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Machine learning is an increasingly important and controversial topic in quantitative finance. A lively debate persists as to whether machine learning techniques can be practical investment tools. Although machine learning algorithms can uncover subtle, contextual and non-linear relationships, overfitting poses a major challenge when trying to extract signals from noisy historical data. In this article, we describe some of the basic concepts surrounding machine leaning and provide a simple example of how investors can use machine learning techniques to forecast the cross-section of stock returns while limiting the risk of overfitting.

Spanish Abstract: Este documento resume 1.502 respuestas a una encuesta por realizada a directivos de empresas, a analistas y a profesores de universidad. Los resultados más relevantes de la encuesta son: gran dispersión de las repuestas (los profesores utilizan primas entre 3 y 8%, los analistas entre 2 y 11,9%, y las empresas entre 1,5 y 15%); un elevado número de empresas no utilizan la prima de riesgo del mercado (bastantes de ellas utilizan un WACC mínimo, una TIR mínima... otras utilizan criterios como ebitda/ventas, PER…); la prima promedio utilizada por las empresas (6,1%) es superior a la utilizada por los profesores (5,5%) y a la utilizada por los analistas (5,6%); muchos profesores y directivos justifican la prima que utilizan con libros y artículos publicados (aunque con la misma fuente se utilizan primas de mercado muy diferentes). English Abstract: We analyze the 1,502 answers of a recent survey of executives, analysts and finance professors. We present the required equity premium used for Spain in 2011 by 930 of them and their comments. The range of the professors goes from 3% to 8% (average 5.5%); the range of the analysts goes from 2% to 11.9% (average 5.6%); and the range of the executives goes from 1.5% to 15% (average 6.1%). We also present comments from professors, executives and analysts that do not use any required equity premium.

Green assets delivered high returns in recent years. This performance reflects unexpectedly strong increases in environmental concerns, not high expected returns. German green bonds outperformed their higher-yielding non-green twins as the "greenium" widened, and U.S. green stocks outperformed brown as climate concerns strengthened. Despite that outperformance, we estimate lower expected returns for green stocks than for brown, consistent with theory. We estimate expected returns in two ways: ex ante, using implied costs of capital, and ex post, using realized returns purged of shocks from climate concerns and earnings. A theoretically motivated green factor explains much of value stocks' recent underperformance.

Assets managed by hedge funds have grown faster over the last ten years than assets managed by mutual funds. Hedge funds and mutual funds perform the same economic function, but hedge funds are largely unregulated while mutual funds are tightly regulated. This paper compares the organization, performance, and risks of hedge funds and mutual funds. It then examines whether one can expect increasing convergence between these two investment vehicles and concludes that the performance gap between hedge funds and mutual funds will narrow, that regulatory developments will limit the flexibility of hedge funds, and that hedge funds will become more institutionalized.

The interplay between investors’ demand and providers’ incentives has shaped the evolution of exchange-traded funds (ETFs). While early ETFs invested in broad-based indexes and therefore offered diversification at low cost, more recent products track niche portfolios and charge high fees. Strikingly, over their first 5 years, specialized ETFs lose about 30% (risk-adjusted). This underperformance cannot be explained by high fees or hedging demand. Rather, it is driven by the overvaluation of the underlying stocks at the time of the launch. Our results are consistent with providers catering to investors’ extrapolative beliefs by issuing specialized ETFs that track attention grabbing themes.

Using a large hand-collected dataset from 2001 to 2006, we find that activist hedge funds in the U.S. propose strategic, operational, and financial remedies and attain success or partial success in two thirds of the cases. Hedge funds seldom seek control and in most cases are nonconfrontational. The abnormal return around the announcement of activism is approximately 7%, with no reversal during the subsequent year. Target firms experience increases in payout, operating performance, and higher CEO turnover after activism. Our analysis provides important new evidence on the mechanisms and effects of informed shareholder monitoring.

This study presents a new measure of uncertainty related to climate policy, based on news from major US newspapers. The Climate Policy Uncertainty (CPU) index spikes near important events related to climate policy, such as new emissions legislation, global strikes about climate change and President’s statements about climate policy, among other developments. Our findings suggest that climate policy uncertainty has a strong and negative effect on CO2 emissions.

Spanish Abstract: Se aborda la compra de Endesa en 2007. Este documento contiene una valoración de las acciones de Endesa y 3 artículos publicados en enero y febrero de 2006 sobre el valor de las acciones de Endesa. Finalmente, Enel y Acciona compraron el 92% de las acciones de Endesa a €41,3/acción en 2007. La evolución posterior de la cotización no parece justificar este precio. ¿Cómo se puede justificar? ¿Están contentos los accionistas de Enel con la compra de Endesa? English Abstract: This paper contains three articles published in the economic newspapers Expansion, La Gaceta de los Negocios and Cinco Dias about the value of the shares of Endesa. On January 6 and on January 18, 2006, we published that the value of a share of Endesa was 28 euro. On February 21, E.ON offered 27,5 euro per share of Endesa. The paper also contains the main hypothesis and inputs of our valuation.

