What Leads to the Coexistence between “Funds Making Money” and “Investors Losing Money”？—A Theoretical Explanation Based on Common Agency Theory
LI Xuefeng, QI Xiao, XU Rong
School of Finance, Nankai University; Institute of Chinese Path to Modernization, Nankai University;
School of Public Affairs, Zhejiang University; Happy City Research Institute, Hangzhou City University
Summary:
Mutual fund is a popular financial instrument that a few professionals serve most non-professionals for operating funds to earn higher returns, but it is often complained by lots of fund holders that “funds make money while investors lose money”. Intuitively, in 2022, there are over 10,000 mutual funds with total size over 26 trillion yuan (21.5% of China's GDP that year) in China. Among them, all the stock funds and stock-oriented hybrid funds earned over 1.5 billion average weighted net profit themselves while made about-18.23% average weighted return for their fund holders. Existing research has worked on explaining this phenomenon, criticizing fund holders' irrationality as the main reason. But this only explains why investors lose money, as it ignores the fact that the interest between fund holders, fund managers as well as fund management companies should have been highly consistent due to funds' mechanism. Moreover, most papers, affected by the corporate-based form in the US, take fund management companies and fund managers, or fund management companies and fund holders, as a whole and investigate their relationship, while ignoring the truth that fund management companies and fund holders have heterogenous incentives on fund managers under the form of contractual fund in China. In view of this, based on the common agency theory (multi-principals vs. one agent), we constructed a game model that describes the interests, incentives and behavior among fund management companies, fund managers and fund holders in China. The general framework is as follows: (1) Fund holders' income is determined by fund's performance; fund management companies' income is determined by fund's size (fixed management fee rate); fund managers' income is determined by both fund's size (scale-based compensation) and fund's performance (performance-based compensation). (2) Fund's size is determined by fund holders' purchasing and redemption, and fund holders' purchasing and redemption are determined by their “rationality” (how they react to fund's last-period performance). (3) Fund's performance is determined by fund managers' effort, and fund managers' effort is determined by the incentives of fund management companies (via scale-based compensation and performance-based compensation) and fund holders (via how they purchase and redeem), as well as how fund managers weight them. (4) Fund holders choose how and how much their subscription and redemption react to fund's performance in the last period, fund management companies choose how much they compensate fund managers on both fund's size and performance, and fund managers choose how much they weight different incentives to maximize their net incomes. Under this framework, we then prove that: (1) If fund holders are “rational” (purchase funds with positive last-period performance and redeem funds with negative last-period performance), the “equilibrium” of the game will be that all parties focus on improving or compensating for fund's performance and can all “make money”. (2) If fund holders have a disposition effect (redeem funds with positive last-period performance and keep holding funds with non-positive last-period performance), the equilibrium of the game will be that fund management companies and fund managers both seek to maintain “zero performance” on every single fund and to issue more funds (to make money via management fees), leading to the result that “fund makes money while investor loses money”. Meanwhile, we set proper parameter values according to both market practice as well as academic research to run numerical simulation to prove the robustness of our game model. Thus, we finally propose following policy implications: (1) Since rationality is the key determinant of the coordination of interests of all parties, fund holders should be educated as investors to increase their rationality under the current form of contractual fund. (2) Pilot scheme of the corporate-based form, which may eliminate the potential interest conflicts between fund management companies and fund holders by “merging” them as one. Our marginal contributions may include: (1) Our model takes fund management companies, fund managers and fund holders into account rather than consider either fund management companies and fund managers or companies and fund holders as one single party as most papers did, thus focusing on the governance problem of public funds in China. (2) We are the first to build a theoretical game model describing the contractual funds' operation in China, thus digging out the root of how different market subjects choose to behave and provide a new perspective and the theoretical basis for future research. (3) Using our game model, we provide a fundamental theoretical explanation to why funds make money while investors lose money, giving a deeper understanding of its reasons and solutions. Our future work based on this paper is to refine the model by relaxing assumptions to expand its applicability to more types of funds (such as close-end funds, regular open-end funds, etc.) and explaining more problems (such as floating management rate reform).
李学峰, 齐霄, 徐荣. 基金赚钱与投资者亏钱现象为何并存？——基于共同代理的理论解释[J]. 金融研究, 2024, 526(4): 113-131.
LI Xuefeng, QI Xiao, XU Rong. What Leads to the Coexistence between “Funds Making Money” and “Investors Losing Money”？—A Theoretical Explanation Based on Common Agency Theory. Journal of Financial Research, 2024, 526(4): 113-131.
