As previously mentioned, the assumptions made on the distribution of the value-added may be incorrect, this could question the validity of the results. Furthermore, this research has not conducted the persistence of skilled managers following Berk & van Binsbergen (2015). Future work could add this evaluation, possibly leading to different results. Furthermore, a concern is that trading costs are not included in this research, however, this is relevant for the strategy of active funds. Especially small funds which typically invest in smaller stocks face illiquidity costs and large funds typically deal with market impact, both of these cases were not considered given the complexity. If these costs were taken into the account, the results would possibly be different. Perhaps, future research can take these costs into account when evaluating performance in the active fund space. At last, the results may be subject to different biases, such as survivorship bias in the benchmark and incubation bias in the funds. If future work could add additional screening methods which reduce these biases, such as filtering for all funds that are smaller in size than 5 million USD, then the results would possibly be more credible.
Snapshot 2:
The code below reads the data. By making two separate columns,
‘Year’ and ‘Month’, it is easier to merge different files which also have different date formats. To be able to loop through the different data files in the same order of tickers, the data is ordered by ticker and two date columns are placed at the end of the dataframe.
Appendix
In this section, an overview is given of the code used to conduct the research. Furthermore, each snapshot of code contains a small summary and the logic behind it. The display of repetitive code is avoided, if one image shows how the data files are imported, this may not be shown in other images. The libraries imported and used are Pandas, NumPy, Statsmodels, SciPy, Matplotlib, DateTime, Math, Warnings, Random, and Seaborn. After a script is finished, the results are most of the time exported to a CSV file, to reduce the risk of losing results during the process. Furthermore, CSV files can easily be imported into another script, this also helps with dividing the process into smaller parts since overall it is a lengthy process to, for example, compute 12,000+ time-series regressions from which the intercepts are captured and additional analysis applied to.
Snapshot 1:
Below code is used to clean the expense data, since funds only report the initial expense ratio or when it is changed, the code cleans the blanks by filling it with the last expense ratio reported. After a change in expense ratio, the following blanks in the data are filled with this ratio until the fund reports a new ratio. In the end, the dataset has no blanks and can be merged without dropping unnecessary data.
Snapshot 3:
Code below computes the Sharpe ratios, excess returns, and time series lengths by looping through the dataset, selecting a subset of data, checking if it has at least 30 months of returns, calculating the log return, merging the data with Fama & French factors, calculating the gross return, and then calculating the variables. By changing nav_non_esg.csv to nav_esg.csv, this code switches between ESG and non-ESG funds.
Snapshot 5:
Calculate random net and gross alphas using a combination of random ETFs. The code is similar to Snapshot 4, except a random subsample of 4 ETFs is selected for each iteration, also the process is repeated 500 times. For each iteration, the results are stored in a temporary list and in the end the mean is taken from these lists which is exported to a csv file using a dataframe.
Snapshot 4:
Calculate gross and net alphas by using the factor model as benchmark. For each iteration, a subsample is selected and merged with expenses. Then the log return is calculated and merged with Fama & French. Afterwards, the gross and net return are calculated by subtracting the RF & expense ratio divided by 12. At last, the regression is conducted, and the results are added to a data frame and exported to a csv file. For the subperiod analysis, the following line is added, where xt is the respective year: curr_fd = curr_fd.loc[(curr_fd['Year']
== x1) | (curr_fd['Year'] == x2)| (curr_fd['Year'] == x3)| (curr_fd['Year'] == x4)]
Snapshot 9:
Bootstrap the value-added using the factor models as benchmark. Code is similar to Snapshot 8, except the alpha is subtracted from the (gross/net) return. Afterwards, 1000 iterations are conducted to calculate the value-added based on a random residual from the regression.
Snapshot 6:
Merge three net alpha data files and make the plot, following subplots are conducted in a similar way and are for this reason not shown.
Snapshot 8:
Calculate gross and net value-added using the factor model. For each iteration, the (gross/net) return, the lagged TNA, and the beta are calculated. If the beta is not nan, the value-added is conducted using the formula of Kooli & Stetsyuk (2021) and added to a list. In the end, the list is exported to a csv file using a data frame.
Snapshot 7:
Read net alphas, drop inf and nan values and apply the FDR correction.
Snapshot 10:
Calculate the gross/net value-added using ETFs as benchmark, code is similar to Snapshot 8 where the factor models were used.
Snapshot 11:
Calculate the bootstrapped gross/net value-added using ETFs as benchmark, code is similar to Snapshot 9 where the factor models were used.
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