Index is regressed upon earnings yield, which is defined as earnings (net income) per share of this index (summed over all companies in this index), divided by the current value of this index. This earnings yield is modeled as a simple autoregression. We use 7-year trailing earnings yield, with earnings averaged over the last 7 years. This version of earnings yield has maximal correlation with next year's total real returns. Regression residuals fail standard normality tests, but we still use this model, since we are interested in long-run modeling. To account for shortage of data (1935--2019 annual), we use Bayesian inference. We confirm the conventional wisdom that future long-run stock market returns are likely to be lower than the historical averages.

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.

The potential impact of automation on the labor market is a topic that has generated significant interest and concern amongst scholars, policymakers, and the broader public. A number of studies have estimated occupation-specific risk profiles by examining the automatability of associated skills and tasks. However, relatively little work has sought to take a more holistic view on the process of labor reallocation and how employment prospects are impacted as displaced workers transition into new jobs. In this paper, we develop a new data-driven model to analyze how workers move through an empirically derived occupational mobility network in response to automation scenarios which increase labor demand for some occupations and decrease it for others. At the macro level, our model reproduces a key stylized fact in the labor market known as the Beveridge curve and provides new insights for explaining the curve's counter-clockwise cyclicality. At the micro level, our model provides occupation-specific estimates of changes in short and long-term unemployment corresponding to a given automation shock. We find that the network structure plays an important role in determining unemployment levels, with occupations in particular areas of the network having very few job transition opportunities. Such insights could be fruitfully applied to help design more efficient and effective policies aimed at helping workers adapt to the changing nature of the labor market.

In this paper we address three main objections of behavioral finance to the theory of rational finance, considered as anomalies the theory of rational finance cannot explain: Predictability of asset returns, The Equity Premium, (The Volatility Puzzle. We offer resolutions of those objections within the rational finance. We do not claim that those are the only possible explanations of the anomalies, but offer statistical models within the rational theory of finance which can be used without relying on behavioral finance assumptions when searching for explanations of those anomalies.

We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half. We provide an efficient procedure for transferring such uncertainties from the generator matrix of the Markov chain to the corresponding rating migration probabilities and, crucially, default probabilities.

For our second contribution, we assume access to the full (continuous) data set and propose a tractable and parsimonious self-exciting marked point processes model able to capture the non-Markovian effect of rating momentum. Compared to the Markov model, the non-Markov model yields higher probabilities of default in the investment grades, but also lower default probabilities in some speculative grades. Both findings agree with empirical observations and have clear practical implications.

We illustrate all methods using data from Moody's proprietary corporate credit ratings data set. Implementations are available in the R package ctmcd.

We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking portfolio must also be diverse in order to minimise risk -- a requirement which has only been dealt with by ad-hoc methods before. We introduce the first index tracking method that explicitly optimises both diversity and sparsity in a single joint framework. Diversity is realised by a regulariser based on pairwise similarity of assets, and we demonstrate that learning similarity from data can outperform some existing heuristics. Finally, we show that the way we model diversity leads to an easy solution for sparsity, allowing both constraints to be optimised easily and efficiently. we run out-of-sample backtesting for a long interval of 15 years (2003 -- 2018), and the results demonstrate the superiority of the proposed algorithm.

The emerging autonomous vehicles (AV) can either supplement the public transportation (PT) system or be a competitor with it. This paper focuses on this competition in a hypothetical scenario--"if both AV and PT operators are profit-oriented," and uses an ABM to quantitatively evaluate the system performance in this competition from the perspectives of four stakeholders--AV operator, PT operator, passengers, and public authority. In our model, AV operator updates its supply by changing fleet sizes while PT by adjusting headways, and both use heuristic approaches to update supply in order to increase profits. We implement the model in the first-mile scenario in Tampines. In four regulation scenarios--two by two combinations regarding whether AV and PT are allowed to change supplies--we find that since AV can release the bus operator from low-demand routes, the competition can lead to higher profits of both, and higher system efficiency, simultaneously, rather than a one-sided loss-gain result. For PT, after supply updates, spatially the services are concentrated to short feeder routes directly to the subway station, and temporally concentrated to peak hours. For passengers, the competition reduces their travel time but increases their travel costs. Nonetheless, the generalized travel cost is still reduced when counting the value of time. For system efficiency and sustainability, bus supply adjustment can increase the bus average load and reduce total PCE, while the AV supply adjustment shows the opposite effect. For policy implications, the paper suggests that PT should be allowed to optimize its supply strategies under specific operation goal constraints, and AV operation should be regulated to relieve its externality on the system, including limiting the number of licenses, operation time, and service areas, which makes AV operate like a complementary mode to PT.