The first global cryptocurrency benchmarking study presents a systematic and comprehensive picture of a rapidly evolving industry, illustrating how cryptocurrencies are being used, stored, transacted and mined. The study gathered non-public data from more than 100 cryptocurrency companies and over 30 individual cryptocurrency miners in 38 countries around the world via secure web-based questionnaires, capturing an estimated 75 per cent of the cryptocurrency industry. The study breaks down the cryptocurrency industry into four key sectors – exchanges, wallets, payments and mining. Key findings and highlights from the study include our estimate that over three million unique individuals are actively using cryptocurrency today, data on regulation and compliance practices and costs at firms, and a global map of cryptocurrency mining.

In this paper, we define and model forward risk-free term rates, which appear in the payoff definition of derivatives, and possibly cash instruments, based on the new interest-rate benchmarks that will be replacing IBORs globally. We show that the classical interest rate modeling framework can be naturally extended to describe the evolution of both the forward-looking (IBOR-like) and backward-looking (setting-in-arrears) term rates using the same stochastic process. In particular, we show that the extension of the popular LIBOR Market Model (LMM) to the backward-looking rates completes the model by providing additional information about the rate dynamics not accessible in the LMM.

We summarize some of our own past findings and place them in the context of the historical development of the idea of the equity risk premium and its empirical measurement by financial economists. In particular, we focus on how the theory of compensation for investment risk developed in the 20th century in tandem with the empirical analysis of historical investment performance. Finally, we update our study of the historical performance of the New York Stock Exchange over the period 1792 to the present, and include a measure of the U.S. equity risk premium over more than two centuries. This last section is based upon indices constructed from individual stock and dividend data collected over a decade of research at the Yale School of Management, and contributions by other scholars.

This presentation reviews the main reasons why investment strategies discovered through econometric methods fail. As a solution, it proposes the modernization of the statistical methods used by financial firms and academic authors.This material is part of Cornell University's ORIE 5256 graduate course at the School of Engineering.

The article tests for the presence of short-term continuation and long-term reversal in commodity futures prices. While contrarian strategies do not work, the article identifies 13 profitable momentum strategies that generate 9.38% average return a year. A closer analysis of the constituents of the long-short portfolios reveals that the momentum strategies buy backwardated contracts and sell contangoed contracts. The correlation between the momentum returns and the returns of traditional asset classes is also found to be low, making the commodity-based relative-strength portfolios excellent candidates for inclusion in well-diversified portfolios.

We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask prices. Our study reveals a linear relation between order flow imbalance and price changes, with a slope inversely proportional to the market depth. These results are shown to be robust to intraday seasonality effects, and stable across time scales and across stocks. This linear price impact model, together with a scaling argument, implies the empirically observed "square-root" relation between the magnitude of price moves and trading volume. However, the latter relation is found to be noisy and less robust than the one based on order flow imbalance. We discuss a potential application of order flow imbalance as a measure of adverse selection in limit order executions, and demonstrate how it can be used to analyze intraday volatility dynamics.

This paper uses a sample of 4,750 stock swap mergers, cash mergers, and cash tender offers during 1963 - 1998 to characterize the risk and return in risk arbitrage. For out-of-sample comparison, we also examine the risk/return profile for a sample of active risk arbitrage hedge funds during 1990 - 1998. Results from both samples indicate that risk arbitrage returns are positively correlated with market returns in severely depreciating markets but uncorrelated with market returns in flat and appreciating markets. This result suggests that returns to risk arbitrage are similar to those obtained from selling uncovered index put options. Although linear asset pricing models provide reasonable estimates of the excess returns in risk arbitrage, a contingent claims analysis that incorporates the non-linearity in returns provides a more accurate description of the risk/return relationship. After controlling for both the non-linear return profile and transaction costs, we find that risk arbitrage generates excess returns of 4% per year.

We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning risk models to other constructions, including statistical risk models, risk models based on fundamental industry classifications, and also those utilizing multilevel clustering based industry classifications.

Mean-variance investing is all about diversification. Diversification considers assets holistically and exploits the interaction of assets with each other, rather than viewing assets in isolation. Holding a diversified portfolio allows investors to increase expected returns while reducing risks. In practice, mean-variance portfolios that constrain the mean, volatility, and correlation inputs to reduce sampling error have performed much better than unconstrained portfolios. These special cases include equal-weighted, minimum variance, and risk parity portfolios.

In this paper, we study the relationship between stock fund managers’ facial attractiveness and fund outcomes. Utilizing the state-of-art deep learning technique to quantify facial attractiveness, we find that funds with facial unattractive managers outperform funds with attractive managers by over 2% per annum. We next show that good-looking managers attract significant higher fund flow especially if the funds are available on Fintech platforms where their photos are accessible to investors. Good-looking managers also have greater chance of promotion and tend to move to small firms. The potential explanations for their underperformance include inadequate ability, insufficient effort, overconfidence and inefficient site visits.

