Figure 1: Number and average size of mutual funds,
1999-2023.
This figure shows the average total net assets (TNA) of the 4,853 funds
in our sample, measured in millions of December 2023 dollars, displayed
on the left y-axis. On the right y-axis we show the average number of
funds in our sample for each month.
This is a line chart with dual y-axes showing monthly data from 1999 to 2023. The left y-axis measures average total net assets (TNA) in millions of December 2023 dollars, ranging from 1000 to 4000 million. The right y-axis shows the number of funds, ranging from 1600 to 2800. Two series are displayed: average TNA (shown as a continuous line) and number of funds (shown as a continuous line). The average TNA remained relatively flat at around $1.5 billion from 1999 through 2010, then increased substantially to peak at over $3.5 billion in 2021, before declining to approximately $2.6 billion by December 2023. The number of funds grew from just over 1,000 in 1999 to around 2,700 in 2018, then decreased to about 2,400 by the end of the sample period.
Figure 2: Regression tree for 2023.
This figure describes the optimal tree for the last year of our sample
period, 2023. The number of leaves is determined by five-fold
cross-validation. The sample is split using the state variable and
threshold given in the rectangles. The number of fund-months in each
“leaf,” as well as the proportion of the sample it represents, is
reported.
This is a diagram showing the structure of a regression tree for 2023. The diagram illustrates how the sample of mutual funds is split hierarchically based on specific variables and thresholds. The initial split uses "Rank of ret3" (rank of 3-month returns) at a threshold of 0.8, dividing funds into two groups: the top 20% performers and bottom 80% performers. The top-performing group is further split by the same variable at a threshold of 0.99, separating the top 1% from the next 19%. The lower-performing 80% is split based on "Rank of R²_FF4" (rank of R-squared from the Fama-French 4-factor model) at a threshold of 0.91. The resulting four terminal nodes ("leaves") show the number of fund-months in each group and their proportion of the total sample.
Figure 3: Skill and efficiency of US mutual
funds.
This figure plots skill (\(\psi_i\))
and aggregate efficiency (\(\boldsymbol{\beta_i^{\top}}\boldsymbol{\eta_i}\)),
measured in annualized percent, for all mutual funds in our sample,
averaged over all months for which they are in the sample. The thin
dashed line denotes the “zero abnormal return” line, where skill and
efficiency sum to zero. The thick dashed line is the OLS regression
line. The red circle denotes the average skill and efficiency across all
funds and all periods.
This is a scatter plot showing the relationship between skill (ψ_i) on the x-axis and aggregate efficiency (β_i times η_i) on the y-axis for US mutual funds. Both axes measure values in annualized percent, with the x-axis ranging from approximately -30 to 20 percent and the y-axis ranging from about -20 to 10 percent. Each point represents a mutual fund. The plot includes a thin dashed diagonal line representing the "zero abnormal return" line where skill and efficiency sum to zero, and a thick dashed line showing the OLS regression fit with a negative slope. A red circle marks the average skill (0.95%) and efficiency (-2.64%) across all funds and periods. The scatter pattern reveals a negative correlation (approximately -0.17) between skill and efficiency, with relatively few funds exhibiting both positive efficiency and positive skill.
Figure A1: Distribution of joint tests of
homogeneity.
This figure plots the asymptotic distribution of the joint test of
homogeneity of all lambdas across quintile groups formed using a sorting
variable, and the simulation-based distribution using random group
assignments. The F-statistics associated with tests of homogeneity
across quintiles formed using one of five sorting variables (MO, \(R^2_{FF4}\), TNA, ME and BM) are presented
as vertical lines.
This is a line chart comparing two statistical distributions related to tests of parameter homogeneity across mutual fund groups. The x-axis shows F-statistic values ranging from 0 to 70, while the y-axis represents frequency or density. Two distributions are plotted: the asymptotic distribution (shown as a continuous curve) and the simulation-based distribution (shown as a continuous curve), with the latter shifted to the right of the former. Vertical lines mark the F-statistics associated with tests of homogeneity across quintiles formed using five different sorting variables: MO (momentum), R² (R-squared), TNA (total net assets), BM (book-to-market), and ME (market equity). These vertical lines show where the actual test statistics for different sorting methods fall relative to both the asymptotic and simulation-based distributions.