Our paper aims to model supply and demand curves of electricity day-ahead auction in a parsimonious way. Our main task is to build an appropriate algorithm to present the information about electricity prices and demands with far less parameters than the original one. We represent each curve using mesh-free interpolation techniques based on radial basis function approximation. We describe results of this method for the day-ahead IPEX spot price of Italy.

Using an additional decade of CNLSY data, this study replicated and extended Deming's (2009) evaluation of Head Start's life-cycle skill formation impacts in three ways. Extending the measurement interval for Deming's adulthood outcomes, we found no statistically significant impacts on earnings and mixed evidence of impacts on other adult outcomes. Applying Deming's sibling comparison framework to more recent birth cohorts born to CNLSY mothers revealed mostly negative Head Start impacts. Combining all cohorts shows generally null impacts on school-age and early adulthood outcomes.

We analyze the welfare effects of voucher provision in the DC Opportunity Scholarship Program (OSP), a school voucher program in Washington, DC, that randomly allocated vouchers to students. To do so, we develop new discrete choice tools to show how to use data with random allocation of school vouchers to characterize what we can learn about the welfare benefits of providing a voucher of a given amount, as measured by the average willingness to pay for that voucher, and these benefits net of the costs of providing that voucher. A novel feature of our tools is that they allow specifying the relationship of the demand for the various schools with respect to prices to be entirely nonparametric or to be parameterized in a flexible manner, both of which do not necessarily imply that the welfare parameters are point identified. Applying our tools to the OSP data, we find that provision of the status-quo as well as a wide range of counterfactual voucher amounts has a positive net average benefit. We find these positive results arise due to the presence of many low-tuition schools in the program, removing these schools from the program can result in a negative net average benefit.

The paper proposes a new high-dimensional algorithm, the Groupwise Interpretable Basis Selection (GIBS) algorithm to estimate a new Adaptive Multi-Factor (AMF) asset pricing model, implied by the recently developed Generalized Arbitrage Pricing Theory, which relaxes the convention that the number of risk-factors is small. We first obtain an adaptive collection of basis assets and then simultaneously test which basis assets correspond to which securities. Since the collection of basis assets is quite large and highly correlated, high-dimension methods are used. The AMF model along with the GIBS algorithm is shown to have a significantly better fit than the Fama-French 5-factor model.

In time-series analysis, the term "lead-lag effect" is used to describe a delayed effect on a given time series caused by another time series. lead-lag effects are ubiquitous in practice and are specifically critical in formulating investment strategies in high-frequency trading. At present, there are three major challenges in analyzing the lead-lag effects. First, in practical applications, not all time series are observed synchronously. Second, the size of the relevant dataset and rate of change of the environment is increasingly faster, and it is becoming more difficult to complete the computation within a particular time limit. Third, some lead-lag effects are time-varying and only last for a short period, and their delay lengths are often affected by external factors. In this paper, we propose NAPLES (Negative And Positive lead-lag EStimator), a new statistical measure that resolves all these problems. Through experiments on artificial and real datasets, we demonstrate that NAPLES has a strong correlation with the actual lead-lag effects, including those triggered by significant macroeconomic announcements.

For randomized experiments with noncompliance, I propose a method to identify treatment effects without exclusion restrictions. It exploits a baseline survey that is commonly available in randomized experiments. I show the identification of the average treatment effect on the treated (ATT) and the local average treatment effect (LATE), assuming that a baseline variable maintains similar rank orders to the control outcome. I apply this strategy to a microcredit experiment with one-sided noncompliance to identify the ATT. I find that the instrumental variable (IV) estimate of log revenue is 2.2 times larger than my preferred estimate. Supplemental materials are available online.

