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In this paper we update our 2006 white paper “A Quantitative Approach to Tactical Asset Allocation” with new data from the 2008-2012 period. How well did the purpose of the original paper – to present a simple quantitative method that improves the risk-adjusted returns across various asset classes – hold up since publication? Overall, we find that the models have performed well in real-time, achieving equity like returns with bond like volatility and drawdowns. We also examine the effects of departures from the original system including adding more asset classes, introducing various portfolio allocations, and implementing alternative cash management strategies.

We provide detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility (as an asset class), real estate, distressed assets, cash, cryptocurrencies, miscellany (such as weather, energy, inflation), global macro, infrastructure, and tax arbitrage. Some strategies are based on machine learning algorithms (such as artificial neural networks, Bayes, k-nearest neighbors). We also give: source code for illustrating out-of-sample backtesting with explanatory notes; around 2,000 bibliographic references; and over 900 glossary, acronym and math definitions. The presentation is intended to be descriptive and pedagogical. This is the complete version of the book.

Market efficiency survives the challenge from the literature on long-term return anomalies. Consistent with the market efficiency hypothesis that the anomalies are chance results, apparent over-reaction to information is about as common as under-reaction. And post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal. Consistent with the market efficiency prediction that apparent anomalies can also be due to methodology, the anomalies are sensitive to the techniques used to measure them, and many disappear with reasonable changes in technique.

We survey the nascent literature on machine learning in the study of financial markets. We highlight the best examples of what this line of research has to offer and recommend promising directions for future research. This survey is designed for both financial economists interested in grasping machine learning tools, as well as for statisticians and machine learners seeking interesting financial contexts where advanced methods may be deployed.

The purpose of this paper is to present simple quantitative methods that improve risk-adjusted returns for investing in US equity sectors and global asset class portfolios. A relative strength model is tested on the French-Fama US equity sector data back to the 1920s that results in increased absolute returns with equity-like risk. The relative strength portfolios outperform the buy and hold benchmark in approximately 70% of all years and returns are persistent across time. The addition of a trend-following parameter to dynamically hedge the portfolio decreases both volatility and drawdown. The relative strength model is then tested across a portfolio of global asset classes with supporting results.

We build a simple, but powerful and intuitive, model for when a hockey coach should pull the goalie when trailing. When the model reports that the coaches aren’t doing it nearly early enough, we then ask why, and take away some key lessons for portfolio and risk management, and business in general.

 We investigate whether large language models (LLMs) can successfully perform financial statement analysis in a way similar to a professional human analyst. We provide standardized and anonymous financial statements to GPT4 and instruct the model to analyze them to determine the direction of firms' future earnings. Even without narrative or industry-specific information, the LLM outperforms financial analysts in its ability to predict earnings changes directionally. The LLM exhibits a relative advantage over human analysts in situations when the analysts tend to struggle. Furthermore, we find that the prediction accuracy of the LLM is on par with a narrowly trained state-of-the-art ML model. LLM prediction does not stem from its training memory. Instead, we find that the LLM generates useful narrative insights about a company's future performance. Lastly, our trading strategies based on GPT's predictions yield a higher Sharpe ratio and alphas than strategies based on other models. Our results suggest that LLMs may take a central role in analysis and decision-making.

We examine the potential of ChatGPT and other large language models (LLMs) to predict stock market returns using news. Categorizing headlines with ChatGPT as positive, negative, or neutral for companies' stock prices, we document a significant correlation between ChatGPT scores and subsequent daily stock returns, outperforming traditional methods. Basic models like GPT-1 and BERT cannot accurately forecast returns, indicating return forecasting is an emerging capacity of more complex LLMs, which deliver higher Sharpe ratios. We explain these puzzling return predictability patterns by testing implications from economic theories involving information diffusion frictions, limits to arbitrage, and investor sophistication. Predictability strengthens among smaller stocks and following negative news, consistent with these theories. Only advanced LLMs maintain accuracy when interpreting complex news and press releases. Finally, we present an interpretability technique to evaluate LLMs' reasoning. Overall, incorporating advanced language models into investment decisions can improve prediction accuracy and trading performance.

