On persistence in mutual fund performance 1997翻译

On persistence in mutual fund performance 1997

ABSTRACT摘要

Using a sample free of survivor bias, I demonstrate that common factors in stock returns and investment expenses almost completely explain persistence in equity mutual funds' mean and risk-adjusted returns. Hendricks, Patel and Zeckhauser's (1993) “hot hands” result is mostly driven by the one-year momentum effect of Jegadeesh and Titman (1993), but individual funds do not earn higher returns from following the momentum strategy in stocks. The only significant persistence not explained is concentrated in strong underperformance by the worst-return mutual funds. The results do not support the existence of skilled or informed mutual fund portfolio managers.

使用了一个没有幸存者偏误的样本，我证实了股票收益和投资费用中的共同因素几乎完全解释了股票共同基金平均收益和风险调整收益的持续性。Hendricks, Patel and Zeckhauser's (1993)的“热手”主要是由Jegadeesh和Titman（1993）的一年动量效应驱动的，但单个基金不会从股票的动量策略中获得更高的回报。唯一无法解释的显著持续性在回报最差的共同基金表现不佳。研究结果不支持存在能力强或知情的共同基金投资组合经理。

Persistence in mutual fund performance does not reflect superior stock-picking skill. Rather, common factors in stock returns and persistent differences in mutual fund expenses and transaction costs explain almost all of the predictability in mutual fund returns. Only the strong, persistent underperformance by the worst-return mutual funds remains anomalous.

Mutual fund persistence is well documented in the finance literature, but not well explained. Hendricks, Patel, and Zeckhauser (1993), Goetzmann and Ibbotson (1994), Brown and Goetzmann (1995), and Wermers (1996) find evidence of persistence in mutual fund performance over short-term horizons of one to three years, and attribute the persistence to “hot hands” or common investment strategies. Grinblatt and Titman (1992), Elton, Gruber, Das, and Hlavka (1993), and Elton, Gruber, Das, and Blake (1996) document mutual fund return predictability over longer horizons of five to ten years, and attribute this to manager differential information or stock-picking talent. Contrary evidence comes from Jensen (1969), who does not find that good subsequent performance follows good past performance. Carhart (1992) shows that persistence in expense ratios drives much of the long-term persistence in mutual fund performance.

共同基金业绩的持续性并不反映出优秀的选股技巧。相反，股票回报的共同因素以及共同基金费用和交易成本的持续差异解释了共同基金回报的几乎所有可预测性。只有回报率最差的共同基金表现强势或新股偏弱现象的情况仍然反常。共同基金持续性在金融文献中有很好的记录，但没有很好的解释。Hendricks、Patel和Zeckhauser（1993年）、Goetzmann和Ibbotson（1994年）、Brown和Goetzmann（1995年）以及Wermers（1996年）发现了共同基金业绩在一到三年短期内具有持续性的证据，并将这种持续性归因于“热手”或共同投资策略。Grinblatt和Titman（1992）、Elton、Gruber、Das和Hlavka（1993）以及Elton、Gruber、Das和Blake（1996）记录了五到十年更长时间内共同基金回报的可预测性，并将其归因于经理差异信息或选股人才。Jensen（1969）提供了相反的证据，他没有发现好的过去表现跟着好的后续表现。Carhart（1992）表明，支出比率的持续性在很大程度上推动了共同基金业绩的长期持续性。

My analysis indicates that Jegadeesh and Titman's (1993) one-year momentum in stock returns accounts for Hendricks, Patel, and Zeckhauser's (1993) hot hands effect in mutual fund performance. However, funds that earn higher one-year returns do so not because fund managers successfully follow momentum strategies, but because some mutual funds just happen by chance to hold relatively larger positions in last year's winning stocks. Hot-hands funds infrequently repeat their abnormal performance. This is in contrast to Wermers (1996), who suggests that it is the momentum strategies themselves that generate short-term persistence, and Grinblatt, Titman, and Wermers (1995), who find that funds following momentum strategies realize better performance before management fees and transaction expenses. While measuring whether funds follow the momentum strategy is imperfect in my sample, individual mutual funds that appear to follow the one-year momentum strategy earn significantly lower abnormal returns after expenses. Thus, I conclude that transaction costs consume the gains from following a momentum strategy in stocks.

我的分析表明，Jegadeesh和Titman（1993）的一年期股票收益动量解释了Hendricks、Patel和Zeckhauser（1993）在共同基金业绩中的热手效应。然而，获得了更高一年期回报的基金之所以这样做，并不是因为基金经理成功地遵循了动量策略，而是因为一些共同基金只是碰巧在去年获胜的股票中持有相对较大的头寸。热手效应的基金很少重复其异常表现。这与Wermers（1996）和Grinblatt、Titman和Wermers（1995）形成了对比，Wermers（1996）认为动量策略本身会产生短期持续性，而Grinblatt、Titman和Wermers（1995）发现，遵循动量策略的基金在排除管理费和交易费用之前会实现更好的绩效。虽然在我的样本中，衡量基金是否遵循动量策略并不完善，但似乎遵循一年动量策略的个别共同基金在支出后获得的异常回报显著较低。因此，我得出结论，交易成本消耗了股票动量策略带来的收益。

I demonstrate that expenses have at least a one-for-one negative impact on fund performance, and that turnover also negatively impacts performance. By my estimates, trading reduces performance by approximately 0.95 percent of the trade's market value. Variation in costs per transaction across mutual funds also explains part of the persistence in performance. In addition, I find that fund performance and load fees are strongly and negatively related, probably due to higher total transaction costs for load funds. Holding expense ratios constant, load funds underperform no-load funds by approximately 80 basis points per year. (This figure ignores the load fees themselves.)

我证明了交易费用对基金绩效至少有一比一的负面影响，而基金经理人变动也会对绩效产生负面影响。据我估计，交易会使业绩降低约0.95%的交易市值。共同基金每笔交易成本的变化也解释了业绩持续性的部分原因。此外，我发现基金绩效和销售费用之间存在强烈的负相关，这可能是由于负载基金的总交易成本较高。在费用比率不变的情况下，有销售费用基金的表现每年比无销售费用基金差约80个基点。（此数字忽略了销售费用本身。）

The joint-hypothesis problem of testing market efficiency conditional on the imposed equilibrium model of returns clouds what little evidence there is in this article to support the existence of mutual fund manager stock-picking skill. Funds with high past alphas demonstrate relatively higher alphas and expected returns in subsequent periods. However, these results are sensitive to model misspecification, since the same model is used to rank funds in both periods. In addition, these funds earn expected future alphas that are insignificantly different from zero. Thus, the best past-performance funds appear to earn back their expenses and transaction costs even though the majority underperform by approximately their investment costs.

测试市场效率有条件的返回云层施加的均衡模型的联合假说问题，本文中几乎没有有证据支持共同基金经理选股技巧的存在。过去α较高的基金表现出相对较高的α和后续期间的预期回报。然而，这些结果对模型的错误设定是敏感的，因为在这两个时期使用相同的模型对基金进行排名。此外，这些基金获得的预期未来α不显著等于0。因此，过去表现最好的基金似乎能够赚回其费用和交易成本，尽管大多数基金的表现差于其投资成本。

This study expands the existing literature by controlling for survivor bias, and by documenting common-factor and cost-based explanations for mutual fund persistence. Section I discusses the database and its relation to other survivor-bias corrected data sets. Section II presents models of performance measurement and their resulting pricing error estimates on passively-man-aged benchmark equity portfolios. Section III documents and explains the one-year persistence in mutual fund returns, and Section IV further interprets the results. Section V examines and explains longer-term persistence, and Section VI concludes.

本研究拓展了现有文献控制幸存者偏误，记录共同基金持续性的共同因素和基于成本的解释。第一节讨论了数据库及其与其他幸存者偏误校正数据集的关系。第二节介绍了被动人工基准股票投资组合的绩效衡量模型及其由此产生的定价误差估计。第三节记录并解释了共同基金收益的一年持续性，第四节进一步解释了结果。第五节检查并解释长期持续性，第六节得出结论。

I.Data

My mutual fund database covers diversified equity funds monthly from January 1962 to December 1993. The data are free of survivor bias, since they include all known equity funds over this period. I obtain data on surviving funds, and for funds that have disappeared since 1989, from Micropal/Investment Company Data, Inc. (ICDI). For all other nonsurviving funds, the data are collected from FundScope Magazine, United Babson Reports, Wiesenberger Investment Companies, the Wall Street Journal, and past printed reports from ICDI. See Carhart (1995a) for a more detailed description of database construction.

我的共同基金数据库涵盖1962年1月至1993年12月的月度多种股票基金数据。这些数据没有幸存者偏误，因为它们包括这一时期所有已知的股票基金。我从Micropal/Investment Company data，Inc.（ICDI）获得了幸存基金以及1989年以来已经消失的基金的数据。对于所有其他非存续基金，数据收集自FundScope杂志、United Babson Reports、威森伯格(Wiesenberger)投资公司、《华尔街日报》以及ICDI过去的印刷报告。有关数据库构造的更详细说明，请参见Carhart（1995a）。

Table I reports summary statistics on the mutual fund data. My sample includes a total of 1,892 diversified equity funds and 16,109 fund years. The sample omits sector funds, international funds, and balanced funds. The remaining funds are almost equally divided among aggressive growth, longterm growth, and growth-and-income categories. In an average year, the sample includes 509 funds with average total net assets (TNA) of $218 million and average expenses of 1.14 percent per year. In addition, funds trade 77.3 percent of the value of their assets (Mturn) in an average year. Since reported turnover is the minimum of purchases and sales over average TNA, I obtain Mturn by adding to reported turnover one-half of the percentage change in TNA adjusted for investment returns and mergers. Also, over the full sample, 64.5 percent of funds charge load fees, which average 7.33 percent.

