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In multi-period trading with realistic market impact, determining the dynamic trading strategy that optimizes expected utility of final wealth is a hard problem. In this paper we show that, with an appropriate choice of the reward function, reinforcement learning techniques (specifically, Q-learning) can successfully handle the risk-averse case. We provide a proof of concept in the form of a simulated market which permits a statistical arbitrage even with trading costs. The Q-learning agent finds and exploits this arbitrage.

I review 150 textbooks on corporate finance and valuation published between 1979 and 2009 by authors such as Brealey, Myers, Copeland, Damodaran, Merton, Ross, Bruner, Bodie, Penman, Arzac… and find that their recommendations regarding the equity premium range from 3% to 10%, and that 51 books use different equity premia in various pages. The 5-year moving average has declined from 8.4% in 1990 to 5.7% in 2008 and 2009.Some confusion arises from not distinguishing among the four concepts that the phrase equity premium designates: the Historical, the Expected, the Implied and the Required equity premium (incremental return of a diversified portfolio over the risk-free rate required by an investor). 129 of the books identify Expected and Required equity premium and 82 identify Expected and Historical equity premium.Finance textbooks should clarify the equity premium by incorporating distinguishing definitions of the four different concepts and conveying a clearer message about their sensible magnitudes.

The efficient markets hypothesis (EMH) maintains that market prices fully reflect all available information. Developed independently by Paul A. Samuelson and Eugene F. Fama in the 1960s, this idea has been applied extensively to theoretical models and empirical studies of financial securities prices, generating considerable controversy as well as fundamental insights into the price-discovery process. The most enduring critique comes from psychologists and behavioural economists who argue that the EMH is based on counterfactual assumptions regarding human behaviour, that is, rationality. Recent advances in evolutionary psychology and the cognitive neurosciences may be able to reconcile the EMH with behavioural anomalies.

We examine the performance of the off-shore hedge fund industry over the period 1989 through 1995 using a database that includes both defunct and currently operating funds. The industry is characterized by high attrition rates of funds, low covariance with the U.S. stock market, evidence consistent with positive risk-adjusted returns over the time, but little evidence of differential manager skil.

Spanish Abstract: Este documento contiene 205 preguntas que me han formulado en los últimos años alumnos, antiguos alumnos y otras personas (jueces, árbitros, clientes,…). Se han recopilado para ayudar al lector a recordar, aclarar, reforzar, matizar y, en su caso, discutir, conceptos útiles en finanzas. La mayoría de las preguntas tienen una respuesta clara, pero otras son matizables. Las preguntas se agrupan en 12 apartados: contabilidad y finanzas, flujos, endeudamiento, tasas de descuento, valoración, transacciones, divisas, bolsa e inversión, intangibles, creación de valor, eficiencia, noticias de prensa y crisis 2007-…. A todas las preguntas les sigue una respuesta breve. El anexo 1 contiene un índice de términos y 150 preguntas de autoevaluación. El anexo 2 contiene comentarios a versiones anteriores de este documento. Engish Abstract: This document has 205 questions from students, alumnae and other persons (judges, lawyers, clients, etc.). They are useful to clarify some useful concepts in finance. Most of the questions have a clear answer. The document also has short answers to all questions.

We provide practical insights for investors seeking exposure to the growing cryptocurrency space. Today, crypto is much more than just bitcoin, which historically dominated the space but accounted for just a 21% share of total crypto trading volume in 2021. We discuss a wide variety of tokens, highlighting both their functionality and their investment properties. We critically compare popular valuation methods. We contrast buy-and-hold investing with more active styles. We only deem return data from 2017 representative, but the use of intraday data boosts statistical power. Underlying crypto performance has been notoriously volatile, but volatility-targeting methods are effective at controlling risk, and trend-following strategies have performed well. Crypto assets display a low correlation with traditional risky assets in normal times, but the correlation also rises in the left tail of these risky assets. Finally, we detail important custody and regulatory considerations for institutional investors.[All data updated through June 30, 2022]

This paper examines the economic consequences of mandatory IFRS reporting around the world. We analyze the effects on market liquidity, cost of capital and Tobin's q in 26 countries using a large sample of firms that are mandated to adopt IFRS. We find that, on average, market liquidity increases around the time of the introduction of IFRS. We also document a decrease in firms' cost of capital and an increase in equity valuations, but only if we account for the possibility that the effects occur prior to the official adoption date. Partitioning our sample, we find that the capital-market benefits occur only in countries where firms have incentives to be transparent and where legal enforcement is strong, underscoring the central importance of firms' reporting incentives and countries' enforcement regimes for the quality of financial reporting. Comparing mandatory and voluntary adopters, we find that the capital market effects are most pronounced for firms that voluntarily switch to IFRS, both in the year when they switch and again later, when IFRS become mandatory. While the former result is likely due to self-selection, the latter result cautions us to attribute the capital-market effects for mandatory adopters solely or even primarily to the IFRS mandate. Many adopting countries have made concurrent efforts to improve enforcement and governance regimes, which likely play into our findings. Consistent with this interpretation, the estimated liquidity improvements are smaller in magnitude when we analyze them on a monthly basis, which is more likely to isolate IFRS reporting effects.

