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We study financial returns on alternative collectible investment assets, such as toys, using LEGO sets as an example. Such iconic toys with diminishing over time supply and high collectible values appear to yield high returns on the secondary market. We find that LEGO investments outperform large stocks, bonds, gold, and alternative investments, yielding an average return of at least 11% (8% in real terms) in the sample period 1987–2015. LEGO returns are not exposed to market, value, momentum, and volatility risk factors but have an almost unit exposure to the size factor. A positive multifactor alpha of 4%–5%, a Sharpe ratio of 0.4, a positive return skewness, and low exposure to standard risk factors make the LEGO toy and other similar collectibles an attractive alternative investment with good diversification potential.

In the late stages of long bull markets, a popular question arises: What steps can an investor take to mitigate the impact of the inevitable large equity correction? However, hedging equity portfolios is notoriously difficult and expensive. We analyze the performance of different tools that investors could deploy. For example, continuously holding short-dated S&P 500 put options is the most reliable defensive method but also the most costly strategy. Holding ‘safe-haven’ US Treasury bonds produces a positive carry, but may be an unreliable crisis-hedge strategy, as the post-2000 negative bond-equity correlation is a historical rarity. Long gold and long credit protection portfolios sit in between puts and bonds in terms of both cost and reliability. Dynamic strategies that performed well during past drawdowns include: futures time-series momentum (which benefits from extended equity sell-offs) and a quality strategy that takes long/short positions in the highest/lowest quality company stocks (which benefits from a ‘flight-to-quality’ effect during crises). We examine both large equity drawdowns and recessions. We also provide some out-of-sample evidence of the defensive performance of these strategies relative to an earlier, related paper.

Most investment strategies uncovered by practitioners and academics are false. This partially explains the high rate of failure, especially among quantitative hedge funds (smart beta, factor investing, stat-arb, CTAs, etc.) In this paper we examine why false positives are so prevalent in finance, why researchers fail (in many cases purposely) to detect them, and why firms are able to monetize their scheme. Beyond merely pointing to this industrywide problem, we offer a practical solution. We hope that the machine learning tools presented in this paper will help financial academic journals filter out false positives, and bring up the retraction rate to reasonable levels. The SEC, FINRA and other regulatory agencies worldwide could use these tools to take a more active role in curving this rampant financial fraud. A presentation based on this paper can be found at https://ssrn.com/abstract=3173146.

Managed-futures funds and CTAs trade predominantly on trends. There are several ways of identifying trends, either using heuristics or statistical measures often called “filters.” Two important statistical measures of price trends are time series momentum and moving average crossovers. We show both empirically and theoretically that these trend indicators are closely connected. In fact, they are equivalent representations in their most general forms, and they also capture many other types of filters such as the HP filter, the Kalman filter, and all other linear filters. Further, we show how these filters can be represented through “trend signature plots” showing their dependence on past prices and returns by horizon. Our results unify and broaden a range of trend-following strategies, and we discuss the implications for investors.

This paper presents the "multifractal model of asset returns" ("MMAR"), based upon the pioneering research into multifractal measures by Mandelbrot (1972, 1974). The multifractal model incorporates two elements of Mandelbrot's past research that are now well known in finance. First, the MMAR contains long-tails, as in Mandelbrot (1963), which focused on Levy-stable distributions. In contrast to Mandelbrot (1963), this model does not necessarily imply infinite variance. Second, the model contains long-dependence, the characteristic feature of fractional Brownian Motion (FBM), introduced by Mandelbrot and van Ness (1968). In contrast to FBM, the multifractal model displays long dependence in the absolute value of price increments, while price increments themselves can be uncorrelated. As such, the MMAR is an alternative to ARCH-type representations that have been the focus of empirical research on the distribution of prices for the past fifteen years. The distinguishing feature of the multifractal model is multiscaling of the return distribution's moments under time-rescalings. We define multiscaling, show how to generate processes with this property, and discuss how these processes differ from the standard processes of continuous-time finance. The multifractal model implies certain empirical regularities, which are investigated in a companion paper.

Our study highlights the NFT rarity as a key determinant of price premium in the cross-section. Moreover, well-connected investors, who establish their central positions in the NFT network through early adoption and active trading, enjoy pricing advantages. We also find that experienced investors pay lower prices for NFTs. As an investment class, NFTs exhibit a high-return and high-risk profile when compared to traditional assets, especially in a low-interest-rate environment, and outperform most other alternative assets, such as luxury goods, private equity, and artwork. Overall, we provide novel and comprehensive analyses of NFTs, a digital alternative investment in the Fintech era.