表一报告了共同基金数据的汇总统计数据。我的样本包括总共1892只多样化股票基金和16109只基金年。样本中不包括行业基金、国际基金和平衡基金。其余基金几乎平均分配在积极增长、长期增长以及增长和收入类别中。在平均年份，样本包括509只基金，平均总净资产（TNA）为2.18亿美元，平均每年费用为1.14%。此外，基金平均每年交易占其资产价值（Mturn）的77.3%。由于披露的换手率是平均TNA里面采购和销售最低的，我通过在报告的换手率中加上TNA中根据投资回报和合并调整的百分比变化的一半来获得Mturn。此外，在整个样本中，64.5%的基金收取销售费用，平均为7.33%。

Table I. Mutual Fund Database Summary Statistics表一共同基金数据库汇总统计

By December 31, 1993, about one-third of the total funds in my sample had ceased operations, so a sizeable portion of the database is not observable in most commercially available mutual fund databases. Thus, survivor bias is an important issue in mutual fund research. (See Brown, Goetzmann, Ibbotson, and Ross (1992), Carhart (1995b), and Wermers (1996).) While my sample is, to my knowledge, the largest and most complete survivor-bias-free mutual fund database currently available, Grinblatt and Titman (1989), Malkiel (1995), Brown and Goetzmann (1995), and Wermers (1996) use similar databases to study mutual funds. Grinblatt and Titman (1989) and Wermers (1996) use quarterly “snapshots” of the mutual funds' underlying stock holdings since 1975 to estimate returns gross of transactions costs and expense ratios; whereas my data set uses only the net returns. Malkiel (1995) uses quarterly data from 1971 to 1991, obtained from Lipper Analytical Services. Although Malkiel studies diversified equity funds, his data set includes about 100 fewer funds each year than mine, raising the possibility of some selection bias in the Lipper data set. (We both exclude balanced, sector, and international funds.) Nonetheless, Malkiel's mean mutual fund return estimate from 1982 to 1990, 12.9 percent, is very close to the 13 percent that I find.

截至1993年12月31日，在我的样本中，大约三分之一的基金已经停止运作，所以在大多数市面上可获得的共同基金数据库中，数据库的很大一部分是不可见的。因此，幸存者偏误是共同基金研究中的一个重要问题。（见Brown、Goetzmann、Ibbotson和Ross（1992）、Carhart（1995b）和Wermers（1996）。）据我所知，我的样本是目前可用的最大和最完整的无幸存者偏见共同基金数据库，Grinblatt和Titman（1989）、Malkiel（1995）、布朗和戈茨曼（1995）以及沃默斯（1996）使用类似的数据库来研究共同基金。Grinblatt和Titman（1989）以及Wermers（1996）使用自1975年以来共同基金基础股票持有量的季度“快照”来估计交易成本和费用比率的总回报；而我的数据集只使用净收益。Malkiel（1995）使用了1971年至1991年的季度数据，这些数据来自Lipper分析服务公司。尽管Malkiel研究的是多元化股票基金，但他的数据集每年比我的少约100只基金，这增加了Lipper数据集中某些选择偏差的可能性。（我们都不包括平衡基金、行业基金和国际基金。）尽管如此，Malkiel从1982年到1990年的平均共同基金回报估计为12.9%，非常接近我发现的13%。

Brown and Goetzmann (1995) study a sample of mutual funds very similar to mine, but calculate their returns differently. Their sample is from the Wiesenberger Investment Companies annual volumes from 1976 to 1988. They calculate annual returns from the changes in net asset value per share (NAV), and income and capital gains distributions reported annually in Wiesenberger. As Brown and Goetzmann acknowledge, their data suffer from some selection bias, because the first years of new funds and last years of dead funds are missing. In addition, because funds voluntarily report this information to Wiesenberger, some funds may not report data in years of poor performance. Working in the opposite direction, Brown and Goetzmann calculate return as the sum of the percentage change in NAV (adjusted for capital gains distributions when available) and percentage income return. This procedure biases their return estimates downward somewhat, since it ignores dividend reinvestment. My data set mitigates these problems because I obtain monthly total returns from multiple sources and so have very few missing returns. In addition, I obtain from ICDI the reinvestment NAVs for capital gains and income distributions. Over the 1976 to 1988 period, Brown and Goetzmann report a mean annual return estimate of 14.5 percent, very close to the 14.3 percent in my data set. By these calculations, selection bias accounts for at least 20 basis points per year in Brown and Goetzmann's sample. It could be somewhat more, however, due to the downward bias in their return calculations.

Brown和Goetzmann（1995）研究的共同基金样本与我非常相似，但以不同方式计算回报。他们的样本来自于维森伯格投资公司1976年至1988年的年销售量。他们根据每股净资产（NAV）的变化以及维森伯格每年报告的收入和资本收益分配计算年度回报。正如Brown和Goetzmann所承认的那样，他们的数据存在一些选择偏差，因为新基金的头几年和基金破产清算的最后几年都不存在。此外，由于基金自愿向Wiesenberger报告这些信息，一些基金在业绩不佳的年份可能不会报告数据。Brown和Goetzmann的工作方向相反，他们将回报计算为NAV百分比变化（根据可用的资本收益分配进行调整）和收入回报百分比之和。由于忽略了股息再投资，这一程序会使他们的回报估计值有所下降。而我的数据集减弱了这些问题，因为我从多个来源获得每月总回报，因此缺少的回报很少。此外，我从ICDI获得资本收益和收入分配的再投资资产净值。在1976年至1988年期间，Brown和Goetzmann报告的平均年回报率估计为14.5%，非常接近我的数据集中的14.3%。通过这些计算，在Brown和Goetzmann的样本中，选择偏差每年至少有20个基点。然而，由于回报计算中存在向下的偏差，这可能会更大一些。

II. Models of Performance Measurement

I employ two models of performance measurement: the Capital Asset Pricing Model (CAPM) described in Sharpe (1964) and Lintner (1965), and my (Carhart (1995)) 4-factor model. This section briefly describes these models, and evaluates their performance estimates on quantitatively-managed portfolios of New York Stock Exchange (NYSE), American Stock Exchange (Amex), and Nasdaq stocks. For comparative purposes, this section also reports performance estimates from Fama and French's (1993) 3-factor model.1

我采用两种绩效测量的模型: Sharpe (1964) and Lintner (1965)的资本资产定价模型(CAPM)，和我(CARHART (1995))的四因素模型。本节简要介绍这些模型，并评估他们的表现按纽约证券交易所(NYSE)，美国证券交易所（AMEX)，纳斯达克股市定量管理的投资组合估计。为便于比较，本节还叙述了Fama and French's ( 1993年）的三因子模型的表现估计。

I construct my 4-factor model using Fama and French's (1993) 3-factor model plus an additional factor capturing Jegadeesh and Titman's (1993) one-year momentum anomaly.2 The 4-factor model is consistent with a model of market equilibrium with four risk factors. Alternately, it may be interpreted as a performance attribution model, where the coefficients and premia on the factor-mimicking portfolios indicate the proportion of mean return attributable to four elementary strategies: high versus low beta stocks, large versus small market capitalization stocks, value versus growth stocks, and one-year return momentum versus contrarian stocks. I employ the model to “explain” returns, and leave risk interpretations to the reader.

四因素模型与市场均衡模型是一致的，我建立我的四因素模型使用Fama and French's( 1993年)的三因子模型加上一个额外的因素捕获Jegadeesh和 Titman (1993年)一年的势头异常,四因素模型和四个风险因素市场平衡模型是一致的。另外，它可能会作为业绩归因模型,因子模拟投资组合的系数和溢价，表明平均回报的比例归属四个基本的策略:高与低贝塔的股票，大与小市值个股，价值型与成长型的股票，一年期回报势头投资和相反投资股票。我采用的模型“解释”了回报，并留下风险给读者的诠释。

I estimate performance relative to the CAPM, 3-factor, and 4-factor models as

我估计有关CAPM、三因子和四因子模型为：

r i t = α i T + β i T VWRF t + e i t t = 1 , 2 , ⋯ , T(1)

r i t = α i T + b i T RMRF t + s i T SMB t + h i T HML t + e i t t = 1 , 2 , ⋯ , T(2)

r i t = α i T + b i T RMRF t + s i T SMB t + h i T HML t + p i T PR 1 YR t + e i t t = 1 , 2 , ⋯ , T(3)

where r it is the return on a portfolio in excess of the one-month T-bill return; VWRF is the excess return on the CRSP value-weighted portfolio of all NYSE, Amex, and Nasdag stocks; RMRF is the excess return on a value-weighted aggregate market proxy; and SMB HML, and PR1YR are returns on value-weighted, zero-investment, factor-mimicking portfolios for size, book-to-market equity, and one-year momentum in stock returns.3

Rit，是超过为期一个月的短期国库券的回报的投资组合的回报; VWRF是所有纽约证交所,美国证交所和纳斯达克股票（NYSE,Amex, and Nasdaq stocks）CRSP价值加权组合的超额收益；RMRF是一个超额收益价值加权的总市值代理和中小企业，HML，PR1YR是加权值，零基投资，规模因子模拟投资组合，账面价值和市场价值权，股票回报的一年期的动量。

Summary statistics on the factor portfolios reported in Table II indicate that the 4-factor model can explain considerable variation in returns. First, note the relatively high variance of the SMB HML, and PR1YR zero-investment portfolios and their low correlations with each other and the market proxies. This suggests the 4-factor model can explain sizeable time-series variation. Second, the high mean returns on SMB HML, and PR1YR suggest that these three factors could account for much cross-sectional variation in the mean return on stock portfolios. In addition, the low cross-correlations imply that multicollinearity does not substantially affect the estimated 4-factor model loadings.

总结表二报告的因素组合的统计数据表明,四因子模型可以解释相当大的投资回报变化。首先，请注意相对较高的SMB , HML，PR1YR的零基投资组合和它们彼此与市场代理较低的相关性。这表明四因素模型可以解释相当大的时间序列变化。其次，在SMB,HML，PR1YR上的高平均回报表明这三个因素可以解释很大部分股票投资组合的平均回报的代表性变化。此外，低交叉相关意味着，基本上不影响的MULTICOL非线性估计的4因子模型载荷。

Table II. Performance Measurement Model Summary Statistics, July 1963 to December 1993

表Ⅱ 1963年7月至1993年12月绩效衡量模型汇总统计

In tests not reported, I find that the 4-factor model substantially improves on the average pricing errors of the CAPM and the 3-factor model.4 I estimate pricing errors on 27 quantitatively-managed portfolios of stocks from Carhart, Krail, Stevens, and Welch (1996), where the portfolios are formed on the market value of equity, book-to-market equity and trailing eleven-month return lagged one month. Not surprisingly, the 3-factor model improves on the average pricing errors from the CAPM, since it includes both size and book-to-market equity factors. However, the 3-factor model errors are strongly negative for last year's loser stock portfolios and strongly positive for last year's winner stock portfolios. In contrast, the 4-factor model noticeably reduces the average pricing errors relative to both the CAPM and the 3-factor model. For comparative purposes, the mean absolute errors from the CAPM, 3-factor and 4-factor models are 0.35 percent, 0.31 percent, and 0.14 percent per month, respectively. In addition, the 4-factor model eliminates almost all of the patterns in pricing errors indicating that it well describes the cross-sectional variation in average stock returns.