Most cryptocurrencies rely on Proof-of-Work (PoW) "mining" for resistance to Sybil and double-spending attacks, as well as a mechanism for currency issuance. Hashcash PoW has successfully secured the Bitcoin network since its inception, however, as the network has expanded to take on additional value storage and transaction volume, Bitcoin PoW's heavy reliance on electricity has created scalability issues, environmental concerns, and systemic risks. Mining efforts have concentrated in areas with low electricity costs, creating single points of failure. Although PoW security properties rely on imposing a trivially verifiable economic cost on miners, there is no fundamental reason for it to consist primarily of electricity cost. The authors propose a novel PoW algorithm, Optical Proof of Work (oPoW), to eliminate energy as the primary cost of mining. Proposed algorithm imposes economic difficulty on the miners, however, the cost is concentrated in hardware (capital expense-CAPEX) rather than electricity (operating expenses-OPEX). The oPoW scheme involves minimal modifications to Hashcash-like PoW schemes, inheriting safety/security properties from such schemes.

Rapid growth and improvement in silicon photonics over the last two decades has led to the commercialization of silicon photonic co-processors (integrated circuits that use photons instead of electrons to perform specialized computing tasks) for low-energy deep learning. oPoW is optimized for this technology such that miners are incentivized to use specialized, energy-efficient photonics for computation. Beyond providing energy savings, oPoW has the potential to improve network scalability, enable decentralized mining outside of low electricity cost areas, and democratize issuance. Due to the CAPEX dominance of mining costs, oPoW hashrate will be significantly less sensitive to underlying coin price declines.

We address the problem of optimally exercising American options based on the assumption that the underlying stock's price follows a Brownian bridge whose final value coincides with the strike price. In order to do so, we solve the discounted optimal stopping problem endowed with the gain function $G(x) = (S - x)^+$ and a Brownian bridge whose final value equals $S$. These settings came up as a first approach of optimally exercising an option within the so-called "stock pinning" scenario. The optimal stopping boundary for this problem is proved to be the unique solution, up to certain regularity conditions, of an integral equation, which is then numerically solved by an algorithm hereby exposed. We face the case where the volatility is unspecified by providing an estimated optimal stopping boundary that, alongside with pointwise confidence intervals, provide alternative stopping rules. Finally, we demonstrate the usefulness of our method within the stock pinning scenario through a comparison with the optimal exercise time based on a geometric Brownian motion. We base our comparison on the contingent claims and the 5-minutes intraday stock price data of Apple and IBM for the period 2011-2018. Supplementary materials with the main proofs and auxiliary lemmas are available online.

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible because we are able to find an explicit solution to the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if state constraints are present. To the best of our knowledge, this is the first infinite dimensional generalization of Merton's optimal portfolio problem for which explicit solutions can be found. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.

Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show that this market factor is the index resulting from the daily compounding of a weighted average of implied-volatility returns, with weights based on the options' open interest (OI) and Vega. The authors also analyze the singular vectors derived from the tensor structure of the implied volatilities of S&P500 constituents, and find evidence indicating that some type of OI and Vega-weighted index should be one of at least two significant factors in this market.

In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the corresponding convergence rates.

The greatest harm from highway robbers lies not in seized wallets but in inhibited travel. Similarly, incentives for tax-reducing strategies put much sand in the wheels of the economy. Demands to replace our monumental tax code with a simple, graceful one that does not distort economic incentives heat up periodically in political debate, but such dreams never materialize. A FUNDAMENTAL obstacle, not yet well understood in the economic literature, is the impossibility of objectively evaluating the tax base -- assets, income, etc. One can see this even in toy examples, say, trying to assess the value of a position in chess: great masters' assessments will all differ. Here computer theory can add an insight not provided by classical economics tools.

A way around is to avoid evaluations by expressing the tax in natural units, not in cash. For publicly traded corporations, these could be corporate shares. I discuss a simple (postcard-sized in ALL details) corporate tax system that avoids ANY distortion of incentives. (Tax tools MEANT to influence corporate policies should be set as explicit separate taxes or credits, open to public scrutiny, not hidden between lines of an incomprehensible tax code.) Roughly, the~system is to periodically take a t*i fraction of shares to auction, where t is the tax rate, i is the interest rate. It replaces all income taxes on publicly traded corporations, their subsidiaries, and shareholders.

The interest rate is defined via specially designed bonds, so that the whole system can be shown PRECISELY equivalent to a flat tax on INVESTMENT RETURN. Note that taxing the return DIRECTLY is impossible: it would invite manipulation of stock market~prices. The main feature is that nothing corporations and investors do can change their tax (t*i fraction of shares), so they would do business exactly the SAME WAY they would WITHOUT TAXES.