This paper presents a detailed anatomy of the nearly sevenfold run-up in the price of Tesla stock between March 22, 2013 and February 26, 2014 with the goal of attempting to determine the role played by investor sentiment. Tesla offers a unique opportunity in this context because the run-up was on the order of magnitude experienced by some of the most volatile technology stocks, but Tesla operates in an industry, automotive manufacturing, and a potential industry, battery construction, that are mature and are populated by established competitors. This makes it possible to construct discounted cash flow valuation models that are anchored on established fundamentals. On the basis of these models, in conjunction with a detailed event study and analysis of institutional stock holdings and short sales data, we conclude that the run-up cannot be explained as a rational reaction to fundamental information. Instead, we conclude that at the end of the run-up the stock was overvalued by approximately 150 percent. In our view, the case study provides support for Summers assertion the price and rational value can diverge significantly for prolonged periods of time.

Considerable attention has recently been given to general equilibrium models of the pricing of capital assets. Of these, perhaps the best known is the mean-variance formulation originally developed by Sharpe (1964) and Treynor (1961), and extended and clarified by Lintner (1965a; 1965b), Mossin (1966), Fama (1968a; 1968b), and Long (1972). In addition Treynor (1965), Sharpe (1966), and Jensen (1968; 1969) have developed portfolio evaluation models which are either based on this asset pricing model or bear a close relation to it. In the development of the asset pricing model it is assumed that (1) all investors are single period risk-averse utility of terminal wealth maximizers and can choose among portfolios solely on the basis of mean and variance, (2) there are no taxes or transactions costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest. The main result of the model is a statement of the relation between the expected risk premiums on individual assets and their "systematic risk." Our main purpose is to present some additional tests of this asset pricing model which avoid some of the problems of earlier studies and which, we believe, provide additional insights into the nature of the structure of security returns. The evidence presented in Section II indicates the expected excess return on an asset is not strictly proportional to its B, and we believe that this evidence, coupled with that given in Section IV, is sufficiently strong to warrant rejection of the traditional form of the model given by (1). We then show in Section III how the cross-sectional tests are subject to measurement error bias, provide a solution to this problem through grouping procedures, and show how cross-sectional methods are relevant to testing the expanded two-factor form of the model. We show in Section IV that the mean of the beta factor has had a positive trend over the period 1931-65 and was on the order of 1.0 to 1.3% per month in the two sample intervals we examined in the period 1948-65. This seems to have been significantly different from the average risk-free rate and indeed is roughly the same size as the average market return of 1.3 and 1.2% per month over the two sample intervals in this period. This evidence seems to be sufficiently strong enough to warrant rejection of the traditional form of the model given by (1). In addition, the standard deviation of the beta factor over these two sample intervals was 2.0 and 2.2% per month, as compared with the standard deviation of the market factor of 3.6 and 3.8% per month. Thus the beta factor seems to be an important determinant of security returns.

This paper investigates whether Tether, a digital currency pegged to the U.S. dollar, influenced Bitcoin and other cryptocurrency prices during the 2017 boom. Using algorithms to analyze blockchain data, we find that purchases with Tether are timed following market downturns and result in sizable increases in Bitcoin prices. The flow is attributable to one entity, clusters below round prices, induces asymmetric autocorrelations in Bitcoin, and suggests insufficient Tether reserves before month-ends. Rather than demand from cash investors, these patterns are most consistent with the supply-based hypothesis of unbacked digital money inflating cryptocurrency prices.

Over the past three decades, a sustained surge in inflation has been absent in developed markets. As a result, investors face the challenge of having limited experience and no recent data to guide the repositioning of their portfolios in the face of heighted inflation risk. We provide some insight by analyzing both passive and active strategies across a variety of asset classes for the U.S., U.K., and Japan over the past 95 years. Unexpected inflation is bad news for traditional assets, such as bonds and equities, with local inflation having the greatest effect. Commodities have positive returns during inflation surges but there is considerable variation within the commodity complex. Among the dynamic strategies, we find that trend-following provides the most reliable protection during important inflation shocks. Active equity factor strategies also provide some degree of hedging ability. We also provide analysis of alternative asset classes such as fine art and discuss the economic rationale for including cryptocurrencies as part of a strategy to protect against inflation.

Standard formulas for valuing the equity of going concerns require prediction of payoffs "to infinity" but practical analysis requires that they be predicted over finite horizons. This truncation inevitably involves (often troublesome) "terminal value" calculations. This paper contrasts dividend discount techniques, discounted cash flow analysis, and techniques based on accrual earnings when applied to a finite-horizon valuation. Valuations based on average ex-post payoffs over various horizons, with and without terminal value calculations, are compared with (ex-ante) market prices to give an indication of the error introduced by each technique in truncating the horizon. Comparisons of these errors show that accrual earnings techniques dominate free cash flow and dividend discounting approaches. Further, the relevant accounting features of techniques that make them less than ideal for finite horizon analysis are discovered. Conditions where a given technique requires particularly long forecasting horizons are identified and the performance of the alternative techniques under those conditions is examined.

