Skill or luck: a bootstrapping approach to analysing South African equity unit trust returns

Marinus, Luigi

Skill or luck: a bootstrapping approach to analysing South African equity unit trust returns

Master Thesis

2022

Abstract

The focus of the study is to add to the available literature on the ability of unit trust fund managers to consistently display skill in their investment performance, and to distinguish between skill and luck. The study focussed on South African domestic equity funds and divided these between funds that have an allowance for an offshore allocation and those that are domestic only. Domestic equity funds were specifically selected as sample because they can be analysed in terms of the multi-factor equity pricing models kept up to date by Legae Peresec. These funds were further divided between those that allowed global exposure and those that did not, to test whether this had a notable effect on the performance of the two subsamples. In the South African domestic equity ASISA category (ASISA, 2021), funds have an allowance for a maximum of 30% in offshore holdings, but most funds (roughly two-thirds in this study) choose to not allow offshore holdings in their mandates. The initial sample of 326 funds reduced to 179 funds after the exclusion of tracker funds, funds of funds, multi-managed funds, and funds with either less than 36 months of performance or where required data was missing. The study uses performance data for the period March 2006 to May 2020 for all qualifying funds regardless of whether they were active at the end of the period or not, and therefore caters for survivorship bias. Two methods are used to assess expected performance versus actual performance. The first was a regression analysis that tests fund performance against three multi-factor asset pricing models, namely the Fama and French 3-Factor Model, the Carhart 4-Factor Model, and the Fama and French 5-Factor Model. The second is a bootstrap resampling analysis that indicates whether fund performance is better than a randomised (luck-equivalent) distribution of returns, thereby implying manager skill. A regression was run per fund based on the Carhart 4-factor model with the error terms being resampled. A distribution per fund was then modelled by regression by replacing these error terms 1,000 times. A further regression was run independent of time to obtain the alphas for the comparison to the actual fund alphas. Any specific funds with alphas greater than the distribution performed better than the model suggests at certain percentile levels, which would imply skill was required to attain those performance levels. The first part of the study shows that certain funds outperform the multi-factor model performance over the measurement period, although in all models the average alpha is less than zero. In the second part of the study the bootstrap resampling produces a luck distribution that is compared to the actual distributions. There are no funds where the alpha exceeds the corresponding luck-based percentile level, which could imply that fund manager skill was not present over the measurement period. There are several actual fund alphas that fall within the luck distribution range of alphas, where skill was inconclusive. Funds that have a global allocation tend to perform better than local only funds before fees are taken into account. While this study may not be the final word on whether investment skill is observable in the South African market it gives some insight into the likelihood of skill being present over a certain defined investment period. As passive funds have attracted more assets, the question of whether active investment managers are justified in earning higher fees is becoming increasingly important. The results of this study indicate that this may indeed not in general be the case.

Keywords

finance

tax

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