Optimizing an investment portfolio to maximize returns while minimizing risk is the ultimate goal for investors and their advisers. However, there is no set path and challenges always arise. One such limitation is the high-dimensional, small-sample problem (HDSS). HDSS refers to a portfolio with a large number of assets but little historical data, leading to unreliable portfolio optimization and resulting in weak investment performance.

In research recently published, Rensselaer Polytechnic Institute’s Chanaka Edirisinghe, Ph.D., Kay and Jackson Tai ’72 Senior Professor of Quantitative Finance; together with Jaehwan Jeong, Ph.D., associate professor at Radford University; have developed a data-driven method to improve portfolio selection in the context of HDSS. This work appears in an issue of The Journal of Portfolio Management, in honor of the “father of modern portfolio theory” and Nobel laureate Harry Markowitz.

Many portfolios use mean-variance (MV) optimization, which often results in excessive risk and portfolio fragmentation. To get around this, Edirisinghe and Jeong used cardinality control to restrict the number of assets, as well as a leverage constraint to control the amount of borrowing or short selling to help minimize risk. They also used norm constraints to help manage asset positions effectively. Finally, they used cross-validation to improve portfolio performance when applied to new, previously unseen data. Then, they tested their approach.

“We conducted a case study using large sets of stocks from the S&P 500 Index,” said Edirisinghe. “Our leverage-controlled sparse portfolio selection methodology significantly improved portfolio performance. The result is more manageability and decreased risk.” 

“Professor Edirisinghe’s approach advances portfolio optimization,” said Liad Wagman, Ph.D., dean of Rensselaer’s Lally School of Management. “The integration of sparsity and leverage controls within a data-driven framework leads to better-performing portfolios.”