在没有报告的测试中，我发现四因子模型显着改善CAPM和三因子模型中的平均定价误差。我估计27个定量管理的股票投资组合的定价误差，得自Carhart, Krail, Stevens, and Welch( 1996年)，在投资组合上形成的股权账面市场股票的市场价值，跟踪十一个月再反过来滞后一个月。毫不奇怪地是，三因子模型提高了CAPM的平均定价误差，因为它包括大小和账面市场股票因素。然而，三因子模型误差是去年的输家股票组合强烈的否定和去年的赢家股票组合强烈肯定。与此相反，在4因素模型明显减少有关CAPM和3因子模型的平均定价误差。为便于比较，资本资产定价模型CAPM，3因子，4因子模型的平均绝对误差，分别为0.35%，0.31%，和0.14 %每月。此外，4因子模型消除了儿乎所有的定价误差的模式，表明它很好地描述平均股票收益率的代表性的变化。

III. Persistence in One-Year Return-Sorted Mutual Fund Portfolios

A. Common-Factor Explanations of One-Year Mutual Fund Persistence

In this section, I form portfolios of mutual funds on lagged one-year returns and estimate performance on the resulting portfolios, thus replicating the methodology of Hendricks, Patel, and Zeckhauser (1993). On January 1 of each year, I form ten equal-weighted portfolios of mutual funds, using reported returns. Reported returns are net of all operating expenses (expense ratios) and security-level transaction costs, but do not include sales charges. I hold the portfolios for one year, then re-form them. This yields a time series of monthly returns on each decile portfolio from 1963 to 1993. Funds that disappear during the course of the year are included in the equal-weighted average until they disappear, then the portfolio weights are readjusted appropriately. For added detail, I subdivide the top and bottom portfolios into thirds.

在本节中，我对滞后一年的回报和估计性能所产生的组合形成的共同基金的投资组合，从而复制的方法论ofHendricks，Patel和Zeckhauser（1993 )。在每年的1月1日，我形成十大等于加权投资组合的共同基金，用报告的回报。报告的收益扣除所有经营费用(费用率)和安全级别的交易成本，但不包括销售费用。我认为一年的投资组合，然后再重新形成。这产生了一个时间序列，各等分的投资组合1963年至1993年的月度回报。基金的一年过程中消失，直到他们消失在平等加权平均，然后适当调整投资组合权。为了增加细节，我细分的顶部和底部组合成三分之二。

The portfolios of mutual funds sorted on one-year past returns demonstrate strong variation in mean return, as shown in Table III. The post-formation monthly excess returns on the decile portfolios decrease nearly monotonically in portfolio rank, and indicate a sizeable annualized spread of approximately 8 percent. (This spread is 24 percent in the ranking year.) The subdivided extreme portfolios exhibit even larger return spreads. Portfolio 1A which contains the top thirtieth of funds (14 funds on average), outperforms portfolio 10C, the bottom thirtieth of funds, by 1 percent per month. Cross-sectional variation in return is considerably larger among the previous year's worst performing funds than the previous year's best funds. The subportfolios of the top decile show a modest spread of 12 basis points per month (63 to 75), but the spread in the bottom decile is a substantial 50 basis points. Further, the bottom thirtieth of the previous year's funds seem to demonstrate anomalously poor returns. In the year after their bottom-decile ranking, these funds show high variance and still underperform T-bills by 25 basis points per month.

投资组合的共同基金过去一年的回报排序平均收益表现出强劲的变化,如表三所示。形成后每月等分投资组合的超额收益减少近单调的组合排名，并表示相当大的约8%的年度传播。

(利差为24%，今年的排名。）拆细极端的投资组合表现出更大的回报率差。投资组合1A，其中包含顶级三十次基金（14只基金平均)，优于组合10C，底部资金三十次，每月1%。横截面变化的回报是相当大的比前一年的表现最差的基金之间的前一年的最好的基金。成份基金的最高收入每月12个基点（ 63至75），显示适度传播，但在底部等分蔓延的主要50个基点。此外，底部的三十分前一年的资金似乎表现出异常低回报。一年后，他们的底线等分排名，这些基金高方差和25个基点，每月仍然表现不如国库券。

Table III. Portfolios of Mutual Funds Formed on Lagged I-Year Return

表三：基于滞后一年回报形成的共同基金投资组合

The CAPM does not explain the relative returns on these portfolios. The CAPM betas on the top and bottom deciles and subdeciles are virtually identical, so the CAPM alphas reproduce as much dispersion as simple returns. In addition, the performance estimates from the CAPM indicate sizeable positive abnormal returns of about 22 basis points per month (2.6 percent per year) for the previous year's top-decile funds, and even larger negative abnormal returns of about 45 basis points per month (5.4 percent per year) for the bottom decile funds. If the CAPM correctly measures risk, both the best and worst mutual funds possess differential iñformation yet the worst funds appear to use this information perversely to reduce performance.

资本资产定价模型并不能解释这些投资组合的相对回报率。CAPM贝塔顶部和底部的十分

位数和subdeciles的几乎是相同的，所以很多简单的回报分散CAPM的α重现。此外，性

能估计从CAPM表明约22基础点每月(每年2.6 % )上一年度的最高等分的资金相当大的正异常回报，更大的负异常回报约45基础点每月(每年的5.4% )为底等分资金。如果CAPM的正确衡量风险，最好和最差的共同基金具有差分信息，但出现最坏的基金相反地使用此信息来降低性能。

In contrast to the CAPM, the 4-factor model explains most of the spread and pattern in these portfolios, with sensitivities to the size (SMB) and momentum (PR1YR) factors accounting for most of the explanation. The top decile portfolios appear to hold more small stocks than the bottom deciles. More important, however, is the pronounced pattern in the funds' PR1YR coefficients. The returns on the top decile funds are strongly, positively correlated with the one-year momentum factor, while the returns in the bottom decile are strongly, negatively correlated with the factor. Of the 67-basis-point spread in mean monthly return between deciles 1 and 10, the momentum factor explains 31 basis points, or almost half. Further, of the 28-basis-point spread in monthly return not explained by the 4-factor model, the spread between the ninth and tenth deciles accounts for 20 basis points. Except for the relative underperformance by last year's worst performing funds, the 4 -factor model accounts for almost all of the cross-sectional variation in expected return on porfolios of mutual funds sorted on lagged one-year return.

相反于CAPM，4-因子模型解释在这些组合中的利差和模式，敏感性的尺寸(SMB)和的动量( PR1YR )的因素占大部分的解释。顶部出现等分的投资组合，以容纳更多的小公司的股票比底部十分位数。然而更重要的，是显着的模式在基金PR1YR系数。的顶部等分资金的回报有很强的正相关，与1年期的动量因子，而在底部等分强烈的回报呈负相关因素。十分位数1和10之间的利差平均每月返还67个基点，动量因子解释了31个基点，或几乎一半。此外，四因子模型，第九组和第十组十分位数账户之间的利差为20个基点，每月返还28个基点利差未解释。除相对表现不佳，去年表现最差的基金，四因子模型考虑了几乎所有的横截面排序滞后一年收益的共同基金投资组合的预期回报的变化。

B. Characteristics of the Mutual Fund Portfolios

I now examine whether any of the remaining short-term persistence in mutual fund returns is related to heterogeneity in the average characteristics of the mutual funds in each decile portfolio. In each year, I calculate a cross-sectional average for each decile portfolio of fund age, total net assets (TNA), expense ratio, turnover (Mturn), and maximum load fees.

我现在检查是否有任何剩余的短期持久性共同基金回报的异质性在各等分的投资组合的共

同基金的平均特性。每年，我的横截面平均计算各等分的投资组合基金的年龄，总资产净值

(TNA)，费用率，换手率(Mturn)，和最大销售费用。

The average portfolio characteristics reported in Table IV indicate that expenses and turnover are related to performance. Decile 10 particularly stands out with higher than average expenses and turnover. The 70-basis-point difference in expense ratios between deciles 9 and 10 explains about six of the 20-basis-point spread between monthly 4-factor alphas on these portfo-lios. It does not appear that fund age size, or load fees can explain the large spread in performance on these portfolios, since these characteristics are very similar for the top and bottom deciles.

表四表明投资组合的平均特征，费用和换手率都涉及到性能。10格外引人瞩目，高于平均费用和换手率。费用率70个基点的点差十分位9和10之间，说明6每月4因子α这些组合之间的利差20个基点左右。基金年龄，大小，或销售费可以解释这些投资组合的表现的大利差，因为这些特点都有着非常相似的顶部和底部十分位数。

Table IV. Characteristics of the Portfolios of Mutual Funds Formed on Lagged 1-Year Return

表IV.基于滞后1年回报形成的共同基金投资组合特征

Differences in portfolio turnover do not explain a sizeable portion of the remaining portfolio nine-ten spread in alphas. If funds pay 1 percent in costs per round-trip transaction, the difference in trading frequency between the ninth and tenth deciles accounts for only 0.5 basis points of the spread in 4-factor alphas. After accounting for expense ratios and turnover, tests on the difference between alphas on deciles 9 and 10 yield t-statistics of 2.69 relative to the CAPM, and 2.19 relative to the 4-factor model. Thus, expense ratios and turnover alone cannot explain the anomalous negative abnormal performance by the worst-return decile of funds. This conclusion is even stronger when considering portfolio 10C the bottom thirtieth of funds.

