Tails, Fears, and Risk Premia BOLLERSLEV, TIM; TODOROV, VIKTOR
The Journal of finance (New York),
December 2011, Volume:
66, Issue:
6
Journal Article
Peer reviewed
Open access
We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof, ...we identify and estimate a new Investor Fears index. The index reveals large time-varying compensation for fears of disasters. Our empirical investigations involve new extreme value theory approximations and high-frequency intraday data for estimating the expected jump tails under the statistical probability measure, and short maturity out-of-the-money options and new model-free implied variation measures for estimating the corresponding risk-neutral expectations.
Welch and Goyal (2008) find that numerous economic variables with in-sample predictive ability for the equity premium fail to deliver consistent out-of-sample forecasting gains relative to the ...historical average. Arguing that model uncertainty and instability seriously impair the forecasting ability of individual predictive regression models, we recommend combining individual forecasts. Combining delivers statistically and economically significant out-of-sample gains relative to the historical average consistently over time. We provide two empirical explanations for the benefits of forecast combination: (i) combining forecasts incorporates information from numerous economic variables while substantially reducing forecast volatility; (ii) combination forecasts are linked to the real economy.
This article introduces a groundbreaking method for accurately forecasting financial stock market returns. The approach utilizes a hybrid neuro-autoregressive model, combined with a multi-objective ...decision-making phase, to determine the optimal distribution, offering significant relevance in modern finance. The proposal harnesses the impressive capabilities of the long short-term memory (LSTM) recurrent neural network, synergistically coupled with the autoregressive fractionally integrated moving-average (ARFIMA) model across various distribution options. This synergy enables precise management of a wide range of both linear and nonlinear time series data. Utilized on two prominent American stock market indices (Dow Jones Industrial Average (DJIA) and Dow Jones Islamic Market International Titans 100 (IMXL) between 1/2/2015 and 12/10/2020), the experimental findings unequivocally illustrate the hybrid model's supremacy over baseline models in accuracy and computational efficiency. Notably, the forecasting experiments conducted in both tranquil and turbulent periods underscore the stability and robustness of this approach. The model's adaptability and resilience make it a promising tool for precise financial stock market return forecasts, particularly crucial in informing decision-making within the financial industry. Furthermore, this proposed approach contributes to the expanding research on decision support systems for financial forecasting, potentially influencing policy and strategic financial management, particularly in addressing both stable and volatile market conditions.
•A deep neuro-autoregressive robust model is proposed to forecast financial data.•The method combines the ARFIMA model with the LSTM.•It also optimally specifies the distribution of the data before fitting them.•Comparison with baseline models shows the appeals of the hybrid model.
A groundbreaking, authoritative introduction to how machine learning can be applied to asset pricing Investors in financial markets are faced with an abundance of potentially value-relevant ...information from a wide variety of different sources. In such data-rich, high-dimensional environments, techniques from the rapidly advancing field of machine learning (ML) are well- suited for solving prediction problems. Accordingly, ML methods are quickly becoming part of the toolkit in asset pricing research and quantitative investing. In this book, Stefan Nagel examines the promises and challenges of ML applications in asset pricing.Asset pricing problems are substantially different from the settings for which ML tools were developed originally. To realize the potential of ML methods, they must be adapted for the specific conditions in asset pricing applications. Economic considerations, such as portfolio optimization, absence of near arbitrage, and investor learning can guide the selection and modification of ML tools. Beginning with a brief survey of basic supervised ML methods, Nagel then discusses the application of these techniques in empirical research in asset pricing and shows how they promise to advance the theoretical modeling of financial markets. Machine Learning in Asset Pricing presents the exciting possibilities of using cutting-edge methods in research on financial asset valuation.
Our article comprehensively reexamines the performance of variables that have been suggested by the academic literature to be good predictors of the equity premium. We find that by and large, these ...models have predicted poorly both in-sample (IS) and out-of-sample (OOS) for 30 years now; these models seem unstable, as diagnosed by their out-of-sample predictions and other statistics; and these models would not have helped an investor with access only to available information to profitably time the market.
