Socially responsible investing is booming and is getting popular among practitioners and academics as well. While the social aspect is indisputable, many researchers rightfully doubt that ESG cannot provide an edge in terms of performance. A good example could be an ESG level strategy that buys (and could also short) highest (lowest) ESG score stocks. The profits are small and too little compared to simple, smart beta strategies.
This novel research proves that socially responsible investing and exceptional performance can be achieved. It is possible to obtain a good performing strategy through a combination of ESG scores and price momentum. The ESG scores and momentum anomaly can be related to the famous optimization knapsack problem. One of the most straightforward explanations of the knapsack problem is a robber that has limited capacity in the backpack, and naturally, wants to return from the store with a maximal loot. Therefore, the weight of the loot is limited, and robber wants to maximize his profit by choosing the most valuable combination of items that would fit into his knapsack.
Therefore, it is possible to make classical momentum more „sustainable“ or ESG friendly. In this case, the aim is to pick stocks with the highest momentum, but at the same time, maximize the ESG score of the portfolio. In other words, the momentum represents the weight, the higher the momentum, lower the weight. The limited capacity of the knapsack ensures that only stocks with high momentum (low weight) would be included in a portfolio. The ESG score of each stock represents the value. Therefore, picking stocks with the lowest „weight“ and maximizing the „value“ creates a more ESG friendly momentum strategy. Secondly, the situation can be reversed, and ESG can represent the „weight“ of the stock – higher the ESG, lower the weight. In this case, momentum represents the „value“ of the stock. In practice, such an approach chooses portfolio with as highest ESG as possible while maximizing the momentum of the stocks.
To sum it up, the knapsack algorithm finds the best combination of stocks to achieve a momentum portfolio with high ESG scores, or high ESG scores portfolio with large momentum. As a result, the performance does not suffer; knapsack portfolios only slightly reduce the profits and outperform the classical momentum on a risk-adjusted basis. We would centre our attention around the high ESG portfolios that maximize the momentum since the performance is the most consistent and the strategy delivers the best risk-adjusted return.

There are two reasons for the functionality of the combined ESG and momentum strategies. Firstly, it is a functionality of the momentum anomaly that was repeatedly proven to be working. Secondly, ESG criteria significantly improve the risk characteristics of the portfolio. Research consistently identify high ESG stocks as less risky. Therefore, the momentum largely contributes to the return, while the ESG ensures that the portfolio would not be largely volatile and would have smaller drawdowns. Both characteristics are also supported by the Theil´s regression, where the ESG score explains the volatility or drawdown. The ESG score has a statistically and also economically significant influence on the risk measures.
Additionally, the Knapsack algorithm and the optimization ensures that both the ESG and momentum are mixed most optimally, producing momentum portfolios with high ESG or ESG portfolios with high momentum. Moreover, the Knapsack algorithm also does not try to find the portfolio with the best return, which could lead to an overfitted portfolio that would not be that profitable in the future. The knapsack algorithm instead combines two distinct effects such that the maximal benefit would be achieved in terms of social responsibility, return and risk of the portfolio.
Lastly, the complicated optimization problem which complexity raises with the number of stocks can be efficiently solved using a slightly modified simulated annealing approach proposed in the paper.