投资组合周转的差异无法解释一个相当大的部分，其余组合α上有九十的利差。如果资金支付1%的成本每往返事务，只有0.5个基点的利差在4因子模型α第九和第十的十分位数账户之间的交易频率的差异。经过核算费用率和换手率，十分位9和10组t统计量2.69相对于CAPM，和2.19相对于四因子模型之间的差异阿尔法测试。因此，费用率和换手率单独无法解释的反常的负异常表现资金最坏返回等分。这个结论是更强的是考虑投资组合10C时,底部的三十只基金。

C. Characteristics of Individual Mutual Funds

Mutual fund managers claim that expenses and turnover do not reduce performance, since investors are paying for the quality of the manager's information, and because managers trade only to increase expected returns net of transactions costs. Thus, expenses and turnover should not have a direct negative effect on performance, as implied in the previous section, but rather a neutral or positive effect. I evaluate this claim by directly measuring the marginal effect of these and other variables on abnormal performance. In each month, I estimate the cross-section regression:

共同基金经理声称，费用和换手率不会降低业绩，因为投资者为经理信息的质量买单，而且因为经理交易只是为了增加扣除交易成本后的预期回报。因此，如前一节所述，费用和换手率不应对业绩产生直接的负面影响，而应产生中性或积极的影响。我通过直接测量这些变量和其他变量对异常绩效的边际影响来评估这一说法。在每个月，我估计横截面回归：

α i t = a t + b t x i t + ε i t i = 1 , ⋯ , N , t = 1 , ⋯ , T(4)

where α it is an individual fund performance estimate and x it is a fund characteristic. As in Fama and MacBeth (1973), I estimate the cross-sectional relation each month, then average the coefficient estimates across the complete sample period. This yields 330 cross-sectional regressions which average 350 observations each for a combined sample of about 116,000 observations. To mitigate look-ahead bias, I estimate α it as a one-month abnormal return from the 4-factor model, where the 4-factor model loadings are estimated over the prior three years:

式中，α为单个基金业绩估计，x为基金特征。正如Fama和MacBeth（1973）中所述，我每个月估算横截面关系，然后在整个样本期内平均系数估算值。这就产生了330个横截面回归，对于约116000个观测值的组合样本，每个平均350个观测值。为了缓解前瞻性偏误，我将α估计为4因素模型的一个月异常回报，其中4因素模型载荷在过去三年中进行了估计：

α i t ≡ R i t - R F t - b ^ i t - 1 RMRF t - s ^ i t - 1 SMB t - h ^ i t - 1 HML t + p ^ i t - 1 PR 1 YR t .(5)

I estimate one-month alphas each month on every fund, using a minimum of 30 observations, then estimate the cross-section relation of equation (4) using the Fama-MacBeth estimator.

我估计每个基金每月一个月的α，使用至少30个观察值，然后使用Fama-MacBeth估计器估计方程（4）的横截面关系。

The explanatory variables in equation (4) are expense ratio, turnover (Mturn), ln(TNA) and maximum load fees. Since I intend to explain performance, not predict it, I measure expense ratio and turnover contemporaneous with return. TNA is lagged one year to avoid spurious correlation (Granger and Newbold, 1974). Load fees are lagged one year to avoid the confounding possibility that funds change these fees in response to performance. I construct two additional explanatory variables from turnover to separate the effects of buy and sell trading. The latter two are

方程（4）中的解释变量为费用比率、换手率（Mturn）、ln（TNA）和最大销售费用。因为我打算解释业绩，而不是预测业绩，所以我在衡量费用比率和换手率的同时，还要考虑回报。TNA滞后一年以避免虚假相关性（Granger和Newbold，1974）。销售费用滞后一年，以避免基金因业绩而改变这些费用的混淆可能性。我从换手率中构造了两个额外的解释变量，以分离买卖交易的影响。后两个是

Buy Turnover i t = Turnover i t + max ( Mflow i t , 0 )

And

Sell Turnover i t = Turnover i t - min ( Mflow i t , 0 )

where Mflow it measures the percentage change in TNA adjusted for investment returns and mergers. Because I find expense ratios are strongly related to the other variables, I estimate the cross-section regression for TNA, load, and the turnover measures using returns after adding back expense ratios.

在Mflow中，它衡量投资回报和合并调整后TNA的百分比变化。因为我发现费用比率与其他变量密切相关，所以我使用加回费用比率后的回报来估计TNA、载荷和周转率指标的横截面回归。

The results in Table V indicate a strong relation between performance and size, expense ratios, turnover, and load fees. The resulting relation between performance and expense ratios and modified turnover suggest that mutual funds, on average, do not recoup their investment costs through higher returns. The —1.54 coefficient on expense ratio implies that for every 100-basis-point increase in expense ratios, annual abnormal return drops by about 154 basis points. The turnover coefficient of −0.95 suggests that for every 100-basis-point increase in turnover, annual abnormal return drops by about 95 basis points. We can interpret the turnover coefficient as a measure of the net costs of trading, since it reveals the marginal performance effect of a small change in turnover. Thus, the turnover estimate implies transactions costs of 95 basis points per round-trip transaction. When partitioned into buy turnover and sell turnover, the estimates imply a 21.5 basis point cost for (one-way) buy trades and a 63 basis point cost for sell trades.

表V中的结果表明，性能与规模、费用比率、换手率和负载费用之间存在着密切的关系。由此得出的业绩和费用比率与修正换手率之间的关系表明，平均而言，共同基金不会通过更高的回报来收回投资成本。支出比率的-1.54系数意味着，支出比率每增加100个基点，年度异常回报率就会下降约154个基点。流动系数−0.95表明，换手率每增加100个基点，年度异常回报率就会下降约95个基点。我们可以将换手率系数解释为交易净成本的一种度量，因为它揭示了换手率微小变化的边际绩效效应。因此，换手率估算意味着每次往返交易的交易成本为95个基点。当划分为买入成交量和卖出成交量时，估计值意味着（单向）买入交易的成本为21.5个基点，卖出交易的成本为63个基点。

Table V. Fama-MacBeth (1973) Cross-Sectional Regressions

表V.Fama MacBeth（1973）横截面回归

TNA is insignificantly related to the cross-section of performance estimates but maximum load fees are significantly negatively related to performance. The negative slope on load fees contradicts the oft-cited claim by load funds that their managers are more skilled and investment expenses lower than no-load funds. Although the coefficient appears small, it implies that annual abnormal returns are reduced by about 11 basis points for every 100 basis point increase in load fees. For a load fund with the average total sales charges of 7.3 percent, the reduction in annual return is 79 basis points. To test the sensitivity of this result to the poor-performing outliers, I repeat the analysis after removing the funds in the bottom two deciles. The results (not reported) are virtually unchanged. The underperformance of load funds is probably partially explained by higher total transactions costs, since load funds exhibit higher turnover than no-load funds (Carhart (1995a).)

TNA与性能估计的横截面关系不大，但最大销售费用与业绩表现显著负相关。销售费用的负斜率与有佣金基金经常引用的说法相矛盾，即有佣金基金的经理比无佣金基金更熟练，投资费用更低。尽管该系数看起来很小，但这意味着每年的异常回报率在销售费用每增加100个基点的情况下会减少约11个基点。对于平均总销售费用为7.3%的有佣金基金来说，年回报率下降了79个基点。为了测试这一结果对表现不佳的异常值的敏感性，我在去除底部十分之二的基金后再次分析。结果（未报告）几乎没有变化。有佣金基金表现不佳的部分原因可能是交易总成本较高，因为有佣金基金的换手率高于无佣金基金（Carhart（1995a））

D. Cross-Sectional Variation in Transaction Costs

Thus far, sensitivity to common factors and persistence in expense ratios explain most of the persistence in mutual fund performance. In addition, the cross-section tests indicate that turnover reduces performance for the average fund. However, since turnover ratios on the worst-performing funds are only slightly higher than on the average fund, transaction costs can only explain the anomalous underperformance of the worst funds if these funds also have higher costs per transaction. This section evaluates whether estimates of costs per transaction explain any of the remaining abnormal performance not fully accounted for by the 4-factor model, expense ratios, and turnover.

迄今为止，对共同因素的敏感性和费用比率的持续性解释了共同基金业绩的大部分持续性。此外，横截面检验表明，换手率降低了普通基金的业绩。然而，由于表现最差基金的换手率仅略高于平均基金，如果这些基金的每笔交易成本也较高，交易成本只能解释表现最差基金异常表现不佳的原因。本节评估每笔交易的成本估算是否解释了四因素模型、费用比率和换手率未完全解释的任何剩余异常绩效。

I find that transaction costs describe most of the unexplained mutual fund performance. From the 4-factor model alphas, expense ratios, and turnover ratios, I assume market efficiency to infer the cost per transaction necessary to zero out the gross 4-factor alpha. The average fund's alpha of −0.15 percent, expense ratio of 1.14 percent, and turnover of 77.4 percent imply a cost of 85 basis points per round-trip transaction. The previously reported cross-section estimate of round-trip transactions cost is 95 basis points, with a standard error of 40 basis points. Thus, for the average fund, the implied transactions cost lies well within 0.25 standard errors of the estimated cost.

我发现交易成本描述了大多数无法解释的共同基金业绩。根据4因素模型α、费用比率和换手率，我假设市场的有效性可以推断出将总4因素α归零所需的每笔交易成本。平均基金的阿尔法−0.15%、1.14%的费用率和77.4%的换手率意味着每次往返交易的成本为85个基点。先前报告的往返交易成本横截面估计值为95个基点，标准误差为40个基点。因此，对于平均基金而言，隐含交易成本在估计成本的0.25标准误差范围内。

In addition to explaining performance on the average fund, transaction costs also explain much of the cross-sectional variation in return on the portfolios sorted on lagged one-year return. I sort the sample into quintiles to create subsamples large enough to yield reliable cross-section estimates. After repeating my calculations and cross-section estimates, I find that the implied transaction costs are very near to their cross-section estimates. Only in one quintile (quintile 2) is the estimated round-trip transactions cost more than two standard errors from implied. Although the quintile sort is coarse, cross-sectional variation in costs per transaction explains the return spread on these portfolios unrelated to the 4-factor model and expense ratios.

除了解释平均基金的表现外，交易成本还解释了按滞后一年回报率排序的投资组合回报的大部分横截面变化。我将样本以五分位数分类，以创建足够大的子样本，从而得出可靠的横截面估计值。在重复我的计算和横截面估计之后，我发现隐含的交易成本非常接近它们的横截面估计。只有在五分之一（五分之二）中，估计的往返交易成本高于隐含的两个标准误差。虽然五分位数排序比较粗糙，但每笔交易成本的横截面变化解释了这些投资组合的收益差，与四因素模型和费用比率无关。

However, the estimated round-trip transaction costs in fmer sorts of the bottom quintile are not large enough to explain its underperformance. In order to estimate transaction costs on the relatively small samples of the decile or subdecile portfolios, I pool the cross-section and time-series observations in the estimation. The estimated round-trip transaction costs on decile 10 undershoot the implied costs of 354 basis points by more than four standard errors. The implied costs on the three subportfolios of decile 10 suggest that portfolios 10B and 10C drive this unusually high implied transaction cost estimate. To fully explain 4-factor model abnormal performance, portfolio 10B requires a 356-basis-point round-trip cost, and 10C requires a 582-basis-point cost. At seven and 252 basis points however, the cross-section estimates for these portfolios are considerably less than implied. While their pattern suggests that relative transaction costs play an important role in the cross-section of mutual fund performance, the magnitude of the cross-section estimates leaves unexplained much of the abnormal return in the worst-return mutual funds.