[1]曹兴和秦耀华,2013,《固定费用结构下基金经理管理费激励研究》,《财经理论与实践》第5期,第107～111页。 [2]曹兴、杨春白雪和聂雁威,2012,《持基激励对基金经理投资行为的影响分析》,《重庆大学学报(社会科学版)》第1期,第36～41页。 [3]陈永生和杨宁,2011,《投资者具有正确选择基金的能力吗》,《宏观经济研究》第5期,第50～56+69页。 [4]韩燕和崔鑫,2014,《基金行业的委托代理关系与基金经理的短视行为研究》,《管理评论》第9期,第34～45页。 [5]李学峰、黄亚元和王健,2016,《持有人行为对基金管理人的隐性激励——理论分析与实证检验》,《证券市场导报》第1期,第62～71页。 [6]李学峰、李心印和张舰,2009,《开放式基金持有人申购赎回行为“收益敏感性指标”的分析》,《金融理论与实践》第5期,第21～25页。 [7]李学峰、田元泉和李佳明,2012,《市场竞争的基金治理效应:理论假说与实证检验》,《证券市场导报》第5期,第41～46页。 [8]李学峰、张舰、田元泉和李佳明,2011,《我国证券投资基金的隐性激励——测度、机制与契约优化》,《金融研究》第10期,第185～197页。 [9]李学峰、赵鹏宇和刘晓龙,2022,《浮动管理费能否改善基金治理》,《上海金融》第4期,第69～79页。 [10]廖长友和赵修文,2016,《内部治理、市场约束与基金的窗饰行为》,《证券市场导报》第8期,第55～63+78页。 [11]刘阳、田正磊和罗荣华,2016,《机构持有、业绩追逐与基金窗饰效应》,《投资研究》第8期,第60～76页。 [12]刘洋溢、廖妮和罗荣华,2022,《基金赚钱、基民不赚钱:业绩持续性感知与基金投资者行为》,《中国工业经济》第2期,第156～174页。 [13]刘志远和姚颐,2005,《开放式基金的“赎回困惑”现象研究》,《证券市场导报》第2期,第37～41页。 [14]陆蓉、陈百助、徐龙炳和谢新厚,2007,《基金业绩与投资者的选择——中国开放式基金赎回异常现象的研究》,《经济研究》第6期,第39～50页。 [15]孟庆斌、吴卫星和于上尧,2015,《基金经理职业忧虑与其投资风格》,《经济研究》第3期,第115～130页。 [16]孟庆斌、杨俊华、许伟和吴蕾,2019,《投资者申赎与公募基金业绩粉饰——基于中国基金信息披露差异的经验证据》,《管理评论》第11期,第20～32页。 [17]莫泰山和朱启兵,2013,《为什么基金投资人的投资回报低于基金行业的平均回报——基于“聪明的钱”效应实证检验的解释》,《金融研究》第11期,第193～206页。 [18]帕特里克·博尔顿和马赛厄斯·德瓦特里庞,2008,《合同理论》,费方域等译,格致出版社。 [19]彭文平和陈延,2015,《基金利益冲突与管理努力替代——基于基金经理“一拖多”现象的研究》,《投资研究》第4期,第129～142页。 [20]彭文平和肖继辉,2013,《业绩排名对投资风格影响研究——来自开放式基金的证据》,《证券市场导报》第11期,第47～54+61页。 [21]彭文平和杨蓝蓝,2013,《业绩评价、职业声誉和基金经理行为异化》,《经济管理》第6期,第81～94页。 [22]滕莉莉、韦妃和梁权熙,2013,《管理人持基的投资基金治理效应:理论分析与经验证据》,《投资研究》第12期,第55～67页。 [23]王良和冯涛,2015,《基于声誉及信息操纵考虑的基金经理持股策略演化博弈研究》,《中国管理科学》第9期,第116～123页。 [24]肖继辉、彭文平、许佳和王琦,2016,《业绩排名与预期风险调整——考虑报酬激励与解职风险交互影响的新证据》,《经济学(季刊)》第3期,第1177～1204页。 [25]肖欣荣和田存志,2016,《激励契约、规模报酬递减与组织形式演进:以公募基金和私募基金为例》,《南开经济研究》第4期,第38～55页。 [26]姚伟、黄卓和郭磊,2003,《公司治理理论前沿综述》,《经济研究》第5期,第83～90+94页。 [27]赵道致、郝家芹、杨洁和韩红帅,2020,《考虑平台网络外部性的分享经济中三方演化博弈分析》,《控制与决策》第7期,第1741～1750页。 [28]Arribas, I. and A. Urbano, 2017, “Multiproduct Trading With a Common Agent Under Complete Information: Existence and Characterization of Nash Equilibrium”, Journal of Economic Theory, 167, pp.14～38. [29]Bernheim, B. and M. Whinston, 1985, “Common Marketing Agency as a Device for Facilitating Collusion”, The RAND Journal of Economics, 16(2), pp.269～281. [30]Bernheim, B. and M. Whinston, 1986, “Common Agency”, Econometrica, 54(4), pp.923～942. [31]Biglaiser, G. and C. Mezzetti, 1993, “Principals Competing for an Agent in the Presence of Adverse Selection and Moral Hazard”, Journal of Economic Theory, 61(2), pp.302～330. [32]Brown, S., W. Goetzmann and J. Park, 2001, “Careers and Survival: Competition and Risk in the Hedge Fund and CTA Industry”, The Journal of Finance, 56(5), pp.1869～1886. [33]Chen, J., H. Hong, W. Jiang and J. Kubik, 2013, “Outsourcing Mutual Fund Management: Firm Boundaries, Incentives, and Performance”, The Journal of Finance, 68(2), pp.523～558. [34]Chevalier, J. and G. Ellison, 1997, “Risk Taking by Mutual Funds as a Response to Incentives”, Journal of Political Economy, 105(6), pp.1167～1200. [35]Chevalier, J. and G. Ellison, 1999, “Career Concerns of Mutual Fund Managers”, The Quanterly Journal of Economics, 114(2), pp.389～432. [36]Feng, X., M. Zhou and K. C. Chan, 2014, “Smart Money or Dumb Money？ A Study on the Selection Ability of Mutual Fund Investors in China”, North American Journal of Economics ＆ Finance, 30, pp.154～170. [37]Fudenberg, D. and J. Triole, 1983, “Sequential Bargaining with Incomplete Information”, Review of Economic Studies, 50(2), pp.221～247. [38]Fulkerson, J. and T. Riley, 2017, “Mutual Fund Liquidity Costs”, Financial Management, 46(2), pp.359～375. [39]Grossman, S. and O. Hart, 1986, “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration”, Journal of Political Economy, 94(4), pp.691～719. [40]Grout, P., 1984, “Investment and Wages in the Absence of Binding Contracts: A Nash Bargining Approach”, Econometrica, 52(2), pp.449～460. [41]Hart, O. and J. Triole, 1988, “Contract Renegotiation and Coasian Dynamics”, Review of Economic Studies, 55(4), pp.509～540. [42]Kempf, A., S. Ruenzi and T. Thiele, 2009, “Employment Risk, Compensation Incentives, and Managerial Risk Taking: Evidence from the Mutual Fund Industry”, Journal of Financial Economics, 92(1), pp.92～108. [43]Keswani, A. and D. Stolin, 2008, “Which Money is Smart？ Mutual Fund Buys and Sells of Individual and Institutional Investors”, The Journal of Finance, 63(1), pp.85～118. [44]Kyle, S., H. Ou-Yang and B. Wei, 2011, “A Model of Portfolio Delegation and Strategic Trading”, The Review of Financial Studies, 24(11), pp.3778～3812. [45]Lee, J., C. Trzcinka and S. Venkatesan, 2019, “Do Portfolio Manager Contracts Contract Portfolio Management？”, The Journal of Finance, 74(5), pp.2543～2577. [46]Legros, P. and S. Matthews, 1993, “Efficient and Nearly Efficient Partnerships”, Review of Economic Studies, 60, pp.599～611. [47]Ling, L. and J. J. Arias, 2013, “Mutual Fund Flows and Window-dressing”, The Quarterly Review of Economics and Finance, 53(4), pp.440～449. [48]Lynch, A. and D. Musto, 2003, “How Investors Interpret Past Fund Returns”, The Journal of Finance, 58(5), pp.2033～2058. [49]Mehran, H. and M. Stulz, 2007, “The Economics of Conflicts of Interest in Financial Institution”, Journal of Financial Economics, 85(2), pp.267～296. [50]Mirrlees, J., 1999, “The Theory of Moral Hazard and Unobservable Behaviour: Part I”, Review of Economic Studies, 66(1), pp.3～21. [51]Ross, S., 1973, “The Economic Theory of Agency: The Principal's Problem”, American Economic Review, 63(2), pp.134～139. [52]Sappington, D., 1983, “Limited Liability Contracts between Principal and Agent”, Journal of Economic theory, 29(1), pp.1～21. [53]Shefrin, H. and M. Statman, 1985, “The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence”, The Journal of Finance, 40(3), pp.777～790. [54]Smith, J. M., 1974, “The Theory of Games and the Evolution of Animal Conflicts”, Journal of theoretical biology, 47(1), pp.209～221. [55]Song, Y., 2020, “The Mismatch Between Mutual Fund Scale and Skill”, The Journal of Finance, 75(5), pp.2555～2589. [56]Zhu, M., 2018, “Informative Fund Size, Managerial Skill, and Investor Rationality”, Journal of Financial Economics, 130, pp.114～134.