Using loan-level data, we analyze the quality of subprime mortgage loans by adjusting their performance for differences in borrower characteristics, loan characteristics, and macroeconomic conditions. We find that the quality of loans deteriorated for six consecutive years before the crisis and that securitizers were, to some extent, aware of it. We provide evidence that the rise and fall of the subprime mortgage market follows a classic lending boom-bust scenario, in which unsustainable growth leads to the collapse of the market. Problems could have been detected long before the crisis, but they were masked by high house price appreciation between 2003 and 2005.

In 2013, a paper by Google DeepMind kicked off an explosion in Deep Reinforcement Learning (DRL), for games. In this talk, we show that DRL can also be applied to portfolio allocation given various tricks and adaptation specific to non stationary data in finance. We present in particular how to Boost DRL.

Value stocks have higher returns than growth stocks in markets around the world. For 1975-95, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.60% per year, and value stocks outperform growth stocks in 12 of 13 major markets. An international CAPM cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns.

Spanish Abstract: La valoración de una empresa es un ejercicio de sensatez que requiere unos pocos conocimientos técnicos y mejora con la experiencia. Ambos (sensatez y conocimientos técnicos) son necesarios para no perder de vista: ¿qué se está haciendo?, ¿porqué se está haciendo la valoración de determinada manera? y ¿para qué y para quién se está haciendo la valoración? Casi todos los errores en valoración se deben a no contestar adecuadamente a alguna de estas preguntas, esto es, a falta de conocimientos o a falta de sensatez (o a la falta de ambos).Los métodos conceptualmente “correctos” para valorar empresas con expectativas de continuidad son los basados en el descuento de flujos de fondos: consideran a la empresa como un ente generador de flujos de fondos y, por ello, sus acciones y su deuda son valorables como otros activos financieros. Otro método que tiene lógica y consistencia es el valor de liquidación, cuando se prevé liquidar la empresa. Lógicamente, el valor de las acciones será el mayor entre el valor de liquidación y el valor por descuento de flujos. Comentamos brevemente otros métodos porque - aunque son conceptualmente “incorrectos” y carecen de sentido en la mayoría de los casos - se siguen utilizando con frecuencia. En ciertos casos, los múltiplos pueden utilizarse como aproximación (si se requiere una valoración rápida o si los cash flows son muy inciertos) o como contraste del valor obtenido por descuento de flujos.English Abstract: I describe the four main groups comprising the most widely used company valuation methods: balance sheet-based methods, income statement-based methods, mixed methods, and cash flow discounting-based methods. The methods that are conceptually correct are those based on cash flow discounting. We briefly comment on other methods since - even though they are conceptually incorrect - they continue to be used frequently. I also present a real-life example to illustrate the valuation of a company as the sum of the value of different businesses, which is usually called the break-up value. I finish the paper showing the most common errors in valuations: a list that contains the most common errors that the author has detected in the more than one thousand valuations he has had access to in his capacity as business consultant or teacher.

Momentum is the premier market anomaly. It is nearly universal in its applicability. This paper examines multi-asset momentum with respect to what can make it most effective for momentum investors. We show that both absolute and relative momentum can enhance returns, but that absolute momentum does far more to lessen volatility and drawdown. We see that combining absolute and relative momentum gives the best results.

Using leverage to magnify performance is an idea that has enticed investors and traders throughout history. The critical question of when to employ leverage and when to reduce risk, though, is not often addressed. We establish that volatility is the enemy of leverage and that streaks in performance tend to be beneficial to using margin. The conditions under which higher returns would be achieved from using leverage, then, are low volatility environments that are more likely to experience consecutive positive returns. We find that Moving Averages are an effective way to identify such environments in a systematic fashion. When the broad U.S. equity market is above its Moving Average, stocks tend to exhibit lower than average volatility going forward, higher average daily performance, and longer streaks of positive returns. When below its Moving Average, the opposite tends to be true, as volatility often rises, average daily returns are lower, and streaks in positive returns become less frequent. Armed with this finding, we developed a strategy that employs leverage when the market is above its Moving Average and deleverages (moving to Treasury bills) when the market is below its Moving Average. This strategy shows better absolute and risk-adjusted returns than a comparable buy and hold unleveraged strategy as well as a constant leverage strategy. The results are robust to various leverage amounts, Moving Average time periods, and across multiple economic and financial market cycles.

