Multi-objective Portfolio Optimization Based on the Fama–French Three-Factor Model and the Black–Litterman Framework
This study proposes a robust multi-objective portfolio optimization model that integrates the Fama–French three-factor model with the Black–Litterman framework to generate posterior expected returns while simultaneously minimizing downside risk and maximizing diversification under practical constraints, demonstrating superior performance over benchmark strategies in both in-sample and out-of-sample tests.
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In the world of investing, the central challenge is not simply finding assets that make money, but finding the right mix of assets that can survive when the market turns sour. For decades, the standard way to manage this risk relied on a mathematical concept called variance, which treats every swing in price as a potential danger, whether the price goes up or down. This approach assumes that investment returns follow a predictable, bell-shaped curve, much like the distribution of heights in a large crowd. However, real financial markets are often messier, with sudden, sharp drops that happen more frequently than a simple curve would predict. Furthermore, the most common methods for guessing future returns are notoriously fragile; if an investor's guess about a stock's future performance is slightly off, the resulting investment plan can become wildly unbalanced, putting too much money into a single risky bet. To solve these problems, researchers have long sought a way to build portfolios that focus specifically on the risk of losing money, while also ensuring that the money is spread out enough to avoid disaster if one specific investment fails.
A team of researchers at the Guangdong University of Finance and Economics has proposed a new method to tackle these issues by combining three distinct ideas into a single, cohesive strategy. First, they use a framework known as the Fama–French three-factor model, which looks at three specific drivers of stock performance: the overall market, the size of the company, and its value relative to its book value. Instead of guessing future returns in a vacuum, this model uses historical data to understand how these three factors have influenced specific stocks in the past. Second, they feed these insights into a system called the Black–Litterman model, which acts as a sophisticated filter. This system takes the market's general expectations and blends them with the specific insights from the three-factor model, smoothing out the wild guesses that often plague traditional planning. Finally, the researchers replace the old, all-encompassing measure of risk with a more precise tool called mean absolute semi-deviation, which only counts the times a portfolio loses value, ignoring the times it gains. They also add a measure of "entropy," a concept borrowed from physics that, in this context, simply quantifies how evenly the money is spread across different stocks. If the money is concentrated in just a few stocks, the entropy is low; if it is spread out, the entropy is high.
The researchers tested this new approach using thirty major stocks from China's CSI 300 Index, a collection of the country's largest and most liquid companies. They gathered daily price data from January 1, 2024, through June 30, 2025, to see how their model would perform in a real-world setting. They compared their method against two common benchmarks: the CSI 300 Index itself, which simply tracks the market, and a "1/N" strategy, where an investor puts an equal amount of money into every stock without any complex analysis. The study also accounted for real-world friction, such as the fees paid every time a stock is bought or sold, and strict rules preventing investors from betting more than 30% of their money on any single stock.
The results of the simulation showed that the new model consistently outperformed the simpler strategies. When looking at the total growth of the investment over the test period, the new model generated a cumulative return of approximately 17.5%, significantly higher than the modest gains seen in the equal-weight strategy. More importantly, the new model proved better at protecting the investor's capital during downturns. While the standard market index and the equal-weight approach struggled to maintain their value, the new model's focus on downside risk meant it suffered less during market drops. The researchers measured this using a metric called the Sortino ratio, which evaluates how well an investment performs relative to its bad days rather than all its days. In this test, the new model achieved a peak Sortino ratio above 27, whereas the equal-weight strategy rarely exceeded 5. This suggests that the model was exceptionally good at avoiding losses without sacrificing the potential for gains.
Beyond just making more money, the model also demonstrated greater stability. The researchers tested how the model would hold up if they changed the timing of their decisions, such as how often they rebalanced the portfolio or how much historical data they used to make their predictions. They found that the model remained robust across different settings, suggesting that its success was not a fluke of a specific time frame. The study indicates that by grounding their predictions in the three-factor model and then refining them with the Black–Litterman framework, the researchers created a system that is less sensitive to the errors that usually ruin investment plans. The inclusion of the entropy measure ensured that the portfolio did not become dangerously concentrated, while the focus on semi-deviation kept the strategy alert to the specific danger of losing money.
This work suggests that a more nuanced approach to portfolio construction can yield tangible benefits for investors. By moving away from the idea that all price movement is equal risk, and by grounding future expectations in a structured analysis of market factors, the researchers have created a tool that balances the desire for profit with the need for safety. The study does not claim to have solved the mystery of the market, but it provides strong evidence that combining these specific techniques can lead to portfolios that are not only more profitable but also more resilient when the market turns against them. For institutional investors and wealth managers, this offers a practical path forward, demonstrating that a disciplined, multi-objective approach can navigate the complexities of modern financial markets more effectively than traditional, single-minded strategies.
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