Research on the Proper Size of Investment Funds: Evidence from Chinese Mutual Funds
ZHANG Linlin, SHEN Hongbo, FAN Jianqing
School of Social Development and Public Policy/School of Economics, Fudan University; Operations Research and Financial Engineering, Princeton University
Summary:
Over the last decade, the Chinese mutual fund market has grown enormously. However, compared with the developed mutual fund market, Chinese mutual funds are still relatively small and have much more room for development. Thus, it is worth asking whether a fund's size can expand indefinitely or should be restricted. In addition, previous studies have several limitations. First, the optimal mutual fund size calculated in the literature is mostly the optimal size for investors, rather than fund managers. Second, only a few papers study the optimal size for fund managers, but they fail to consider that the continuous expansion of fund size may lead to large-scale redemption by investors due to the diminishing marginal returns to scale, which makes the optimal size for fund managers impossible to achieve in practice. Third, this paper shows that principal-agent conflict, diminishing marginal returns, and large-scale redemption exist objectively in the fund market, and play a role in determining fund size. However, in the literature so far, the impacts of these constraints have not been included in the determination of optimal fund size. In view of the above problems and the limitations of research, this paper finds that fund size cannot be expanded indefinitely due to diminishing marginal returns to scale in the fund market. Based on the three identified constraints (principal-agent conflict, diminishing marginal returns to scale, and redemption of investors), this study proposes the concept of a proper fund size interval. It also improves the classical Berk and Green model (BG model) and proposes a theoretical model of the proper fund size interval and its evaluation index. Determining the proper fund size interval is practically relevant, because it takes into account the interests of both investors and fund managers and the market constraints on fund size. This paper also develops a method for determining whether the fund size matches its managers' ability. The evaluation index of proper fund size constructed in this paper can effectively identify and judge oversized funds, funds with the proper size, and undersized funds. Using Chinese stock and hybrid funds between 2011 and 2019 as a sample, this paper empirically examines the appropriateness of fund size. The main conclusions are as follows. First, we find that the average size of Chinese mutual funds is generally too large from 2011 to 2015, is appropriate from 2016 to 2018, and is too small in 2019. There is a significant negative relationship between fund performance and fund size, which indicates the existence of diminishing marginal returns to scale in the fund market. In the long run, the average net excess return tends to approach zero, and the probability of large-scale redemption of the fund with a nonnegative net excess return is far less than that of the fund with a negative net excess return. Second, as the market impact cost decreases annually, the upper bound and lower bound of the proper size interval are also decreasing, whereas the width of the proper size interval is increasing. The reason is that the upper and lower bounds of the proper size interval are influenced by managers' ability and impact cost, and the width of the proper size interval is only influenced by the impact cost. Third, the performance of funds with the proper size is much better than that of oversized and undersized funds. The net excess return of oversized funds is negative. Fourth, the proportion of undersized funds is the largest and increases with each passing year. Due to the rapid growth in the number of start-up funds, and the relatively slow growth in the number of funds with the proper size, the proportion of oversized funds is the second largest and is decreasing annually. However, the proportion of funds with the proper size is the smallest. In summary, funds with the proper size have better fund performance and fund flow. Therefore, for fund companies to increase the market share of funds with the proper size, they should constantly harness the latent potential of fund managers and keep improving their ability. At the same time, fund managers should be given timely payoff incentives, to match their ability and the fund performance. Regulators should continue to rapidly improve the evaluation system of the fund industry. Rather than paying attention only to fund performance, they should also consider investors' investment interests and evaluate the appropriateness of the fund size and fund managers' ability.
张琳琳, 沈红波, 范剑青. 证券投资基金规模适度性研究——基于中国市场的证据[J]. 金融研究, 2022, 501(3): 189-206.
ZHANG Linlin, SHEN Hongbo, FAN Jianqing. Research on the Proper Size of Investment Funds: Evidence from Chinese Mutual Funds. Journal of Financial Research, 2022, 501(3): 189-206.