There is substantial evidence that indicates that stocks that perform the best (worst) over a three to 12 month period tend to continue to perform well (poorly) over the subsequent three to 12 months. Up until recently, trading strategies that exploit this phenomenon were consistently profitable in the United States and in most developed markets. Similarly, stocks with high earnings momentum outperform stocks with low earnings momentum. This article reviews the momentum literature and discusses some of the explanations for this phenomenon.

This paper contains the statistics of a survey about the Risk-Free Rate (RF) and of the Market Risk Premium (MRP) used in 2015 for 41 countries. We got answers for 68 countries, but we only report the results for 41 countries with more than 25 answers. The average (RF) used in 2015 was smaller than the one used in 2013 in 26 countries (in 11 of them the difference was more than 1%). In 8 countries the average (RF) used in 2015 was more than a 1% higher than the one used in 2013. The change between 2013 and 2015 of the average Market risk premium used was higher than 1% for 13 countries. Most of the respondents use for US, Europe and UK a Risk-Free Rate (RF) higher than the yield of the 10-year Government bonds.

This paper examines the correlation between stock and bond returns. It first documents that the major trends in stock-bond correlation for G7 countries follow a similar reverting pattern in the past forty years. Next, an asset pricing model is employed to show that the correlation of stock and bond returns can be explained by their common exposure to macroeconomic factors. The link between the stock-bond correlation and macroeconomic factors is examined using three successively more realistic formulations of asset return dynamics. Empirical results indicate that the major trends in stock-bond correlation are determined primarily by uncertainty about expected inflation. Unexpected inflation and the real interest rate are significant to a lesser degree. Forecasting this stock-bond correlation using macroeconomic factors also helps improve investors' asset allocation decisions. One implication of this link between trends in stock-bond correlation and inflation risk is the Murphy's Law of Diversification: Diversification opportunities are least available when they are most needed.

There is a strong presumption in economics that, in a competitive environment, profitability is mean reverting. We provide corroborating evidence. In a simple partial adjustment model, the estimated rate of mean reversion is about 40 percent per year. But a simple partial adjustment model with a uniform rate of mean reversion misses rich non-linear patterns in the behavior of profitability. Specifically, we find that mean reversion is faster when profitability is below its mean and when it is further from its mean in either direction. We also show that the mean reversion in profitability produces predictable variation in earnings.

Portfolio optimization is one of the problems most frequently encountered by financial practitioners. To our knowledge, the Critical Line Algorithm (CLA) is the only algorithm specifically designed for inequality-constrained portfolio optimization problems, which guarantees that the exact solution is found after a given number of iterations. Furthermore, CLA does not only compute a single portfolio, but it derives the entire efficient frontier. In the context of portfolio optimization problems, this approach is clearly more adequate than generic-purpose quadratic programming algorithms. The main goal of this paper is to fill a gap in the literature by providing a well-documented, step-by-step open-source implementation of CLA in a scientific language. The code is implemented as a Python class object, which allows it to be imported like any other Python module, and integrated seamlessly with pre-existing code. We discuss the logic behind CLA following the algorithm’s decision flow. In addition, we have developed several utilities that facilitate the answering of recurrent practical problems. We hope that this publication will offer a better alternative to financial practitioners, many of whom are currently relying on generic-purpose optimizers which often deliver suboptimal solutions. The source code can be downloaded at the authors' websites.

We test whether the low-risk effect is driven by (a) leverage constraints and thus risk should be measured using beta vs. (b) behavioral effects and thus risk should be measured by idiosyncratic risk. Beta depends on volatility and correlation, where only volatility is related to idiosyncratic risk. We introduce a new betting against correlation (BAC) factor that is particularly suited to differentiate between leverage constraints vs. lottery explanations. BAC produces strong performance in the US and internationally, supporting leverage constraint theories. Similarly, we construct the new factor SMAX to isolate lottery demand, which also produces positive returns. Consistent with both leverage and lottery theories contributing to the low-risk effect, we find that BAC is related to margin debt while idiosyncratic risk factors are related to sentiment.

It is common to apply multipliers to earnings and book value to calculate approximate equity values. However, applying a price-earnings multiple or a price-to-book multiple typically produces two valuations and the analyst is left with the question of how to combine these into one valuation. This paper calculates weights that do this. It shows that these weights differ over the difference between earnings and book value and systematically so over time: when earnings are small compared to book value the weights are different from when earnings are large relative to book value, and they vary in a non-linear way over the difference between the two. The weights have the interpretation of combining forecasts of future earnings based on earnings and book value separately into one composite forecast that uses both pieces of information together. So the paper calculates a second set of weights to ascertain how the two numbers are combined to forecast one-year-ahead earnings and three-years-ahead earnings. The calculated weights are applied out of sample to ascertain their predictive ability against other benchmarks.

