ST-metric, arising from relative entropy can be thought as the distance between two discrete curves in the unit interval. Any data set can also be viewed as a discrete curve and can be transformed into the unit interval. The first method is to define a utility function for risk averse investors as the ST-metric between the returns of risk-free and risky investments, and then to rank the performances of fund managers (Tulunay 2017). The second method is about finding factor weights in a factor model. That is an optimization problem where the objective is minimizing the distance between the benchmark and the constructed portfolio. Usually, the absolute value distance between the benchmark and the constructed portfolio at each time point is used. Ang et.al. (2018) used Tracking Error method, absolute value distance, smoothed by multiplying the standard deviation over some period. Using ST-metric between the curves of the benchmark and the portfolio as objective function gives better estimation of the factor weights than tracking error method. Furthermore, ST-metric is more sensitive to the fluctuations than absolute value (L1) and L2-distances.
Dr ILKNUR TULUNAY is awarded in her PhD, titled “Cuspidal Modules of Finite General Linear Groups” on representation of reductive algebraic groups at School of Mathematics and Statistics, USYD in 2001. After her post-doctoral fellowship, JSPS (Japan Society for Promotion of Science) in 2003-2005, she worked as a financial analyst on infrastructure projects from all over the world in a private company for 8 years. She completed her 2nd master on Quantitative Finance, UTS in 2015. She is currently working as an independent researcher and as a casual academic at School of Mathematics and Statistics, UNSW and Market Department, Business School, UTS.