Spanish Abstract: El libro (7ª edición) está compuesto por 16 capítulos. Cada uno de ellos puede descargarse gratuitamente en el link que aparece en el documento.El libro proporciona al lector a) los conocimientos necesarios para comprender y utilizar los distintos métodos de valoración; b) las herramientas necesarias para valorar cualquier empresa por compleja que sea; y c) criterios para enjuiciar cualquier valoración de una empresa. Para ayudar al lector en la asimilación de los conceptos, el libro contiene figuras, tablas, ejemplos, y comentarios de lectores a los distintos capítulos.English Abstract: This document contains the index of the chapters of a book (Company Valuation and Common Sense) that may be freely downloaded.It highlights the differences among the cash flows used in valuation (equity cash flow, debt cash flow, free cash flow, capital cash flow) and the differences among the discount rates used in valuation (required return to equity, WACC, required return to debt, WACC before taxes). It highlights also the differences among four related concepts: expected return, required return, historical return and implicit return.

Investors have seen countless charts of US stock market performance which start in 1926 and end near the present. But US trading long predates 1926, and the foreshortened perspective that results from a focus on post-1926 data can be misleading. To compound the problem, visual and arithmetic frailties, as catalogued in behavioral finance, make it difficult for investors to draw appropriate inferences from long-term records of performance. As a partial corrective, this paper displays a novel set of charts, with some rooted in the 19th rather than the 20th century, and others ending well before the present. The goal is to challenge shibboleths about the expected outcomes of buy-and-hold stock market investing, and to raise questions about the expected performance of stocks versus bonds over long periods. [This paper has been partially replaced by later work. See revision notes that follow this abstract.]

This research evaluates the fundamental causes of the current financial crisis. Close financial analysis indicates that theoretical modeling based on unrealistic assumptions led to serious problems in mispricing in the massive unregulated market for credit default swaps that exploded upon catalytic rises in residential mortgage defaults. Recent academic research implies solutions to the crisis that are appraised to be far less costly than a bailout of investors who made poor financial decisions with respect to credit analysis.

This paper shows 10 valuation methods based on equity cash flow; free cash flow; capital cash flow; APV (Adjusted Present Value); business’s risk-adjusted free cash flow and equity cash flow; risk-free rate-adjusted free cash flow and equity cash flow; economic profit; and EVA.All 10 methods always give the same value. This result is logical, as all the methods analyze the same reality under the same hypotheses; they differ only in the cash flows or parameters taken as the starting point for the valuation.The disagreements among the various theories of firm valuation arise from the calculation of the value of the tax shields (VTS). The paper shows and analyses 9 different theories on the calculation of the VTS, lists the most important assumptions and valuation equations according to each of these theories, and provides an example in which the VTS of a company with debt of 1,500 goes from zero to 745.

While researchers in the asset management industry have mostly focused on techniques based on financial and risk planning techniques like Markowitz efficient frontier, minimum variance, maximum diversification or equal risk parity, in parallel, another community in machine learning has started working on reinforcement learning and more particularly deep reinforcement learning to solve other decision making problems for challenging task like autonomous driving, robot learning, and on a more conceptual side games solving like Go. This paper aims to bridge the gap between these two approaches by showing Deep Reinforcement Learning (DRL) techniques can shed new lights on portfolio allocation thanks to a more general optimization setting that casts portfolio allocation as an optimal control problem that is not just a one-step optimization, but rather a continuous control optimization with a delayed reward. The advantages are numerous: (i) DRL maps directly market conditions to actions by design and hence should adapt to changing environment, (ii) DRL does not rely on any traditional financial risk assumptions like that risk is represented by variance, (iii) DRL can incorporate additional data and be a multi inputs method as opposed to more traditional optimization methods. We present on an experiment some encouraging results using convolution networks.

Recent studies have shown that transformers can model high-dimensional distributions of semantic concepts at scale, opening up the intriguing possibility of formalizing sequential decision-making problems as reinforcement learning (RL). New research from a UC Berkeley, Facebook AI Research and Google Brain explores whether generative trajectory modelling — i.e. modelling the joint distribution of a sequence of states, actions, and rewards — could serve as a replacement for conventional RL algorithms. We present a paper review of this research