A Privacy-preserving mean–variance optimal portfolio
Introduction
Since the 2008 financial crisis, the strong regulations for the financial industry and the rapid growth of information technologies (IT) have promoted the emergence of financial technology (fintech1) (Puschmann, 2017). Based on emerging technological innovations such as artificial intelligence, big data analysis, blockchain, and cybersecurity, various fintech companies are providing robo-advising, peer-to-peer lending, and cryptocurrency services (Chen and Ren, 2022, Daud et al., 2022, Goldstein et al., 2019, Ko et al., 2022, Li et al., 2022).
Among these, the robo-advisor has risen as a digital platform that guides customers through an automated investment advisory process using IT. Robo-advisor has attracted the public’s interest, reaching a market share of over $4.51 billion in 2019, with an expected growth rate of approximately 30% to 41% (Jung et al., 2018, Tiberius et al., 2022). In order to provide digital asset management, the robo-advisor companies require customers to submit surveys that pertain to their age, attitude to risk, the current level of wealth, and income, to approximate their risk aversion. Further, with the calibrated level of risk aversion, the companies advise and recommend customized investment strategies for managing portfolios.
Meanwhile, cybersecurity-related privacy has emerged as one of the paramount issues in the fintech industry (Gai et al., 2016). The level of security directly indicates the authority to access customers’ financial accounts in any financial service. Moreover, unprotected personal data can be used as auxiliary information to facilitate an attack. As subtle security flaws can cause catastrophic failure of the entire financial system, regulatory bodies all across the globe force financial companies to strictly abide by the rules regarding security flaws (Demertzis et al., 2018). For instance, the General Data Protection Regulation in Europe was adopted to safeguard personal privacy, which requires general and reliable protection in the use of data by third parties (Voigt and Von dem Bussche, 2017).
Despite the vitality and urgency of privacy issues in the fintech industry, preserving privacy in the robo-advisor sector still remains rarely explored. To the best of our knowledge, researchers in academia have made no attempts to address these issues from the financial point of view. Specifically, an individual’s risk aversion must be protected as important personal information because it works as a proxy for personal characteristics regarding their decision-making2 (Hartog et al., 2002, Kaustia and Torstila, 2011, Sapienza et al., 2009, van der Ploeg, 1992). However, unfortunately, this can be used for unexpected commercial use or malicious attacks.
For fintech companies to follow the privacy rules, homomorphic encryption (HE) has been in the spotlight as one of the most superior privacy-preserving methods and is used in various IT systems (Ibarrondo and Viand, 2021, Li and Huang, 2020, Wang et al., 2018). Using HE, encrypted data can be processed without compromising the information in the data3. However, as pointed out in Abowd and Schmutte (2019), privacy protection always induces a trade-off, where accuracy (e.g., obtaining the accurate weight of portfolio) is sacrificed in the name of privacy (e.g., protecting risk aversion).
Motivated by the demand to mitigate privacy issues, we examine a new framework that applies HE to the existing asset allocation strategy to protect the individual privacy of investors. Concretely, we first propose a novel algorithm to protect investors’ risk aversion for the mean–variance portfolio, a standard asset allocation methodology in the robo-advisor industry. Particularly, we examine the results of two cases. The first is portfolio optimization without an inequality constraint, where HE can be applied trivially. The second is portfolio optimization with an inequality constraint, where the solution must be calculated using numerical methodologies, which has not yet been explored in HE-related literature. The results confirm that the proposed model requires only an acceptable drop in accuracy in both cases when applied to real-world data.
This study’s main contribution is that we, as a first attempt, introduce the concept of privacy-preserving with HE in constructing the mean–variance portfolio widely used in the robo-advisory field. The proposed framework works well irrespective of inequality constraints because we effectively mitigate the difficulty of constrained optimization with HE. Furthermore, the study contributes to the existing literature by confirming the empirical performance regarding the number of stocks and the degree of correlation. Consequently, this pioneering study fills a research gap concerning the financial benefit of the privacy-preserving concept.
This study proceeds as follows: Section 2 presents the methodology. Section 3 discusses the empirical findings. Section 4 concludes the study.
Section snippets
Mean–variance portfolio
According to the Modern Portfolio Theory expounded by the seminar study of Markowitz (1952), maximum utility portfolio (MUP)45
Data and experimental design
We use simple returns of stock prices.12 included in the lists of the S&P 500 index for portfolio construction.13 We use a 3-month treasury-bill rate as a proxy for the risk-free rate. Table 1 summarizes the statistics of our data.
For the empirical results, we conduct the in- and out-of-sample tests. We perform the tests using a rolling window method
Concluding remarks
Summarizing the aforementioned empirical results, we find that the encrypted optimal portfolio with HE can be adequately approximated to the existing unencrypted portfolio using the proposed framework to protect an individual’s privacy. Another finding is that the number of assets and the degree of correlation affect the quality of the privacy-preserving portfolio construction regarding MSE of , SR, and CEQ, from an economic viewpoint.
Our study has crucial financial implications to all
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2019R1A2C2002358, No. 2022R1A5A6000840), and partly by the Institue of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No. 2022-0-00984).
References (41)
- et al.
Do AI-powered mutual funds perform better?
Finance Res. Lett.
(2022) - et al.
FinTech and financial stability: Threat or opportunity?
Finance Res. Lett.
(2022) - et al.
Stock market aversion? Political preferences and stock market participation
J. Financ. Econ.
(2011) - et al.
The economic value of NFT: Evidence from a portfolio analysis using mean–variance framework
Finance Res. Lett.
(2022) - et al.
How does the fintech sector react to signals from central bank digital currencies?
Finance Res. Lett.
(2022) The opportunity cost of mean–variance choice under estimation risk
European J. Oper. Res.
(2014)- et al.
Forecasting the future of robo advisory: A three-stage Delphi study on economic, technological, and societal implications
Technol. Forecast. Soc. Change
(2022) Temporal risk aversion, intertemporal substitution and Keynesian propensities to consume
Econom. Lett.
(1992)- et al.
An economic analysis of privacy protection and statistical accuracy as social choices
Amer. Econ. Rev.
(2019) - et al.
(Leveled) fully homomorphic encryption without bootstrapping
ACM Trans. Comput. Theory (TOCT)
(2014)
Parameter-free HE-friendly logistic regression
Adv. Neural Inf. Process. Syst.
Efficient homomorphic encryption framework for privacy-preserving regression
Appl. Intell.
Numerical method for comparison on homomorphically encrypted numbers
Homomorphic encryption for arithmetic of approximate numbers
The future of fintech
Financ. Manage.
Capital markets union and the fintech opportunity
J. Financ. Regul.
Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?
Rev. Financ. Stud.
Security and privacy issues: A survey on FinTech
Applications of Division by Convergence
To FinTech and beyond
Rev. Financ. Stud.
Cited by (5)
A novel integration of the Fama–French and Black–Litterman models to enhance portfolio management
2024, Journal of International Financial Markets, Institutions and MoneySequence and longevity risks of South Korean retirees: Insights and potential remedies
2024, Pacific Basin Finance JournalA privacy-preserving robo-advisory system with the Black-Litterman portfolio model: A new framework and insights into investor behavior
2023, Journal of International Financial Markets, Institutions and Money