Existing measures of ESG (environmental, social, and governance) performance -- ESG ratings -- are noisy and, therefore, standard regression estimates of the effect of ESG performance on stock returns are biased. Addressing this as a classical errors-in-variables problem, we develop a noise-correction procedure in which we instrument ESG ratings with ratings of other ESG rating agencies. With this procedure, the median increase in the regression coefficients is a factor of 2.1. The results are similar when we use accounting profitability measures as outcome variables. In simulations, our noise-correction procedure outperforms alternative approaches such as simple averages or principal component analysis.

Past industry returns predict future industry returns, and this predictability is at its strongest at the one-month horizon. We show that the cross section of factor returns shares this property and that industry momentum stems from factor momentum. Factor momentum transmits into the cross section of industry returns through variation in industries’ factor loadings. We show that momentum in "systematic industries," mimicking portfolios built from factors, subsumes industry momentum as does momentum in industry-neutral factors. Industry momentum is therefore a byproduct of factor momentum, not vice versa. Momentum concentrates in its entirety in the first few highest-eigenvalue factors.

We learn from data that volatility is mostly path-dependent: up to 90% of the variance of the implied volatility of equity indexes is explained endogenously by past index returns, and up to 65% for (noisy estimates of) future daily realized volatility. The path-dependency that we uncover is remarkably simple: a linear combination of a weighted sum of past daily returns and the square root of a weighted sum of past daily squared returns with different time-shifted power-law weights capturing both short and long memory. This simple model, which is homogeneous in volatility, is shown to consistently outperform existing models across equity indexes and train/test sets for both implied and realized volatility. It suggests a simple continuous-time path-dependent volatility (PDV) model that may be fed historical or risk-neutral parameters. The weights can be approximated by superpositions of exponential kernels to produce Markovian models. In particular, we propose a 4-factor Markovian PDV model which captures all the important stylized facts of volatility, produces very realistic price and (rough-like) volatility paths, and jointly fits SPX and VIX smiles remarkably well. We thus show that a continuous-time Markovian parametric stochastic volatility (actually, PDV) model can practically solve the joint SPX/VIX smile calibration problem. This article is dedicated to the memory of Peter Carr whose works on volatility modeling have been so inspiring to us.

We develop a simple stock selection model to explain why active equity managers tend to underperform a benchmark index. We motivate our model with the empirical observation that the best performing stocks in a broad market index often perform much better than the other stocks in the index. Randomly selecting a subset of securities from the index may dramatically increase the chance of underperforming the index. The relative likelihood of underperformance by investors choosing active management likely is much more important than the loss to those same investors from the higher fees for active management relative to passive index investing. Thus, active management may be even more challenging than previously believed, and the stakes for finding the best active managers may be larger than previously assumed.

In this paper, we examine the yield premium of green bonds. We use a matching method, followed by a two-step regression procedure, to estimate the yield differential between a green bond and an otherwise identical synthetic conventional bond from July 2013 to December 2017. The results suggest a small negative premium: the yield of a green bond is lower than that of a conventional bond. On average, the premium is -2 basis points for the entire sample as well as for EUR and USD bonds separately. We show that the main determinants of the premium are the rating and the issuer type: the negative premia are more pronounced for financial and low-rated bonds.

Momentum trading strategies are thoroughly described in the academic literature and used in many trading strategies by hedge funds, asset managers, and proprietary traders. Baz et al. (2015) describe a momentum strategy for different asset classes in great detail from a practitioner’s point of view. Using a geometric Brownian Motion for the dynamics of the returns of financial instruments, we extensively explain the motivation and background behind each step of a momentum trading strategy. Constants and parameters that are used for the practical implementation are derived in a theoretical setting and deviations from those used in Baz et al. (2015) are shown. The trading signal is computed as a mixture of exponential moving averages with different time horizons. We give a statistical justification for the optimal selection of time horizons. Furthermore, we test our approach on global currency markets, including G10 currencies, emerging market currencies, and cryptocurrencies. Both a time series portfolio and a cross-sectional portfolio are considered. We find that the strategy works best for traditional fiat currencies when considering a time series based momentum strategy. For cryptocurrencies, a cross-sectional approach is more suitable. The momentum strategy exhibits higher Sharpe ratios for more volatile currencies. Thus, emerging market currencies and cryptocurrencies have better performances than the G10 currencies. This is the first comprehensive study showing both the underlying statistical reasons of how such trading strategies are constructed in the industry as well as empirical results using a large universe of currencies, including cryptocurrencies.

Portfolio optimization should provide large benefits to investors, but standard mean-variance optimization (MVO) works so poorly in practice that optimization is often abandoned. The approaches developed to address this issue are often surrounded by mystique regarding how, why, and whether they really work, so we seek to simplify, unify, and demystify optimization. We identify the portfolios that cause problems in standard MVO and present a simple enhanced portfolio optimization (EPO) method. Applying EPO to industry momentum and time series momentum across equities and global asset classes, we find significant alpha beyond the market, the 1/N portfolio, and standard asset pricing factors.Citation: Pedersen, Lasse Heje, Abhilash Babu, and Ari Levine, Enhanced Portfolio Optimization, Financial Analysts Journal, 2021, 77(2): 124-151.Available at SSRN: https://ssrn.com/abstract=3530390Published version (open access) at https://doi.org/10.1080/0015198X.2020.1854543