A new factor model consisting of the market factor, an investment factor, and a return-on-equity factor is a good start to understanding the cross-section of expected stock returns. Firms will invest a lot when their profitability is high and the cost of capital is low. As such, controlling for profitability, investment should be negatively correlated with expected returns, and controlling for investment, profitability should be positively correlated with expected returns. The new three-factor model reduces the magnitude of the abnormal returns of a wide range of anomalies-based trading strategies, often to insignificance. The model's performance, combined with its economic intuition, suggests that it can be used to obtain expected return estimates in practice.

We study the performance of nearly 1400 U.S. buyout and venture capital funds using a new dataset from Burgiss. We find better buyout fund performance than has previously been documented – performance consistently has exceeded that of public markets. Outperformance versus the S&P 500 averages 20% to 27% over a fund’s life and more than 3% annually. Venture capital funds outperformed public equities in the 1990s, but underperformed in the 2000s. Our conclusions are robust to various indices and risk controls. Performance in Cambridge Associates and Preqin is qualitatively similar to that in Burgiss, but is lower in Thomson Venture Economics.

Value investing has been a part of the investment lexicon for at least the better part of a century. In particular the diversified systematic “value factor” or “value effect” has been studied extensively since at least the 1980s. Yet, there are still many areas of confusion about value investing. In this article we aim to clarify many of these matters, focusing in particular on the diversified systematic value strategy, but also exploring how this strategy relates to its more concentrated implementation. We highlight many points about value investing and attempt to prove or disprove each of them, referencing an extensive academic literature and performing simple tests based on easily accessible, industry-standard public data.

The first global blockchain benchmarking study presents a systematic and comprehensive picture of a rapidly evolving industry, examining how blockchain and distributed ledger technology (DLT) are being used in the public sector and enterprise. The study analysed non-publicly available data gathered from over 200 central banks, other public sector institutions, DLT start-ups, and established companies. Findings from the study include which protocols central banks and are testing (57% of surveyed central banks are experimenting with the Ethereum codebase), targeted use cases, emerging revenue models, timing of deployment, and key challenges.

We examine the effectiveness of applying a trend following methodology to global asset allocation between equities, bonds, commodities and real estate. The application of trend following offers a substantial improvement in risk-adjusted performance compared to traditional buy-and-hold portfolios. We also find it to be a superior method of asset allocation than risk parity. We believe the discipline of trend following overcomes many of the behavioural biases investors succumb to, such as regret and herding. The other side of behavioural biases is that they may be exploited by investors: the clearest example of this is momentum investing where herding leads to continuation of returns and has been identified across many asset classes. Also, momentum and trend following have often been used interchangeably although the former is a relative concept and the latter absolute. By combining the two we find that one can achieve the higher return levels associated with momentum portfolios but with much reduced volatility and drawdowns due to trend following. We compare the performance of selected strategies using measures based on the utility function of a representative investor. These results reinforce the superiority of combining trend following with momentum strategies. We observe that a flexible asset allocation strategy that allocates capital to the best performing instruments irrespective of asset class enhances this further.

Many quantitative firms have suffered substantial losses as a result of the COVID-19 selloff. In this note we highlight three lessons that quantitative researchers could learn.

We reconsider the idea of trend-based predictability using methods that flexibly learn price patterns that are most predictive of future returns, rather than testing hypothesized or pre-specified patterns (e.g., momentum and reversal). Our raw predictor data are images---stock-level price charts---from which we elicit the price patterns that best predict returns using machine learning image analysis methods. The predictive patterns we identify are largely distinct from trend signals commonly analyzed in the literature, give more accurate return predictions, translate into more profitable investment strategies, and are robust to a battery of specification variations. They also appear context-independent: Predictive patterns estimated at short time scales (e.g., daily data) give similarly strong predictions when applied at longer time scales (e.g., monthly), and patterns learned from US stocks predict equally well in international markets.