然而，在最底层五分之一的其他类别中，估计的往返交易成本不足以解释其表现不佳的原因。为了估算十分位或次十分位投资组合中相对较小样本的交易成本，我在估算中汇集了横截面和时间序列观察结果。十分位10的估计往返交易成本低于354个基点的隐含成本四个以上的标准误差。十分位10的三个子投资组合的隐含成本表明，投资组合10B和10C推动了这一异常高的隐含交易成本估算。为了充分解释4因素模型的异常表现，投资组合10B需要356个基点的往返成本，10C需要582个基点的成本。然而，在7个基点和252个基点上，这些投资组合的横截面估计值远低于隐含值。虽然他们的模式表明，相对交易成本在共同基金业绩的横截面中起着重要作用，但横截面估计的大小使得回报最差的共同基金中的大部分异常回报无法解释。

For robustness, I employ a second method for inferring cross-sectional variation in transaction costs that exploits the time-series properties of the mutual fund portfolios. Since round-trip transactions costs should decrease in the trading liquidity of the underlying securities, mutual funds holding illiquid securities should be correlated with a factor-mimicking portfolio for trading liquidity. Assuming that the time-series properties of illiquid stocks differ from liquid stocks, a portfolio long in illiquid stocks and short in liquid stocks should capture these patterns.

为了稳健性，我采用了第二种方法来推断交易成本的横截面变化，该方法利用了共同基金投资组合的时间序列特性。由于往返交易成本应降低标的证券的交易流动性，持有非流动性证券的共同基金应与模拟交易流动性投资组合的因素相关联。假设非流动性股票的时间序列特性不同于流动性股票，那么长时间持有非流动性股票和短时间持有流动性股票的投资组合应该能够捕捉这些模式。

The liquidity factor-mimicking portfolio, VLMH, is the spread between returns on low- and high-trading-volume stocks orthogonalized to the 4-factor model.6 I find that the VLMH-loading estimates on mutual fund portfolios are strongly related to performance. The best one-year-return portfolios load significantly and negatively on VLMH, indicating relatively more liquid stocks. The worst portfolios load significantly and positively, indicating relatively more illiquid stocks. Since illiquid stocks are more costly to trade, the VLMH loadings suggest that the costs per transaction are higher for the lower-past-return portfolios. Although these results do not measure the incremental cost of trading illiquid stocks, they do suggest that higher transaction costs might explain the strong underperformance of the worst funds.

模拟投资组合的流动性因素VLMH是与四因素模型正交化的低成交量和高成交量股票回报之间的利差。6我发现对共同基金投资组合的VLMH负载估计与绩效密切相关。最好的一年回报投资组合对VLMH的影响显著且为负，表明相对流动性更强的股票。最差的投资组合表现出显著的正向负荷，表明流动性相对较高的股票。由于非流动性股票的交易成本更高，VLMH载荷表明，对于过去回报率较低的投资组合，每笔交易的成本更高。尽管这些结果并未衡量非流动性股票交易的增量成本，但它们确实表明，交易成本较高可能解释了最差基金表现不佳的原因。

Overall, my results suggest that short-run mutual fund returns persist strongly, and that most of the persistence is explained by common-factor sensitivities, expenses, and transaction costs. The net gain in returns from buying the decile of past winners and selling the decile of losers is 8 percent per year. I explain 4.6 percent with size, book-to-market and one-year momentum in stock returns; 0.7 percent with expense ratios; and 1 percent with transaction costs. However, of the 5.4 percent spread between deciles 1 and 9, the 4-factor model explains 4.4 percent and expense ratios and transaction costs explain 0.9 percent, leaving only 0.1 percent annual spread unexplained. Underperforming by twice its expense ratio and estimated transaction costs, the performance on the lowest decile is still anomalous after these explanations. Thus, the cross-section of average mutual fund returns not explained by the variables is almost entirely concentrated in the spread between the bottom two past-returns sorted decile portfolios.

总的来说，我的研究结果表明短期共同基金回报率持续性很强，而这种持续性的主要原因是共同因素敏感性、费用和交易成本。购买过去赢家的十分之一和出售输家的十分之一的净收益每年为8%。我用规模、账面市值和股票回报的一年动量解释了4.6%；费用比率为0.7%；交易费用占1%。然而，在十分位1和9之间的5.4%差价中，4因素模型解释了4.4%，费用比率和交易成本解释了0.9%，只剩下0.1%的年差价无法解释。由于其费用比率和估计交易成本的两倍，最低十分位的表现仍然异常。因此，未被变量解释的平均共同基金收益的横截面几乎完全集中在过去收益最低的两个十分位投资组合之间的利差。

IV. Interpreting the Performance on Past-Winner Mutual Funds

Previous sections demonstrated strong patterns in 4-factor model coefficients on portfolios of mutual funds sorted on one-year return. This finding suggests sorting funds on one-year return groups with similar time-series properties, at least over the period while they are ranked in a particular decile. There are at least two possible explanations for this groupwise commonality. First, the funds in each portfolio might be relatively stable with consistent strategies through time. Second, the funds in each portfolio might be unstable through time, but the funds in a particular decile might hold similar securities while they are in that portfolio. The implications of these two explanations differ drastically, since the former suggests that managers follow consistent strategies that determine their expected returns, whereas the latter is consistent with managers choosing securities randomly but holding them for one to two years.

前几节展示了按一年期回报率排序的共同基金投资组合的4因素模型系数的强模式。这一发现表明，至少在一年期内，基金按时间序列性质相似的回报率组进行分类，而这些回报率组的排名是在特定的十分位。对于这种群体共性，至少有两种可能的解释。首先，随着时间的推移，每个投资组合中的基金可能相对稳定，且策略一致。其次，每个投资组合中的基金可能随着时间的推移而不稳定，但特定十分位中的基金在该投资组合中可能持有类似的证券。这两种解释的含义大不相同，因为前者表明管理者遵循一致的策略来决定他们的预期回报，而后者则与管理者随机选择证券但持有一到两年一致。

A. Consistency in Ranking

I test the consistency in fund ranking by constructing a contingency table of initial and subsequent one-year mutual fund rankings. I use simple returns gross of expense ratios to remove the predictable expense element in reported returns. The contingency table is displayed in Figure 1. The bars for initial rank i and subsequent rank j represent Pr (rank j) next year rank i last year).

我通过构建初始和后续一年期共同基金排名的列联表来测试基金排名的一致性。我使用简单的回报-费用总额比率来替代报告回报中的可预测费用元素。列联表如图1所示。初始等级i和后续等级j的条形图表示Pr（等级j）明年（去年等级i）。

Figure 1图1

Contingency table of initial and subsequent one-year performance rankings.

初始和后续一年绩效排名列联表。

In each calendar year from 1962 to 1992, funds are ranked into decile portfolios based on one-year gross return. These initial decile rankings are paired with the fund's subsequent one-year gross return ranking. Funds that do not survive the complete subsequent year are placed in a separate category for dead funds. The bars in cell (j, i) represent the conditional probability of achieving a subsequent ranking of decile j (or dying) given an initial ranking of decile i. I estimate gross returns by adding back expense ratios to reported returns.

From the figure, it is apparent that winners are somewhat more likely to remain winners, and losers are more likely to either remain losers or perish. However, the funds in the top decile differ substantially each year, with more than 80 percent annual turnover in composition. In addition, last year's winners frequently become next year's losers and vice versa, which is consistent with gambling behavior by mutual funds. Further, the probability of disappearing from the database decreases monotonically in the previous-year's return. Thus, while the ranks of a few of the top and many of the bottom funds persist, the year-to-year rankings on most funds appear largely random.

以上都是对图1的解释

B. Returns on the Portfolios of Mutual Funds after Ranking

The large number of top-decile funds that revert to lower ranks suggests that the relatively high returns on the funds in this portfolio are short-lived. Figure 2 presents the average returns of the funds in each decile portfolio in each of the five years after their original formation. From the figure, it is clear that one-year performance persistence is mostly eliminated after one year. Except for the persistent underperformance by the worst funds, mean returns and abnormal performance across deciles do not differ statistically significantly after one year.

大量顶级十分位基金回归到较低级别，这表明该投资组合中相对较高的基金回报率是短暂的。图2显示了在最初成立后的五年中，每十分位投资组合中基金的平均回报。从图中可以明显看出，一年的绩效持续性在一年后基本上被消除。除了最差基金的持续表现不佳外，十分位的平均回报和异常表现在一年后在统计上没有显著差异。

Figure 2图2

Post-formation returns on portfolios of mutual funds sorted on lagged one-year return.

共同基金投资组合的形成后回报按滞后的一年回报排序。

In each calendar year from 1962 to 1987, funds are ranked into equal-weight decile portfolios based on one-year return. The lines in the graph represent the excess returns on the decile portfolios in the year subsequent to initial ranking (the “formation” year) and in each of the next five years after formation. Funds with the highest one-year return comprise decile 1 and funds with the lowest comprise decile 10. The portfolios are equally weighted each month, so the weights are readjusted whenever a fund disappears from the sample.

从1962年到1987年的每个日历年，基金都根据一年的回报率被划分为等重的十分位投资组合。图中的线条表示初始排名后一年（“形成”年）以及形成后五年中的每一年十位数投资组合的超额回报。一年回报率最高的基金为十分之一，回报率最低的基金为十分之一。投资组合每个月的权重相等，因此每当一只基金从样本中消失时，权重就会重新调整。

Furthermore, the returns on the top and bottom decile funds are not nearly so strongly related to the one-year momentum effect in stock returns outside of the ranking and formation years. In the year before ranking, funds that will comprise decile 1 have a PR1YR loading of 0.18, and funds that will comprise decile 10 have a PR1YR loading indistinguishable from zero. In the year after portfolio formation, decile 1 funds have a PR1YR loading of only 0.14, and decile 10 funds have a PR1YR loading of 0.04. These coefficients contrast sharply with the top- and bottom-decile PR1YR loadings in the portfolio formation year of 0.29 and −0.09. (See Table III.)

