ESG, Price Momentum and Stochastic Optimization

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.

Fundamental reason

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.

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Markets Traded
equities

Financial instruments
stocks

Confidence in anomaly's validity
Strong

Backtest period from source paper
2010-2019

Notes to Confidence in Anomaly's Validity

Indicative Performance
17.47%

Period of Rebalancing
Monthly

Notes to Indicative Performance

data from Table 1, Panel A, ESG-MOM


Notes to Period of Rebalancing

Estimated Volatility
13.49%

Number of Traded Instruments
691

Notes to Estimated Volatility

data from Table 1, Panel A, ESG-MOM


Notes to Number of Traded Instruments

The investment universe consists of large US stocks for which OWL Analytics ESG data were provided


Maximum Drawdown
18%

Complexity Evaluation
Very complex strategy

Notes to Maximum drawdown

data from Table 1, Panel A, ESG-MOM


Notes to Complexity Evaluation

Sharpe Ratio
1.29

Simple trading strategy

The investment universe consists of large US stocks for which OWL Analytics ESG data were provided. Firstly, consider a scaled total ESG score, that is between zero and one, and classical equity 12-months momentum signal where the last month is omitted. The knapsack problem consists of finding the combination of objects (stocks) that maximize the value, given the condition of the maximal weight. In the case of ESG-MOM strategy (a strategy that wants the highest ESG stocks with the largest momentum), the weight is represented by the reversed value (absolute value of 1 minus ESG score) to ensure that the condition of maximal weight is meaningful. Maximal weight (weight cap) is set to be a sum of the top 10% of reversed ESG scores, which ensures that only top ESG stocks should be included. The value is represented by the ranked momentum, where the higher the rank of the stock is, the higher momentum is. The combination of weight, weight cap and value creates an optimization problem represented by equation 1 in the paper. The optimization problem is solved by the simulated annealing and results in the optimized long-only portfolio consisting of high ESG, high Momentum stocks. The strategy is equally-weighted and rebalanced monthly.

Hedge for stocks during bear markets

Partially - Based on figure 1, the performance is very consistent and largely reduces drawdowns, however, the strategy could not be applicable as a complete hedge

Source paper
Other papers

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