슬로프 방식을 이용한 평균-숏폴 포트폴리오 최적화
Mean-shortfall portfolio optimization via sorted L-one penalized estimation
조해인a, 박세영1,b
Haein Choa, Seyoung Park1,b
a성균관대학교 핀테크융합전공; b연세대학교 응용통계학과
aDepartment of Fintech, Sungkyunkwan University; bDepartment of Applied Statistics, Yonsei University
1Department of Applied Statistics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea. E-mail: ishspsy@yonsei.ac.kr
Received October 19, 2023; Revised December 6, 2023; Accepted January 15, 2024.
- Abstract
- 기대 수익률은 높이고, 재무적 위험은 낮추는 것을 목표로 하는 금융 포트폴리오 최적화 분야에서는 위험측정 지표에 관한 연구가 활발히 진행되어 왔다. 적은 자산으로 효율적인 포트폴리오를 구성하기 위해 다양한 페널티 항을 활용한 연구 또한 지속해서 진행되어 왔다. 본 논문에서는 평균-숏폴 포트폴리오와 SLOPE 페널티 항을 결합한 새로운 포트폴리오 최적화 식을 제안하였다. 이 과정에서 선형계획법으로 표현되지 않는 최적화식을 새로운 변수를 도입해 표현하고, 이를 ADMM 알고리즘을 사용해 해결하는 방식을 제안하였다. SLOPE 페널티 항이 갖는 그룹화 특징이 본 논문에서 제안하는 평균-숏폴 포트폴리오에서도 해당 특징이 유효함을 시뮬레이션 데이터를 바탕으로 확인하였다. 실증 데이터 분석을 통해서는 본 논문에서 제안한 모형을 기반으로 실제 투자 환경에서 고려할 수 있는 4가지 종류의 포트폴리오 구성 방식을 제안하고, 평가하였다.
- Research in the area of financial portfolio optimization, with the dual goals of increasing expected returns and reducing financial risk, has actively explored various risk measurement indicators. At the same time, the incorporation of various penalty terms to construct efficient portfolios with limited assets has been investigated. In this study, we present a novel portfolio optimization formula that combines the mean-shortfall portfolio and the SLOPE penalty term. Specifically, we formulate this optimization expression, which differs from linear programming, by introducing new variables and using the alternating direction method of multipliers (ADMM) algorithms. Through simulations, we validate the automatic grouping property of the SLOPE penalty term within the proposed mean-shortfall portfolio. Furthermore, using the model introduced in this paper, we propose and evaluate four different types of portfolio compositions relevant to real-world investment scenarios through empirical data analysis.
- 주요어 : 포트폴리오 최적화, 숏폴, 슬로프, ADMM
- Keywords : portfolio selection, shortfall, SLOPE, ADMM
- References
- Artzner P, Delbaen F, Eber JM, and Heath D (1999). Coherent measures of risk, Mathematical Finance, 9, 203-228.
- Bawa VS (1975). Optimal rules for ordering uncertain prospects, Journal of Financial Economics, 2, 95-121.
- Bertsimas D, Lauprete GJ, and Samarov A (2004). Shortfall as a risk measure: Properties, optimization and applications, Journal of Economic Dynamics & Control, 28, 1353-1381.
- Bogdan M, van den Berg E, Su W, and Cades E (2013). Statistical estimation and testing via the sorted L1 norm,Available from: https://arxiv.org/abs/1310.1969
- Bogdan M, van den Berg E, Su W, and Cades E (2015). SLOPE-adaptive variable selection via convex optimization, The Annals of Applied Statistics, 9, 1103-1140.
- Fishburn PC (1977). Mean-risk analysis with risk associated with below-target returns, The American Economic Review, 67, 116-126.
- Harlow WV and Rao R (1999). Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence, The Journal of Financial and Quantitative Analysis, 24, 285-311.
- Huang CF and Litzenberger RH (1988). Foundations for financial economics, The Review of Financial Studies, 4, 447-449.
- Kremer P, Lee S, Bogdan M, and Paterlini S (2020). Sparse portfolio selection via the sorted ℓ1-Norm, Journal of Banking & Finance, 110, 105687, 1-15.
- Markowitz H (1952). Portfolio selection, Journal of Finance, 7, 77-91.
- Markowitz H (1959). Portfolio Selection: Efficient Diversification of Investments, JohnWiley & Sons, New York.
- Park S, Song H, and Lee S (2019). Linear programing models for portfolio optimization using a benchmark, The European Journal of Finance, 25, 435-457.
- Rockafella RT and Uryasev S (2000). Optimization of conditional value-at-risk, Journal of Risk, 2, 493-517.
- Roy AD (1952). Safety first and the holding of assets, Econometrica, 20, 431-449.
- Sharpe WF (1966). Mutual fund performance, The Journal of Business, 39, 119-138.
- Zeng X and Figueiredo M (2014). Decreasing weighted sorted l1 regularization, IEEE Signal Processing Letters, 21, 1240-1244.
Full Text(PDF) Free