此外，顶部和底部十分位基金的回报与排名和形成年份以外的股票回报的一年动量效应的相关性几乎没有那么强。在排名前一年，包含十分位1的基金的PR1年负荷为0.18，而包含十分位10的基金的PR1年载荷不显著为零。在投资组合形成后的一年中，十分之一基金的PR1年负荷仅为0.14，十分之一基金的PR1年负荷为0.04。这些系数与投资组合形成年的顶部和底部十分之一PR1年负荷（0.29和0.29）形成鲜明对比−0.09. （见表三）

C. Portfolios Sorted on PR1YR Loadings

The results from the previous two sections suggest that most top-ranked mutual funds do not maintain their high relative returns. However, funds that follow a momentum strategy in stocks might consistently earn above-average returns, even if their 4-factor model performance is not abnormal. To test whether momentum managers earn consistently higher returns, I sort mutual funds into portfolios on their 4-factor model PRIYR loadings and find that one-year momentum funds do not earn substantially higher returns than contrarian funds.7 Relative to the 4-factor model, in fact, one-year momentum funds underperform one-year contrarian funds. Momentum funds also have high turnover and expense ratios, suggesting that most of the gains from following the one-year momentum strategy are consumed by higher expenses and transaction costs. This result contrasts with Wermers (1996), who finds that momentum funds outperform on a gross performance basis.

前两部分的结果表明，大多数排名靠前的共同基金并没有保持较高的相对回报。然而，在股票中遵循动量策略的基金可能会持续获得高于平均水平的回报，即使它们的4因素模型表现并非异常。为了测试动量基金经理是否能持续获得更高的回报，我将共同基金按其4因素模型的PRIYR负荷分类到投资组合中，发现一年期动量基金的回报率并不比反向基金高很多。7事实上，相对于4因素模型，一年期动量基金的表现逊于一年期反向基金。动量基金的周转率和费用比率也很高，这表明遵循一年动量策略的大部分收益都被更高的费用和交易成本所消耗。这一结果与Wermers（1996）形成对比，Wermers发现动量基金在总体业绩基础上表现出色。

My results suggest that Jegadeesh and Titman's (1993) spread in mean return among last-year's winning and losing stocks is not an investable strategy at the individual security level. My results also suggest that there is a simple explanation for the strong pattern in PR1YR loadings on portfolios sorted on lagged one-year returns: These mutual funds don't follow the momentum strategy, but are funds that accidentally end up holding last year's winners. Since the returns on these stocks are above average in the ensuing year, if these funds simply hold their winning stocks, they will enjoy higher one-year expected returns and incur no additional transaction costs for this portfolio. With so many mutual funds, it does not seem unlikely that some funds will be holding many of last year's winning stocks simply by chance.

我的研究结果表明，Jegadeesh和Titman（1993年）在去年的赢家和输家股票中的平均回报差价在个人安全水平上不是一种可投资的策略。我的研究结果还表明，根据滞后的一年回报率排序的投资组合的PR1年负荷的强劲模式有一个简单的解释：这些共同基金不遵循动量策略，而是意外地持有去年的赢家的基金。由于这些股票在接下来的一年中的回报高于平均水平，如果这些基金仅仅持有它们的中奖股票，它们将享受更高的一年预期回报，并且不会为此投资组合产生额外的交易成本。由于有如此多的共同基金，一些基金似乎不太可能仅仅出于偶然而持有许多去年成功的股票。

D. Evidence that PR1YR and VLMH Loadings Capture Momentum and Trading Volume

Daniel and Titman (1997) suggest that firms' actual size and book-to-market equity contain more explanatory power for mean returns than do time-series estimates of factor loadings. Their results suggest that generalizations about the securities held or strategies followed by mutual funds based on time-series factor loadings might be misleading. Fama and French (1993) find that SMB and HML loadings are related to the average market capitalization and book-to-market equity on their test portfolios. Thus, I examine the information content of PR1YR and VLMH loadings by comparing the factor loadings with direct measures of momentum and trading liquidity. If the factor loadings capture the liquidity and momentum of these quantitatively-managed portfolios, they should strongly correlate with direct measures of liquidity and momentum.

Daniel和Titman（1997）认为，与因子载荷的时间序列估计相比，企业的实际规模和账面市值对平均收益的解释力更强。他们的结果表明，基于时间序列因素载荷的共同基金持有的证券或遵循的策略可能会产生误导。Fama和French（1993）发现，SMB和HML负荷与其测试投资组合的平均市值和账面市值相关。因此，我通过将因子载荷与动量和交易流动性的直接度量进行比较，来检验PR1YR和VLMH载荷的信息含量。如果因子载荷捕获了这些定量管理的组合的流动性和动量，则它们应与流动性和动量的直接度量密切相关。

To test this hypothesis, I construct two sets of 25 value-weighted stock portfolios by sorting all NYSE, AMEX, and Nasdaq stocks first on size, and then on one-year momentum or trading volume. The patterns in VLMH loadings on the size-trading volume portfolios support my previous generalizations about the relative liquidity of stocks held by mutual funds.8 Within each size quintile, the VLMH loadings decrease in the dollar volume of trading. Since VLMH is long in low-trading-volume stocks and short in high-volume stocks, I expect this inverse relation between trading volume and VLMH loading. Further, VLMH is constructed orthogonally to the size factor, so the VLMH loading does not reveal the magnitude of trading volume, only the magnitude of trading relative to firm size. After subtracting the average trading volume for each size quintile, the correlation between trading volume and VLMH coefficients is 0.74.

为了验证这一假设，我构建了两组25个价值加权的股票组合，首先对所有纽约证券交易所、美国证券交易所和纳斯达克股票进行大小排序，然后根据一年的动量或交易量排序。VLMH在交易量投资组合规模上的载荷模式支持我之前关于共同基金所持股票的相对流动性的概括。8在每五分位中，VLMH载荷在美元交易量中减少。由于VLMH在低成交量股票中做多，而在高成交量股票中做空，我预计成交量和VLMH负载之间存在这种反向关系。此外，VLMH的构造与规模因子正交，因此VLMH载荷不显示交易量的大小，仅显示相对于公司规模的交易量大小。减去每个五分位数的平均交易量后，交易量与VLMH系数之间的相关性为0.74。

I also find that PR1YR loadings are informative on the momentum of stocks in each portfolio. On the size-momentum portfolios, the PR1YR loadings are monotonic in momentum within every size quintile, and the overall correlation between momentum and factor loadings is 0.95. Thus, covariance with the PR1YR factor appears to be a relatively good indication of the momentum of the underlying stocks in a portfolio.

我还发现，PR1年的载荷是关于每个投资组合中股票动量的信息。在规模动量投资组合中，每个规模五分位数内的PR1年载荷动量单调，动量和因子载荷之间的总体相关性为0.95。因此，PR1年因子的协方差似乎是投资组合中基础股票动量的一个相对较好的指标。

V. Longer-Term Persistence in Mutual Fund Portfolios

A. Two- to Five-Year-Return Sorted Portfolios

Contrary to the suggestions of Hendricks, Patel, and Zeckhauser (1993), mutual fund manager stock-picking skill is not required to explain the one-year persistence in mutual fund returns. However, if manager skill exists, a one-year return is probably a noisy measure. To reduce the noise in past-performance rankings, I form portfolios of mutual funds on lagged two- to five-year returns. I then repeat my earlier analyses to examine how much cross-sectional variation in mean return can be explained by the 4-factor model, expense ratios, and transaction costs. Figure 3 summarizes these and the results from the one-year past-return sorted portfolios.

与Hendricks、Patel和Zeckhauser（1993）的建议相反，共同基金经理选股技巧不需要用来解释共同基金收益的一年持续性。然而，如果存在管理技能，一年的回报可能是一个干扰项的衡量标准。为了减少过去业绩排名中的干扰，我根据滞后的2至5年回报率形成了共同基金投资组合。然后，我重复我先前的分析，以检验平均回报的横截面变化可以用4因素模型、费用比率和交易成本解释多少。图3总结了这些以及过去一年收益分类投资组合的结果。

Figure 3图3

Summary of explanations for persistence in mutual fund performance.

共同基金业绩持续性的解释摘要。

On January 1 of each year, funds are ranked into equal-weight decile portfolios based on returns over the prior one-, two-, three-, four-, and five-year periods. Funds with the highest return comprise decile 1, and funds with the lowest comprise decile 10. The height of the graph represents the annual spread in mean return between deciles 1 and 10 for the portfolios formed on one- to five-year returns. The top shaded region represents the spread in annual return that is explained by the 4-factor model, where the 4-factor model captures common variation in return associated with size, book-to-market equity, and one-year return momentum. The second region from the top represents the difference in the average expense ratios of deciles 1 and 10. The third region from the top represents the difference in estimates of total transaction costs for deciles 1 and 10. Total transaction costs are modified turnover times the cross-section estimates of roundtrip transaction costs. Of the remaining spread in annual return after the 4-factor model, expense ratios and transaction costs explanations, the fourth region from the top represents the portion of the unexplained spread attributable to the difference between returns on deciles 1 and 9. The bottom region represents the unexplained spread attributable to the difference between returns on deciles 9 and 10.

以上是对图3的解释

Using longer intervals of past returns does not reveal more information about expected future mutual fund return or 4-factor performance. While the 4-factor model explains more than half the spread in return on the one-year-return portfolios, it explains a smaller fraction of return spread in the two- to four-year portfolios, and none of the spread in the five-year portfolios. It turns out that the 4-factor model explains less of the return spread because of a less-pronounced pattern in PR1YR loadings and a more pronounced pattern in HML loadings. Past-winner mutual funds load negatively on HML and positively on PR1YR while past-loser mutual funds do not load significantly on either factor. Expense ratios explain a similar return spread across sorting intervals, approximately 1 percent per year. Estimates of total transaction costs from turnover and cross-section estimates of costs per transaction explain between zero and 2.6 percent of the spread in annual return. Of the spread in annual return remaining after the 4-factor model, expense ratios, and transaction costs, approximately two-thirds is attributable to the spread between the ninth and tenth decile portfolios. This amounts to approximately 1.5 percent.9

使用更长的过去收益间隔并不能揭示更多关于预期未来共同基金收益或四因素模型绩效的信息。虽然四因素模型解释了一年期回报投资组合中超过一半的回报利差，但它只解释了二至四年期投资组合中回报利差的一小部分，而五年期投资组合中没有任何利差。结果表明，由于PR1年载荷模式不太明显，而HML负荷模式更为明显，因此4因素模型解释的收益利差较小。过去的赢家共同基金在HML上负载荷，在PR1年上正载荷，而过去的输家共同基金在这两个因素上均不显著。费用比率解释了排序间隔内类似的回报分布，大约每年1%。根据换手率估算的总交易成本和每笔交易成本的横截面估算解释了年回报差价的0%至2.6%。在四因素模型、费用比率和交易成本之后剩余的年度回报利差中，约三分之二归因于第九和第十十分位投资组合之间的利差。这大约占1.5%。

These results differ somewhat from Grinblatt and Titman (1992), who study persistence in five-year mutual fund returns and find slightly stronger evidence of persistence with a similar methodology. However, Grinblatt and Titman condition on five-year subsequent survival, and their sample period includes the very high attrition period of 1975 to 1978 (see Carhart (1995b)). Further, Grinblatt and Titman's (1989) P-8 benchmark does not capture the one-year momentum effect in stock returns. They construct the P-8 model to explain variation in return associated with firm size, dividend yield, three-year past returns, interest-rate sensitivity, co-skewness, and beta. As evidence that the omission of a momentum factor is significant, the intercept from the regression of PR1YR on the P-8 benchmark over Grinblatt and Titman's sample period yields a statistically significant intercept of 0.46 percent per month, with an r-squared of only 0.6. Finally, Grinblatt and Titman do not attempt to account for differences in performance attributable to expenses or transaction costs.