The basic financial purpose of an enterprise is maximization of its value. Inventory management should also contribute to realization of this fundamental aim. The enterprise value maximization strategy is executed with a focus on risk and uncertainty. This article presents the consequences for the recipients firm that can result from operating risk that is related to delivery risk generated by the suppliers. The present article offers a method that uses portfolio management theory to chose the suppliers.

We investigate carbon risk in global equity prices. We develop a measure of carbon risk using industry standard databases and study return differences between brown and green firms. We observe two opposing effects: Brown firms are associated with higher average returns, while decreases in the greenness of firms are associated with lower announcement returns. We construct a carbon risk factor-mimicking portfolio to understand carbon risk through the lens of a factor-based asset pricing model. While carbon risk explains systematic return variation well, we do not find evidence of a carbon risk premium. We show that this may be the case because of: (1) the opposing price movements of brown firms and firms becoming greener, and (2) that carbon risk is associated with unpriced cash-flow changes rather than priced discount-rate changes. We extend our analysis to different geographic regions and time periods to confirm the missing risk premium.

Spanish Abstract: Este documento resume 1.466 respuestas a una encuesta realizada a directivos de empresas y a profesores de finanzas europeos. 1.143 personas utilizan rentabilidad exigida y 824 utilizan betas para calcularlas. La mayoría (717) de estas 824 personas justifican las betas que utilizan con regresiones, webs, bases de datos, libros o artículos. Solamente 70 personas justifican las betas que utilizan empleando únicamente el sentido común. La proporción de directivos que utilizan rentabilidad exigida pero no utilizan betas para su cálculo (44%) es muy superior a la de los profesores (8%). La proporción de directivos que utilizan sólo el sentido común para justificar las betas que utilizan (15%) es muy superior a la de los profesores (2%). Sorprende que, con los problemas que presentan las betas calculadas por regresión, un gran porcentaje de los profesores y directivos todavía las utilicen para calcular la rentabilidad exigida. La mayoría admite que hay muchos problemas en su determinación, pero continúan enseñándola y utilizándola por diversas razones: “ha obtenido el Premio Nobel en Economía”, “se utiliza mucho”, “permite defender una valoración, impresionar a la dirección y parecer un gurú financiero”… English Abstract: We report 1,466 answers from European managers and professors. 1,143 respondents use required return and 824 use betas to calculate it. 44.4% of the managers and 8% of the professors do not use beta to justify the required return. Only 2% of the professors and 15% of the managers justify the beta using exclusively personal judgement (named qualitative, common sense, intuitive, and logical magnitude betas by different persons). The paper includes interesting comments from 235 respondents.

In this paper, we provide a trend factor that captures simultaneously all three stock price trends: the short-, intermediate-, and long-term, by exploiting information in moving average prices of various time lengths whose predictive power is justified by a proposed general equilibrium model. It outperforms substantially the well-known short-term reversal, momentum, and long-term reversal factors, which are based on the three price trends separately, by more than doubling their Sharpe ratios. During the recent financial crisis, the trend factor earns 0.75% per month, while the market loses −2.03% per month, the short-term reversal factor loses −0.82%, the momentum factor loses −3.88%, and the long-term reversal factor barely gains 0.03%. The performance of the trend factor is robust to alternative formations and to a variety of control variables. From an asset pricing perspective, it also performs well in explaining cross-section stock returns.

The promise of deep reinforcement learning (DRL) is to make no initial assumptions in terms of decisions or rules and let the machine find the best solution. In this thesis, we show that this type of machine learning method provides a new solution for portfolio allocation. In the first part, we present how to apply DRL to portfolio allocation and take into account the specific nature of financial time series. We introduce the concept of contextual variables allowing better learning. We change the cross-validation to a stepwise approach to ensure that the training data does not contain any future points compared to the validation and test data. We empirically show that DRL makes it possible to go beyond the state of the art of portfolio allocation methods by finding portfolios better adapted to market conditions, thanks to layers of convolutions allowing us to capture the dependence between market data and allocation decisions. We conclude this part with a model-based approach where DRL selects volatility-targeting models. In the second part, we present theoretical results justifying the DRL approach. We show how the DRL approach generalises classical portfolio theories. We study how DRL methods achieve variance reduction. We find similarities between reinforcement learning and supervised learning.