[1]李科、陆蓉、夏翊和胡凡,2019,《基金经理更换、股票联动与股票价格》,《金融研究》第1期,第188~206页。
[2]李金龙,2020,《基金极端收益与资金流动——来自中国开放式基金的证据》,《财经研究》第9期,153~168页。
[3]李志冰和刘晓宇,2019,《基金业绩归因与投资者行为》,《金融研究》第2期,第188~206页。
[4]梁珊、王正刚和郭葆春,2016,《基金规模与业绩关系的再检验——基于 DGTW方法的业绩评价》,《投资研究》第3期,第151~58页。
[5]刘静,2000,《证券投资基金的功能缺陷与委托代理问题》,《经济理论与经济管理》第5期,第36~39页。
[6]杨坤、曹晖和宋双杰,2013,《基金业绩与资金流量: 明星效应与垫底效应》,《管理科学学报》第5期,第29~38页。
[7]吴偎立和常峰源,《ETF、股票流动性与流动性同步性》,《经济学(季刊)》第2期,第645~670页。
[8]Amihud, Yakov. 2002. “Illiquidity and Stock Returns: Cross-section and Time-series Effects,” Journal of Financial Markets, 5(1):31~56.
[9]Barras, Laurent, Scaillet Olivier, and Russ Wermers. 2010. “False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alphas,” The Journal of Finance, 65(1): 179~216.
[10]Berk, Jonathan B., and Richard C. Green. 2004. “Mutual Fund Flows and Performance in Rational Markets,” Journal of Political Economy, 112(6): 1269~1295.
[11]Brown, David P., and Youchang Wu. 2016. “Mutual Fund Flows and Cross‐fund Learning Within Families,” The Journal of Finance, 71(1): 383~424.
[12]Chen, Joseph, Harrison Hong, Ming Huan, and Jeffrey D. Kubik. 2004. “Does Fund Size Erode Mutual Fund Performance? The Role of Liquidity and Organization,” American Economic Review, 94(5): 1276~1302.
[13]Chen, Qi, Itay Goldstein, and Wei Jiang. 2010. “Payoff Complementarities and Financial Fragility: Evidence from Mutual Fund Outflows,” Journal of Financial Economics, 97(2): 239~262.
[14]Chevalier, Judith, and Glenn Ellison. 1997. “Risk Taking by Mutual Funds as A Response to Incentives,” Journal of Political Economy, 105(6): 1167~1200.
[15]Collins, Sean, and Phillip Mack. 1997. “The Optimal Amount of Assets under Management in the Mutual Fund Industry,” Financial Analysts Journal, 53(5): 67~73.
[16]Fama, Eugene F., and Kenneth R. French. 2010. “Luck Versus Skill in the Cross‐section of Mutual Fund Returns,” The Journal of Finance, 65(5): 1915~1947.
[17]Pástor, Luboš, and Robert F. Stambaugh. 2012. “On the Size of the Active Management Industry,” Journal of Political Economy, 120(4): 740~781.
[18]Ross, Stephen A. 1973. “The Economic Theory of Agency: The Principal's Problem,” The American Economic Review, 63(2): 134~139.
[19]Sirri, Erik R., and Peter Tufano. 1998. “Costly Search and Mutual Fund Flows,” The Journal of Finance, 53(5): 1589~1622.
[20]Song, Yang. 2020. “The Mismatch between Mutual Fund Scale and Skill,” The Journal of Finance, 75(5): 2555~2589.
[21]Yin, Chengdong. 2016. “The Optimal Size of Hedge Funds: Conflict between Investors and Fund Managers,” The Journal of Finance, 71(4): 1857~1894.
[22]Zhu, Min. 2018. “Informative Fund Size, Managerial Skill, and Investor Rationality,” Journal of Financial Economics, 130(1): 114~134.