MATCHED FILTER APPROACH TO PORTFOLIO OPTIMIZATION

Given a fixed amount of capital, how to invest it optimally by distributing it among a set of stocks and securities so as to maximize the return while minimizing the overall risk is addressed here. Given that one has full freedom in selecting the type of stocks, a new strategy is outlined here by maximizing the ratio of the gain to risk-rather than minimizing the risk alone-to determine the fraction of capital that must go to each stock. An optimum gain versus variance plot can be used to determine the type of stocks to be selected in addition to their relative quantity for maximum yield over the duration of interest. By modifying the definition of risk to include a function of the covariance matrix of secondary stocks that are sympathetic to the primary stocks of interest, an alternate investment strategy is also developed here. If short selling of stocks and securities is not allowed in a portfolio, then stock selection becomes important so as to maintain the desired fractions to be positive. In this context, a new iterative method that incrementally increases the diagonal loading of the covariance matrix of the primary returns so as to achieve positive weight factors is also developed.