Value and momentum ubiquitously generate abnormal returns for individual stocks within several countries, across country equity indices, government bonds, currencies, and commodities. We study jointly the global returns to value and momentum and explore their common factor structure. We find that value (momentum) in one asset class is positively correlated with value (momentum) in other asset classes, and value and momentum are negatively correlated within and across asset classes. Liquidity risk is positively related to value and negatively to momentum, and its importance increases over time, particularly following the liquidity crisis of 1998. These patterns emerge from the power of examining value and momentum everywhere simultaneously and are not easily detectable when examining each asset class in isolation.

Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo simulation methods for this class of models. This paper considers several new algorithms for time-discretization and Monte Carlo simulation of Heston-type stochastic volatility models. The algorithms are based on a careful analysis of the properties of affine stochastic volatility diffusions, and are straightforward and quick to implement and execute. Tests on realistic model parameterizations reveal that the computational efficiency and robustness of the simulation schemes proposed in the paper compare very favorably to existing methods.

Several papers argue that financial economics faces a replication crisis because the majority of studies cannot be replicated or are the result of multiple testing of too many factors. We develop and estimate a Bayesian model of factor replication, which leads to different conclusions. The majority of asset pricing factors: (1) can be replicated, (2) can be clustered into 13 themes, the majority of which are significant parts of the tangency portfolio, (3) work out of sample in a new large data set covering 93 countries, and (4) have evidence that is strengthened (not weakened) by the large number of observed factors.

We study the out-of-sample and post-publication return-predictability of 97 variables that academic studies show to predict cross-sectional stock returns. Portfolio returns are 26% lower out-of-sample and 58% lower post-publication. The out-of-sample decline is an upper bound estimate of data mining effects. We estimate a 32% (58% - 26%) lower return from publication-informed trading. Post-publication declines are greater for predictors with higher in-sample returns, and returns are higher for portfolios concentrated in stocks with high idiosyncratic risk and low liquidity. Predictor portfolios exhibit post-publication increases in correlations with other published-predictor portfolios. Our findings suggest investors learn about mispricing from academic publications.

The equity risk premium is the price of risk in equity markets and is a key input in estimating costs of equity and capital in both corporate finance and valuation. Given its importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating the equity risk premium, historical returns are used, with the difference in annual returns on stocks versus bonds, over a long period, comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.

According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, especially uncertainty about the expected return. The same uncertainties reduce desired stock allocations of long-horizon investors contemplating target-date funds.

Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating costs of equity and capital in both corporate finance and valuation. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time period comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. We also look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.

What would you do if you were invited to play a game where you were given $25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61 young, quantitatively trained men and women to play this game. The results, in a nutshell, were that the majority of these 61 players didn’t place their bets very well, displaying a broad panoply of behaviorial and cognitive biases. About 30% of the subjects actually went bust, losing their full $25 stake. We also discuss optimal betting strategies, valuation of the opportunity to play the game and its similarities to investing in the stock market. The main implication of our study is that people need to be better educated and trained in how to approach decision making under uncertainty. If these quantitatively trained players, playing the simplest game we can think of involving uncertainty and favourable odds, didn’t play well, what hope is there for the rest of us when it comes to playing the biggest and most important game of all: investing our savings? In the words of Ed Thorp, who gave us helpful feedback on our research: ‘This is a great experiment for many reasons. It ought to become part of the basic education of anyone interested in finance or gambling.’

We propose a theory in which each stock’s environmental, social, and governance (ESG) score plays two roles: 1) providing information about firm fundamentals and 2) affecting investor preferences. The solution to the investor’s portfolio problem is characterized by an ESG-efficient frontier, showing the highest attainable Sharpe ratio for each ESG level. The corresponding portfolios satisfy four-fund separation. Equilibrium asset prices are determined by an ESG-adjusted capital asset pricing model, showing when ESG increases or lowers the required return. Combining several large data sets, we compute the empirical ESG-efficient frontier and show the costs and benefits of responsible investing. Finally, we test our theory’s predictions using commercial ESG measures, governance, sin stocks, and carbon emissions.

Are market experts prone to heuristics, and if so, do they transfer across closely related domains—buying and selling? We investigate this question using a unique dataset of institutional investors with portfolios averaging $573 million. A striking finding emerges: while there is clear evidence of skill in buying, selling decisions underperform substantially—even relative to random selling strategies. This holds despite the similarity between the two decisions in frequency, substance and consequences for performance. Evidence suggests that an asymmetric allocation of cognitive resources such as attention can explain the discrepancy: we document a systematic, costly heuristic process when selling but not when buying.

We provide some new tools to evaluate trading strategies. When it is known that many strategies and combinations of strategies have been tried, we need to adjust our evaluation method for these multiple tests. Sharpe Ratios and other statistics will be overstated. Our methods are simple to implement and allow for the real-time evaluation of candidate trading strategies. Related papers are: Backtesting as well as ... and the Cross-Section of Expected Returns.