The low-risk anomaly violates basic tenets of financial theories that suggest that high risk should command a commensurately higher return. Low-risk anomalies are evident in the markets of both developed and developing markets and occur in equity, currency, commodity, and option markets. The causes of this anomaly include investor preference for irrational assets, investor focus on success stories reported in the media instead of the high number of failures, investor overconfidence, and limits to arbitrage.  

Two ways investors and practitioners exploit low-risk anomalies are (1) buying low-beta stocks and (2) short-selling high-beta stocks. The authors create an optimal portfolio strategy that takes advantage of low-risk anomalies in the Black–Litterman framework based on their view that high-risk assets will underperform low-risk assets. After predicting the volatility levels of each asset class using the appropriate volatility forecasting model, the authors build a Black–Litterman portfolio to exploit the low-risk anomaly.

The authors compare the performance of the low-risk Black–Litterman portfolio with that of the market portfolio and of the CAPM-based market equilibrium portfolio that excludes the low-risk view in the Black–Litterman framework. The results reveal that incorporating the low-risk view in the CAPM-based market equilibrium portfolio greatly improves the Sharpe ratio and the alpha and that this view outperforms the market portfolio. Because low-risk anomalies are a global phenomenon, practitioners and investors can seek ways to exploit them in different markets and can combine low-risk anomalies in each market to create an optimal portfolio.

Volatility forecasting is a critical component of a volatility-based investment strategy, and the authors assess three state-of-the-art machine-learning predictive models (Gaussian process regression, or GPR; support vector regression, or SVRa; and artificial neural network, or ANN) to forecast asset volatility. The best-performing volatility forecasting model is selected, and assets are classified into high- and low-risk groups to construct a view portfolio. The return on the view portfolio is estimated using return predictions of the Fama–French factor model. The market equilibrium portfolio is then combined with the view portfolio to estimate posterior expected returns and the covariance matrix in the Black–Litterman framework.

Asset-related data from 2000 to 2016 are from Quantiwise and Bloomberg. The stocks listed on the KOSPI 200 are classified as low  or high beta in order to explore the existence of the low-risk anomaly in the South Korean stock market. The authors compare the predictive power of different volatility prediction models and historical volatilities, and they select ANN as the best predictive model.

          Based on their belief that low-risk assets will outperform high-risk assets, the authors develop a portfolio in order to exploit the low-risk anomaly. They use the Black–Litterman framework, which introduces parameters to mitigate against estimation errors in traditional Markowitz optimization, notably concerning expected returns and covariance. Stocks are divided into the top 30% and bottom 30% based on expected volatility. The result is that the low-risk view contributes greatly to portfolio performance and dominates the market portfolio from 2005 to 2016.

The authors demonstrate that the low-risk anomaly has occurred in the KOSPI 200, a stock market less widely followed than the US market and many European markets. The existing literature indicates that the low-risk anomaly has occurred in the markets of both developed and developing markets, as well as in equity, currency, commodity, and option markets. The phenomenon seems to be largely attributable to irrational behavior, and the anomaly should continue to generally persist over time. Practitioners should recognize the existence of low-risk anomalies in different markets and incorporate elements of the authors’ research in their investment decisions.