Portfolio Risk in Multiple Frequencies

Portfolio risk, introduced by Markowitz in 1952, and defined as the standard deviation of the portfolio return, is an important metric in the Modern Portfolio Theory (MPT). A popular method for portfolio selection is to manage the risk and return of a portfolio according to the cross-correlations of returns for various financial assets. In a real world scenario, estimated empirical financial correlation matrix contains significant level of intrinsic noise that needs to be filtered prior to risk calculations. In this paper, we present basic concepts of risk engineering in finance applications. Then, we extend our discussion to the eigenfiltering of measurement noise for hedged portfolios. Moreover, we extend risk measurement methods for trading in multiple frequencies. Finally, three novel risk management methods are proposed as an independent overlay of the underlying investment decision mechanism, i.e. the trading strategy. We highlight performance and merit of the risk engineering techniques introduced by presenting the back-testing results of an investment strategy for the stocks listed in the NASDAQ 100 index. It is shown in the paper that managing portfolio risk more intelligently may offer advantages for improved return on investment