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During my research I found that fund active returns (alpha), measured by Fama and French four factor model, decreases as the fund increases in size (asset under management).

What are some reasons that explains such relationship?

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Most of this will be the sheer nature of statistics. Big funds tend to have more average results, small funds have more variance and thus have more of the high returns, but also likely more of the heavy losses.

The same statistical effect is visible in the context of school performance : https://marginalrevolution.com/marginalrevolution/2010/09/the-small-schools-myth.html

An alternative way to view it is that a large fund could be divided into several smaller funds, each representing a part of the portfolio. Keeping them separate, a stellar year in a large fund's credit position would stand out, but averaged in with the other positions (even if they are no worse than market average) would dilute the effect.

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The main reason in the academic literature for alphas to decrease with fund size has to do with decreasing returns to ability. Think about it this way:

  1. Managers first allocate funds to the most profitable opportunities; So the first dollars invested in fund have high returns (and so small funds perform well);
  2. As the fund size increases managers allocate money to the remaining available opportunities that are not as good as the first ones and therefore overall returns decrease.

The effect above that I described in words is called decreasing returns to ability. It was first highlighted by Berk and Green in their paper Mutual Fund Flows and Performance in Rational Markets.

In their own words:

In our model, investments with active managers do not outperform passive benchmarks because investors competitively supply funds to managers and there are decreasing returns for managers in deploying their superior ability. Managers increase the size of their funds, and their own compensation, to the point at which expected returns to investors are competitive going forward.

Check the paper for the algebra of the model and more intuition.

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    $\begingroup$ Unfortunately, Financial Academics tend to "steal" other people's works. Berk&Green's celebrated (and empirically risible) model is nothing more than another iteration of what Robert F. Ferguson has proposed in the following article in 1979: cfapubs.org/doi/abs/10.2469/faj.v35.n2.56 It would be decency to start calling it the Ferguson model or, at least, the Ferguson-Berk-Green model. $\endgroup$ – fni May 28 '18 at 10:05
  • $\begingroup$ That's fair enough. It is indeed unfortunate that they either overlooked that reference or worse they knew it and did not reference it ... That is unfortunately pervasive in academia and there are countless other examples. I am curious about the Ferguson reference, unfortunately I do not seem to have access to it. $\endgroup$ – phdstudent May 28 '18 at 13:20
  • $\begingroup$ For free here: sci-hub.tw/https://www.jstor.org/stable/… Unfortunately, one of the two authors has a story in these regards... $\endgroup$ – fni May 29 '18 at 13:26
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I thought I'd contribute an answer that's more empirical and experience-based. I worked at an asset allocator earlier on in my career, and the company has a very strong bias toward NOT investing in large funds. Several reasons drive this bias:

  1. Performance Gap: Empirically, there is a measurable difference in returns between large funds and small funds – funds with lower AUM (assets under management) tend to outperform larger peers.
  2. Motivation: It is perceived that small funds, which tend to be younger, are more motivated to succeed.
  3. Alignment of Interest: Related to 2), larger funds can do very well just by collecting management fees and gradually become "asset aggregators," while small funds can have difficulty surviving on management fees alone – they make most of their money from incentive fees. So from this perspective, the interests of smaller funds and allocators are more aligned – both want more returns.
  4. Opportunity Set: Larger funds simply can't be nimble and fail to exploit a lot of dislocations that smaller funds can more easily exploit.
  5. Style Drift: Large funds, in its quest to put increasingly large amount of capital to work, tends to drift away from strategies that initially make them successful.
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