这些结果与Grinblatt和Titman（1992）有所不同，他们研究了五年期共同基金收益的持续性，并用类似的方法找到了更有力的持续性证据。然而，Grinblatt和Titman的情况取决于随后五年的存活率，他们的样本期包括1975年至1978年的非常高的磨蚀期（见Carhart（1995b））。此外，Grinblatt和Titman（1989）的P-8基准并没有捕捉到股票回报的一年动量效应。他们构建了P-8模型来解释与公司规模、股息收益率、过去三年收益率、利率敏感性、协偏和贝塔相关的回报变化。作为忽略动量因子的显著证据，Grinblatt和Titman样本期P-8基准上PR1YR回归的截距产生了每月0.46%的统计显著截距，r平方仅为0.6。最后，Grinblatt和Titman没有试图解释可归因于费用或交易成本的绩效差异。

B. Three-Year 4-Factor, Alpha-Sorted Portfolios

Since I evaluate performance relative to the 4-factor model, sorting mutual funds on alphas from the same model should measure stock-picking talent more accurately. However, using the same asset pricing model to sort and estimate performance will also pick up the model bias that appears between ranking and formation periods. For example, if the factor-mimicking portfolios impose risk premia that are too high or too low, funds with consistent 4-factor model loadings will show persistent 4-factor model performance. A similar problem exists if there is an omitted factor in the model. Because of the joint-hypothesis problem, I cannot directly test model bias. Therefore, I interpret the results from these tests with caution.

由于我评估了与4因素模型相关的绩效，因此在同一模型的α上对共同基金进行排序应该可以更准确地衡量选股人才。然而，使用相同的资产定价模型对绩效进行排序和评估也会发现在排名和形成期之间出现的模型偏差。例如，如果模拟投资组合的因子施加了过高或过低的风险溢价，则具有一致的4因子模型载荷的基金将表现出持续的4因子模型绩效。如果模型中存在遗漏因子，则存在类似问题。由于联合假设的问题，我不能直接测试模型偏差。因此，我谨慎地解释这些测试的结果。

Table VI reports statistics on decile portfolios formed on lagged three-year alpha estimates from the 4-factor model. Sorting on 4-factor alphas does not achieve as large a spread in mean return as one-year past return (0.43 percent per month versus 0.67 percent), but it does identify funds with larger positive and negative abnormal performance relative to the 4-factor model. The spread in 4-factor alphas is 0.45 percent, substantially greater than the 0.28 percent for portfolios sorted on one-year simple return in Table III.

表六展示了根据四因素模型的滞后三年α估计形成的十分位数投资组合的统计数据。按4因素α排序的平均收益率差不如一年前的收益率大（每月0.43%对0.67%），但它确实能识别出相对于4因素模型具有更大正负异常表现的基金。四因素α的利差为0.45%，大大高于表III中按一年简单收益率排序的投资组合的0.28%。

Table VI. Portfolios of Mutual Funds Formed on 3-Year Past 4-Factor Model Alphas

表六：基于过去3年4因素模型Alpha形成的共同基金投资组合

The Spearman test for rank independence (not reported) fails to reject with a p-value of 7.2 percent, but the top and bottom past-performance deciles are clearly separated from the average-performing midranked funds. The top decile achieves a positive 4-factor model alpha that is eight basis points per month and almost two standard errors above the second-ranked portfolio. Likewise, the bottom past-performance decile underperforms the ninth by 24 basis points per month, a difference of more than three standard errors. Patterns in 4-factor model loadings are not as pronounced, with both the top and bottom past-performance decile funds concentrating in small, growth, and momentum stocks. As in the one-year past-return sorted portfolios, the CAPM beta estimates of the alpha-sorted portfolios are very similar to one another (not reported), so the CAPM does not explain the cross-sectional variation in return either. Using longer-term estimates or appraisal ratios ( α i / σ i e ) , as suggested by Brown et al. (1992), does not substantially affect the results.

Spearman测试排名独立性（未报告）以7.2%的p值未能拒绝，但过去业绩前十名和后十名与平均业绩的中等基金明显分开。前十分位达到正4因素模型α，即每月8个基点，几乎比排名第二的投资组合高出两个标准误差。类似地，过去表现最差每月比第九位低24个基点，相差超过三个标准差。四因素模型载荷的模式并不明显，过去业绩十分位基金的顶部和底部都集中在小型股、成长股和动量股。与过去一年收益分类投资组合一样，用α分类投资组合的CAPM贝塔估计值彼此非常相似（未报告），因此CAPM也无法解释收益的横截面变化。正如Brown等人（1992）所建议的，使用长期估计或评估比率（αi/σi e）不会对结果产生实质性影响。

While the 4-factor model explains none of the spread in return on past alpha-sorted portfolios, expenses and transaction costs explain about 2 percent of the spread. The expense ratio on the lowest-ranked portfolio exceeds the expense ratio on the highest-ranked fund by 0.63 percent per year. Further, estimates of round-trip transaction costs of the two extreme deciles differ by 1.41 percent. Since the lowest-ranked portfolio trades slightly more frequently, the net difference in total transaction cost estimates is 1.35 percent per year. Thus, of the 5 percent annual spread in mean return between the highest and lowest past alpha-ranked portfolios, the 4-factor model explains nothing, and expenses and transaction costs explain slightly less than one-half.

虽然4因素模型无法解释过去α分类投资组合的回报利差，但费用和交易成本约占利差的2%。排名最低的投资组合的费用比率每年超过排名最高的基金的费用比率0.63%。此外，两个极端十分位的往返交易成本估计相差1.41%。由于排名最低的投资组合的交易频率稍高，因此总交易成本估算的净差额为每年1.35%。因此，在过去α排名最高和最低的投资组合之间5%的年平均回报差价中，4因素模型解释不了什么，而费用和交易成本的解释略低于一半。

Underperformance by decile 10 funds relative to decile 9 is still quite pronounced and statistically significant in these portfolios. Decile 10 underperforms decile 9 by 18 basis points per month in mean return, and by 24 basis points'per month in 4-factor performance. Differences in expense ratios of 0.5 percent account for only four basis points of the nine-ten spread. Differences in turnover of 24 percent and estimated transaction costs of 1.24 percent explain only another 2.5 basis points of the spread. Even after considering the higher expense ratios and turnover for decile 10, the spread in 4-factor alphas between deciles 9 and 10 is a statistically significant 18 basis points.

在这些投资组合中，十分位-10基金相对于十分位-9基金的表现仍然相当明显，且在统计上具有显著性。十分位10的平均回报率每月比十分位9低18个基点，运用四因素评估绩效每月比十分位-9低24个基点。0.5%的费用比率差异仅占9-10利差的4个基点。24%的营业额和1.24%的估计交易成本的差异只能解释差价的另外2.5个基点。即使考虑到十分位-10的较高费用比率和营业额，十分位-9和十分位-10之间的4因素α差异在统计学上是显著的18个基点。

Unlike the highest one-year past-return mutual funds, the returns on high past-alpha mutual funds remain above average long after fund ranking. Figure 4 displays the mean monthly excess returns on the funds in each decile portfolio in the first five years after funds are ranked in past-alpha deciles. Although the mean returns on the lowest nine past-performance deciles converge after two years, the highest decile maintains a persistently high mean return a full five years after the portfolio is initially formed. Apparently, a relatively high 4-factor model alpha is a reasonably good indicator of the relative long-term expected return on a mutual fund. However, the 4-factor model alpha on this portfolio over the five-year post-ranking period (not reported) averages only three basis points per month and is not reliably different from zero. This suggests that these funds aren't providing returns substantially beyond those predicted by the 4-factor model. Thus, high-alpha funds also have high sensitivities to the factors in the 4-factor model.

与过去一年回报率最高的共同基金不同，过去共同基金的回报率在基金排名后很长一段时间α仍高于平均水平。图4显示了在过去的阿尔法十分位数排名后的前五年内，每个十分位数投资组合中基金的平均月度超额回报。尽管过去最低的九个业绩十分位数的平均回报在两年后趋于一致，但在投资组合最初形成后整整五年内，最高十分位数的平均回报一直保持在较高水平。显然，相对较高的4因素模型α是共同基金相对长期预期回报的一个相当好的指标。然而，在排名后五年期间（未报告）该投资组合的4因素模型α平均每月只有三个基点，与零没有显著差异。这表明，这些基金的回报率并没有远远超过4因素模型的预测。因此，高阿尔法基金对4因素模型中的因素也具有较高的敏感性。

Figure 4图4

Post-formation returns on portfolios of mutual funds sorted on lagged three-year estimates of 4-factor alpha.

共同基金投资组合的形成后回报按滞后的四因子阿尔法三年估计排序。

In each calendar year from 1962 to 1987, funds are ranked into equal-weight decile portfolios based on three-year estimates of 4-factor alpha. The lines in the graph represent the excess returns on the decile portfolios in the year subsequent to initial ranking (the “formation” year) and each of the next five years after formation. Funds with the highest 4-factor alpha comprise decile 1, and funds with the lowest comprise decile 10. The portfolios are equally weighted each month, so the weights are readjusted whenever a fund disappears from the sample.

以上是对图4的解释

If alpha measures portfolio manager skill, mutual funds should maintain their 4-factor alpha ranking in subsequent, nonoverlapping periods. A contingency table of fund ranks (not reported) finds that relatively few funds stay in their initial decile ranking. Only funds in the top and bottom deciles maintain their rankings more frequently than expected. Funds initially in decile 1 have a 17 percent probability of remaining in that decile, and funds in decile 10 have a 46 percent chance of remaining in decile 10 or disappearing from the sample altogether. Given the high five-year expected return on the highest decile funds versus the second-highest decile, it is surprising that so few funds are able to maintain their top ranking.