We break average returns on value and growth portfolios into dividends and three sources of capital gain, (i) growth in book equity primarily due to earnings retention, (ii) convergence in price-to-book ratios (P/B) due to mean reversion in profitability and expected returns, and (iii) upward drift in P/B during 1927-2006. The capital gains of value stocks trace mostly to convergence: P/B rises as some value firms become more profitable and move to lower expected return groups. Growth in book equity is trivial to negative for value portfolios, but it is a large positive factor in the capital gains of growth stocks. For growth stocks, convergence is negative: P/B falls because growth stocks do not always remain highly profitable with low expected returns. Relative to convergence, drift is a minor factor in average returns.

Extending price momentum tests to the longest available histories of global financial assets, including country equities, government bonds, currencies, commodities, sectors and U.S. stocks, we create a 215-year history of cross-sectional multi-asset momentum, and confirm the significance of the momentum premium inside and across asset classes. Consistent with stock-level results, we document a large variation of momentum portfolio betas, conditional on the direction and duration of the state of the asset class in which the momentum portfolio is built. A significant recent rise in pair-wise momentum portfolio correlations suggests features of the data important for empiricists, theoreticians and practitioners alike.

This paper examines factors that influence prices of most common five cryptocurrencies such as Bitcoin, Ethereum, Dash, Litecoin, and Monero over 2010-2018 using weekly data. The study employs ARDL technique and documents several findings. First, cryptomarket-related factors such as market beta, trading volume, and volatility appear to be significant determinant for all five cryptocurrencies both in short- and long-run. Second, attractiveness of cryptocurrencies also matters in terms of their price determination, but only in long-run. This indicates that formation (recognition) of the attractiveness of cryptocurrencies are subjected to time factor. In other words, it travels slowly within the market. Third, SP500 index seems to have weak positive long-run impact on Bitcoin, Ethereum, and Litcoin, while its sign turns to negative losing significance in short-run, except Bitcoin that generates an estimate of -0.20 at 10% significance level.Lastly, error-correction models for Bitcoin, Etherem, Dash, Litcoin, and Monero show that cointegrated series cannot drift too far apart, and converge to a long-run equilibrium at a speed of 23.68%, 12.76%, 10.20%, 22.91%, and 14.27% respectively.

The copula-opinion pooling (COP) approach extends in principle the Black-Litterman methodology to non-normally distributed markets and views. However, the implementations of the COP framework presented so far rely on restrictive quasi-normal assumptions. Here we present a general recipe to implement the COP approach in practice under all possible market and views specifications.

The sharp economic downturn and turmoil in the financial markets, commonly referred to as the “global financial crisis,” has spawned an impressive outpouring of blame. The efficient market hypothesis - the idea that competitive financial markets ruthlessly exploit all available information when setting security prices - has been singled out for particular attention. Like all good theories, market efficiency has major limitations, even though it continues to be the source of important and enduring insights. Despite the theory’s undoubted limitations, the claim that it is responsible for the current worldwide crisis seems wildly exaggerated. This essay discusses many of those claims. These include claims that belief in the notion of market efficiency was responsible for an asset bubble, for investment practitioners miscalculating risks, and for regulators worldwide falling asleep at the switch. Other claims are that the collapse of Lehman Bros. and other large financial institutions implies market inefficiency, and that an efficient market would have predicted the crash. These claims are without merit. Despite the evidence of widespread anomalies and the advent of behavioral finance, we continue to follow practices that assume efficient pricing.

Past trading volume predicts both the magnitude and persistence of future price momentum. In the intermediate-term, a strategy of buying past high-volume winners and selling past high-volume losers outperforms a similar strategy based on price momentum alone by 2% to 7% per year. In the long-term, a strategy of buying low-volume winners and selling high-volume losers exhibits return continuation up to three years, while a strategy of buying high-volume winners and selling low-volume losers exhibits return reversals in years two and three. These findings are consistent with behavioral models in which stock prices initially underreact, but ultimately overreact, to fundamental news. In this context, past trading volume provides information about the level of investor interest, and indirectly, about the imminence of price reversals.

In this paper we develop and demonstrate the workings of a copula-based technique that allows the derivation of dynamic trading strategies, which generate returns with statistical properties similar to hedge funds. We show that this technique is not only capable of replicating fund of funds returns, but is equally well suited for the replication of individual hedge fund returns. Since replication is accomplished by trading futures on traditional assets only, it avoids the usual drawbacks surrounding hedge fund investments, including the need for extensive due diligence, liquidity, capacity, transparency and style drift problems, as well as excessive management fees. As such, our synthetic hedge fund returns are clearly to be preferred over real hedge fund returns.