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| Research on the Proper Size of Investment Funds: Evidence from Chinese Mutual Funds |
| ZHANG Linlin, SHEN Hongbo, FAN Jianqing
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School of Social Development and Public Policy/School of Economics, Fudan University;
Operations Research and Financial Engineering, Princeton University |
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Abstract 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.
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Received: 29 June 2020
Published: 25 April 2022
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