Enhancing Portfolio Performance in the 21st Century

AO, Mengmeng | 李瑩瑩 | 鄭星華

Mean-variance analysis is a tool used to make investment decisions by weighing risk (or variance) against expected returns. It helps investors determine how much risk they are willing to accept in exchange for bigger (or smaller) rewards. In 1952, to help risk-averse investors identify acceptable risk and returns on assets, Harry Markowitz proposed the mean-variance portfolio theory. However, implementing this theory in practise is challenging, which HKUST professors Yingying Li and Xinghua Zheng, working with a former HKUST student Mengmeng Ao, set out to address.

According to this theory, risk-averse investors aim to combine assets to maximize return subject to a specified risk constraint. This is known as mean-variance efficiency. A portfolio that is mean-variance efficient yields the highest return given a risk constraint. However, sample-based portfolios do not always fully represent the real-world environment, particularly when many assets are involved. This is an increasingly pressing problem, the authors explain, because “modern portfolios often involve a large number of assets.”

The standard approach, resulting in a “plug-in” portfolio, carries almost twice the specified level of risk. Even more concerningly, say the authors, “this high risk is not adequately compensated by a high return.” Clearly, a new method is needed to simultaneously achieve mean-variance efficiency and meet risk constraint for portfolios with a large number of assets. Accordingly, the researchers developed a new methodology for estimating a mean-variance efficient portfolio, which they called the maximum Sharpe ratio estimated and sparse regression (MAXSER) method.

“MAXSER is a general approach that can be applied to various situations in which the number of assets is not small compared with the sample size,” the authors explain. It considers not only the three traditional Fama–French factors—firm size, book-to-market value, and excess return on the market—but also investment in individual stocks. The researchers tested this novel approach in a range of scenarios, using “stock universes” derived from two leading market indices, the Dow Jones Industrial Average and Standard & Poor’s 500.

The results were promising. “The sound theoretical properties of MAXSER are supported by comprehensive numerical analysis,” report the researchers. This makes MAXSER the first method of its kind to both effectively constrain risk and achieve mean-variance efficiency for portfolios with a large number of assets. “To the best of our knowledge,” say the authors, “this is the first method that simultaneously achieves these two goals.”

The authors’ pioneering method has considerable potential to improve the performance of modern portfolios relative to benchmark strategies. “Investing in individual stocks in addition to the Fama–French three factors can significantly enhance portfolio performance,” they report, adding that “the advantage of MAXSER is not only statistically significant but also economically large.” Investors will undoubtedly benefit from this novel extension of Markowitz’s theory in a world in which assets are increasing and portfolios are becoming ever more unwieldy and difficult to manage.


Finance Information Systems, Business Statistics & Operations Management


Information Systems, Business Statistics & Operations Management