Comparing, or benchmarking, of optimization algorithms is a complicated task that involves many subtle considerations to yield a fair and unbiased evaluation. In this paper, we systematically review ...the benchmarking process of optimization algorithms, and discuss the challenges of fair comparison. We provide suggestions for each step of the comparison process and highlight the pitfalls to avoid when evaluating the performance of optimization algorithms. We also discuss various methods of reporting the benchmarking results. Finally, some suggestions for future research are presented to improve the current benchmarking process.
The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We motivate our study with ...analytical results on the distortions caused by some widely used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. We then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of “robust” loss functions. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.
Goyal and Welch (2007) argue that the historical average excess stock return forecasts future excess stock returns better than regressions of excess returns on predictor variables. In this article, ...we show that many predictive regressions beat the historical average return, once weak restrictions are imposed on the signs of coefficients and return forecasts. The out-of-sample explanatory power is small, but nonetheless is economically meaningful for mean-variance investors. Even better results can be obtained by imposing the restrictions of steady-state valuation models, thereby removing the need to estimate the average from a short sample of volatile stock returns.
Financial engineering is crucial for effectively combining finance with quantitative approaches. This study aims to forecast the performance of the Nasdaq stock market by considering numerous factors ...like wind, hydro, thermal, gas, and nuclear variables. To accomplish this, we utilize sophisticated predictive models, namely adaptive lasso (ALasso), elastic net (Enet), artificial neural network (ANN), convolutional neural network (CNN), and long short-term memory (LSTM). By using these advanced methods, our goal is to offer perceptive and precise predictions, which will enhance comprehension of the complex dynamics within the financial markets. The evidence suggests that the LSTM model has demonstrated superior accuracy in predicting changes in the Nasdaq stock market when compared to ALasso, Enet, ANN, and CNN. While ALasso, Enet, ANN, and CNN exhibit comparable RMSE and MAE values, their performance is slightly less competitive than that of the LSTM model. The marginal differences in RMSE (ALasso: 0.319, Enet: 0.317, ANN: 0.3, CNN: 0.32) and MAE (ALasso: 0.277, Enet: 0.276, ANN: 0.252, CNN: 0.278) emphasize the comparable effectiveness of various methods, but they somewhat drop below the LSTM model in terms of precision. The findings showed the significance of well-known and advanced ML techniques, particularly LSTM, for enhanced accuracy in financial market predictions.
We provide a general framework for finding portfolios that perform well out-of-sample in the presence of estimation error. This framework relies on solving the traditional minimum-variance problem ...but subject to the additional constraint that the norm of the portfolio-weight vector be smaller than a given threshold. We show that our framework nests as special cases the shrinkage approaches of Jagannathan and Ma (Jagannathan, R., T. Ma. 2003. Risk reduction in large portfolios: Why imposing the wrong constraints helps. J. Finance 58 1651–1684) and Ledoit and Wolf (Ledoit, O., M. Wolf. 2003. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J. Empirical Finance 10 603–621, and Ledoit, O., M. Wolf. 2004. A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Anal. 88 365–411) and the 1/ N portfolio studied in DeMiguel et al. (DeMiguel, V., L. Garlappi, R. Uppal. 2009. Optimal versus naive diversification: How inefficient is the 1/ N portfolio strategy? Rev. Financial Stud. 22 1915–1953). We also use our framework to propose several new portfolio strategies. For the proposed portfolios, we provide a moment-shrinkage interpretation and a Bayesian interpretation where the investor has a prior belief on portfolio weights rather than on moments of asset returns. Finally, we compare empirically the out-of-sample performance of the new portfolios we propose to 10 strategies in the literature across five data sets. We find that the norm-constrained portfolios often have a higher Sharpe ratio than the portfolio strategies in Jagannathan and Ma (2003), Ledoit and Wolf (2003, 2004), the 1/ N portfolio, and other strategies in the literature, such as factor portfolios.
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