Global financial markets have been experiencing low-risk anomalies for decades. In a low-risk anomaly, low-risk stocks offer better returns than high-risk stocks, violating the fundamental tenets of many financial theories. We developed an optimal portfolio strategy that exploits low-risk anomalies in the Black–Litterman framework. Our view is that low-risk assets will outperform high-risk assets. Forecasting volatility is the most important factor in constructing a view portfolio and in determining portfolio performance. To increase the predictive power regarding volatility, the best-performing prediction model should be selected.
We compared predictive power between three state-of-the-art machine-learning prediction models (GPR, SVR, and ANN) and the GARCH and historical volatilities. SVR and ANN showed better predictive power than GARCH in all error metrics. ANN was chosen as the best model because it showed higher predictive stability than SVR. We predicted the volatility levels of each asset by the chosen ANN model and used these to construct a Black–Litterman portfolio in order to exploit the low-risk anomaly. We compared the performance of the low-risk Black–Litterman portfolio with the market portfolio and the CAPM-based market equilibrium portfolio that excludes the low-risk view in the Black–Litterman framework.
Reflecting the low-risk view was found to improve the performance of the market equilibrium portfolio, which dominated the market portfolio. The equilibrium portfolio showed a lower Sharpe ratio than the market portfolio and a negative alpha. However, reflecting the low-risk view in the portfolio greatly improved the Sharpe ratio and the alpha. In addition, the estimation error of the expected returns and covariance matrix with the low-risk view decreased as τ decreased, contributing to the improvement of the portfolio's performance.
Since low-risk anomalies are global phenomena, the market for volatility strategies is expected to be enormous. We can also combine low-risk anomalies in each market to form an optimal portfolio.

Professor Hand argued that there are reasons why pattern recognition may not do better than the traditional linear regression algorithms—namely, nonstationarity, small signal/noise, and overfitting. Up to this point, we have considered many interesting ideas, some of which are backed by economic intuition, but we have yet to see a significant amount of empirical evidence. Future research should focus on actionable ideas regarding machine learning and big data in the entire spectrum of the investment process—that is, alpha, beta, risk management, and execution and trading.

We use data from 1999 to 2015 for 45 different assets. We compare risk-return characteristics in an out-of-sample framework of all network-based asset allocation strategies with their respective benchmark models. Within our sample, we show that utilizing information on the interconnectedness of various asset returns given the topological structure of a network improves the risk-return characteristics of standard benchmark portfolios. It is quite clear that the constructed network takes into account complex relationships between assets beyond those measured by correlations.

We propose the so-called ρ-dependent strategy and test its performances against the extremely simple yet effective 1/N naïve rule and two Markowitz-related policies. Our out-of-sample results show that the ρ-dependent strategy tends to present significant higher portfolio Sharpe ratios and lower portfolio variance relative to these well-known benchmarks. Additionally, this enhanced performance is not explained by large exposures to traditional risk factors as indicated by the reported positive and statistically significant Carhart's alphas. More importantly, our results are robust to several portfolio configurations, time periods and markets even after accounting for transaction costs.

The MVO algorithm treats all variables as interrelated, assuming a complete cluster. In other words, traditional asset allocation does not recognize the complexity immerse in the data. This work presents some novel, robust and flexible methods with visual interpretations to construct risk-adjusted portfolios. Clustering methods showed a better trade-off between return and risk than MVO algorithm. The empirical results indicate that hierarchical algorithms have a better performance when building diversified portfolios measured by the Omega ratio. One of the most important results is the stable behavior of clustering-based portfolios addressing a special issue in financial markets, the volatility.