f-Betas and portfolio optimization with f-divergence induced risk measures
利用f-散度诱导的一致风险测度进行投资组合优化，推导出CAPM格式的最优条件，并提出了新的f-贝塔指标，通过数值实验比较了Hellinger-贝塔与标准贝塔和回撤贝塔的表现。
In this paper, we build on using the class of f-divergence induced coherent risk measures for portfolio optimization and derive its necessary optimality conditions formulated in CAPM format. We derive a new f-Beta similar to the Standard Betas and also extended it to previous works in Drawdown Betas. The f-Beta evaluates portfolio performance under an optimally perturbed market probability measure, and this family of Beta metrics gives various degrees of flexibility and interpretability. We conduct numerical experiments using selected stocks against a chosen S&P 500 market index as the optimal portfolio to demonstrate the new perspectives provided by Hellinger-Beta as compared with Standard Beta and Drawdown Betas. In our experiments, the squared Hellinger distance is chosen to be the particular choice of the f-divergence function in the f-divergence induced risk measures and f-Betas. We calculate Hellinger-Beta metrics based on deviation measures and further extend this approach to calculate Hellinger-Betas based on drawdown measures, resulting in another new metric which is termed Hellinger-Drawdown Beta. We compare the resulting Hellinger-Beta values under various choices of the risk aversion parameter to study their sensitivity to increasing stress levels.