Journal of Risk

Farid AitSahlia
Warrington College of Business, University of Florida

The fundamental tenet of high expected return associated with high risk has been challenged by the relative success of the so-called low-risk anomaly: a topic that is addressed in this issue of The Journal of Risk. Another topic of increasing interest is that of applying machine learning tools to finance, with an illustration on portfolio optimization also provided herein. A paper dealing with ruin models and another regarding stochastic dominance round out the present offering.

Our first paper, “Ruin problems in a discrete risk model in a Markovian environment”, is by Hyun Joo Yoo and Jerim Kim, who correct a compound binomial risk model, deriving the joint distribution of ruin time, surplus before ruin, and deficit at ruin by relying on the matrix analytic method. The latter is particularly well suited for Markov chains that have finite states in one dimension (eg, ruin–no ruin) but that can grow unboundedly in others (eg, number of claims).

In the second paper in the issue, “Covariance estimation for risk-based portfolio optimization: an integrated approach”, Andrew Butler and Roy H. Kwon propose the use of an integrated prediction and optimization (IPO) framework to tackle the estimation of covariance in the context of portfolio optimization. In contrast to the traditional approach, which seeks first to estimate as well as possible, then to optimize, the IPO relies on neural networks to conduct covariance estimation with a view toward minimizing errors due to portfolio decisions. Through a real-world-based numerical illustration, Butler and Kwon show that this method is less prone to model misspecification than the standard “predict-then-optimize” approach.

Next, in “Are there multiple independent risk anomalies in the cross section of stock returns?”, Benjamin R. Auer and Frank Schuhmacher conduct an empirical study to assess the veracity of the low-risk anomaly through cross-section portfolio constructions in combination with a variety of risk measures. This study documents the existence – across the different measures – of independent low-risk anomalies that can be gainfully exploited by traders.

Fractional degree stochastic dominance captures various levels of risk attitudes when comparing statistical distributions. In the fourth and final paper in this issue, “Test for fractional degree stochastic dominance with applications to stock preferences for China and the United States”, Jianli Wang, Xiong Xiong, Lin Zhou and Xu Guo construct test statistics for which they obtain asymptotic distributions to assess fractional degree stochastic dominance. Using daily returns for the Standard & Poor’s 500 and the Shanghai Stock Exchange Composite Index, Wang et al show that risk-averse investors and those who are risk prone only up to a point are more likely to invest in the US stock market than in the Chinese stock market. They further contend that markets that are populated only by such investors cannot be efficient.