如果用α衡量投资组合经理的能力，共同基金应在随后的非重叠期内保持其4因素模型的α排名。一份基金排名列联表（未报告）发现，相对较少的基金保持在最初的十分位。只有排名在前十分位和后十分位的基金保持排名的频率高于预期。最初处于十分位1的基金保留在该十分位的概率为17%，而处于十分位-10的基金保留在十分位-10或从样本中完全消失的概率为46%。鉴于最高十分位基金的五年预期回报率高于第二高十分位基金，因此令人惊讶的是很少有基金能够保持其最高排名。

Apparently, neither expense ratios nor turnover completely explain the persistent spread and pattern in 4-factor abnormal returns on mutual funds. About 0.6 percent of the 5 percent annual spread in net alphas can be explained by expense ratios; variation in transaction costs accounts for another 1.4 percent. The most striking result is the size of the spread captured by the strong underperformance in the lowest-ranked funds, even after adjustments for expenses and transaction costs.

显然，无论是费用比率还是换手率都不能完全解释共同基金4因素异常回报的持续利差和模式。在5%的年度净α利差中，约0.6%可以用费用比率来解释；交易成本的变化占另外1.4%。最引人注目的结果是，排名最低的基金表现不佳，即使在对费用和交易成本进行调整后，利差的大小也是如此。

VI. Conclusion

This article does much to explain short-term persistence in equity mutual fund returns with common factors in stock returns and investment costs. Buying last year's top-decile mutual funds and selling last year's bottom-decile funds yields a return of 8 percent per year. Of this spread, differences in the market value and momentum of stocks held explain 4.6 percent, differences in expense ratios explain 0.7 percent, and differences in transaction costs explain 1 percent. Sorting mutual funds on longer horizons of past returns yields smaller spreads in mean returns, all but about 1 percent of which are attributable to common factors, expense ratios, and transaction costs. Further, the spread in mean return unexplained by common factors and investment costs is concentrated in strong underperformance by the bottom decile relative to the remaining sample. Of the spread in annual return remaining after the 4-factor model, expense ratios, and transaction costs, approximately two-thirds is attributable to the spread between the ninth- and tenth-decile portfolios.

本文通过股票收益和投资成本的共同因素，对股票共同基金收益的短期持续性进行了许多解释。购买去年绩效最高的共同基金，出售去年最低的十分位基金，每年的回报率为8%。在这一利差中，所持股票市值和动量的差异解释了4.6%，费用比率的差异解释了0.7%，交易成本的差异解释了1%。将共同基金按过去收益的较长期限进行分类，平均收益的利差较小，但约1%的利差归因于共同因素、费用比率和交易成本。此外，普通因素和投资成本无法解释的平均收益利差集中在相对于剩余样本的底部十分之一的强劲表现中。在四因素模型、费用比率和交易成本之后剩余的年度回报利差中，约三分之二归因于第九和第十十分位投资组合之间的利差。

I also find that expense ratios, portfolio turnover, and load fees are significantly and negatively related to performance. Expense ratios appear to reduce performance a little more than one-for-one. Turnover reduces performance about 95 basis points for every buy-and-sell transaction. Differences in costs per transaction account for some of the spread in the best- and worst-performing mutual funds. Surprisingly, load funds substantially underperform no-load funds. After controlling for the correlation between expenses and loads, and removing the worst-performing quintile of funds, the average load fund underperforms the average no-load fund by approximately 80 basis points per year.

我还发现，费用比率、投资组合换手率和销售费用与绩效显著负相关。费用比率似乎按照略高于一比一降低了绩效。每一笔买卖交易的换手都会使业绩下降约95个基点。每笔交易的成本差异是业绩最好和最差的共同基金的部分价差的原因。令人惊讶的是，有佣金基金的表现远远逊于无佣金基金。在控制费用和载荷之间的相关性，并剔除表现最差的五分之一基金后，平均有佣金基金的表现比平均无佣金基金每年差约80个基点。

This article offers only very slight evidence consistent with skilled or informed mutual fund managers. Mutual funds with high 4-factor alphas demonstrate above-average alphas and expected returns in subsequent periods. However, these results are not robust to model misspecification specification, since the same model is used to estimate performance in both periods. In addition, the higher expected performance for high-alpha funds is only relative, since these funds do not earn significantly positive expected future alphas. The evidence is consistent with the top mutual funds earning back their investment expenses with higher gross returns.

本文仅提供了与技能强或信息先知的共同基金经理相一致的非常微小的证据。具有高4因子模型的α的共同基金在后续期间表现出高于平均水平的α和预期回报。然而，这些结果对模型错误规范不具有鲁棒性，因为在这两个时期种使用相同的模型来估计绩效。此外，高α基金有较高的预期业绩只是相对的，因为这些基金不会获得显著积极的预期未来α。这一证据与顶级共同基金以更高的总回报和其投资费用是一致的。

Overall, the evidence is consistent with market efficiency, interpretations of the size, book-to-market, and momentum factors notwithstanding. Although the top-decile mutual funds earn back their investment costs, most funds underperform by about the magnitude of their investment expenses. The bottom-decile funds, however, underperform by about twice their reported investment costs. Apparently, these results are not confined to mutual funds: Christopherson, Ferson, and Glassman (1995) reach qualitatively similar conclusions about pension fund performance. However, the severe underperformance by the bottom-decile mutual funds may not have practical significance, since they are always the smallest of the funds, averaging only $50 to $80 million in assets, and because the availability of these funds for short positions is doubtful.10

总体而言，证据与市场效率、规模解释、账面市值和动量因素一致。尽管排名前十分之一的共同基金收回了投资成本，但大多数基金的表现都低于其投资费用。然而，最底层的十分之一基金的表现比报告的投资成本低约两倍。显然，这些结果并不局限于共同基金：Christopherson、Ferson和Glassman（1995）对养老基金的绩效得出了质量上相似的结论。然而，底部十分之一共同基金的糟糕表现可能没有实际意义，因为它们总是规模最小的基金，平均资产只有5000万至8000万美元，而且这些基金是否可用于空头头寸也值得怀疑。

Buying last year's winners is an implementable strategy for capturing Jegadeesh and Titman's (1993) one-year momentum effect in stock returns virtually without transaction costs, since the actual trading costs are shifted to the long-term holders of mutual funds. However, the current mutual fund practice of selling shares at NAV cannot be a long-run equilibrium after this strategy is widely followed: Equilibrium requires mutual funds to charge transaction fees to incoming and outgoing investors to compensate for their perturbing effects on performance. This practice is already becoming common among many funds that hold illiquid stocks such as the Vanguard Small Capitalization Index Fund and Dimensional Fund Advisors Emerging Markets Index Fund.

购买去年的赢家是一种可实施的策略，可以捕捉Jegadeesh和Titman（1993）在股票回报中的一年动量效应，几乎没有交易成本，因为实际交易成本转移到共同基金的长期持有人身上。然而，在这种策略被广泛采用之后，目前以资产净值出售股票的共同基金实践不可能是长期均衡：均衡要求共同基金向流入和流出的投资者收取交易费用，以补偿其对业绩的扰动影响。这种做法在持有非流动性股票的许多基金中已经很普遍，如先锋小额资本化指数基金（Vanguard Small Capitalize Index Fund）和Dimensional Fund Advisors新兴市场指数基金（Dimensional Fund Advisors Emerging Markets Index Fund）。

The evidence of this article suggests three important rules-of-thumb for wealth-maximizing mutual fund investors: (1) Avoid funds with persistently poor performance; (2) funds with high returns last year have higher-than-average expected returns next year, but not in years thereafter; and (3), the investment costs of expense ratios, transaction costs, and load fees all have a direct, negative impact on performance. While the popular press will no doubt continue to glamorize the best-performing mutual fund managers, the mundane explanations of strategy and investment costs account for almost all of the important predictability in mutual fund returns.

本文的证据为财富最大化的共同基金投资者提供了三条重要的经验法则：（1）避免使用业绩持续不佳的基金；（2）去年回报率高的基金明年的回报率高于平均预期，但此后几年的回报率则不高；（3）费用比率的投资成本、交易成本和销售费用都会对绩效产生直接的负面影响。尽管大众媒体无疑将继续美化表现最佳的共同基金经理，但对战略和投资成本的平淡解释几乎解释了共同基金回报的所有重要可预测性。

读后感

近几年来，投资成为了人们身边的热词，大学生的共同话题中增加了“基金”一词，无论我们从银行渠道、第三方支付平台渠道或者是基金公司渠道，眼前的基金都是眼花缭乱，那么我们如何从众多的基金选取出未来可能能带来较高回报的优质基金，本文给了我们一些参考性的建议。

对于文章中投资基金经理业绩低于其投资成本的问题我感到非常疑惑，而且这种情况在发达国家股票市场并不少见，我国基金经理动辄一年有20%以上的收益，难度我们国家的基金经理能力比别国要强这么多吗？答案显然是否定的，正是因为我们国家的投资者中散户投资者占大多数，且大部分散户投资者的投资能力是很弱的，在交易的博弈中，具有专业性和信息优势的基金经理人自然占了上风，获取了超额收益，所以我们国家主动型投资的优秀基金经理人往往业绩会非常好，而被动投资收益显然较低。发达国家股票市场，如美国股票市场，被动投资收益经常性地能超越主动投资收益。

浏览支付宝基金页面，他总会给用户推荐一些“爆款”基金，观察后发现，它总是优先推荐过去一年表现较好的基金，一年翻一倍甚至是两倍等等或许更夺人眼球，更能刺激潜在的客户进行购买。但是读完这篇文章后，我知道原先排名较高的基金之后业绩的持续性是不能保证的，特别是行业基金，更不可能保持一直的高排名。因此，这篇文章给予我们的启示是，不能光光依靠基金经理过去的业绩买入基金，所谓的“爆款”基金，仅仅代表的是过去的业绩，未来不一定就能获取高于平均水平的绩效。

这篇文章对于数据的分组还是值得学习的，基金产品有很多，怎么样进行比较合理地归类研究，才能让研究过程不那么复杂而且得出的结论会比较可靠是简化的关键。本文在幸存者偏误上花了很多精力，为了调取清盘了的基金数据，付出了财力和精力，在以后的学术研究中，这个可以作为创新点，研究得出的结论就更加真实，参考意义将更大。