Month upon month, we see that articles and studies out about active management under performing their benchmarks, some say it use due to fees and others due to managers having no skill. Personally I think it’s a bit of both, I will demonstrate mathematically how fund constraints combined with fees can make outperformance very difficult.

First we will define active share, the active share of a fund is the % of the fund that is weighted differently than the benchmark.
Wb-Wp=Wa

If the active share of the fund is 10% that means that 10% of the fund is different than the benchmark. Let’s assume that the fund manager is charging a 2% management fee.
Let’s take a simple example: assume the S&P 500 (the fund’s benchmark) goes up 10%, our manager needs to make 30% total return on the portion he is stock picking on [see formula under].

In generalisation The Active Component needs a total return of ActiveComponentReturn=((TotalRequiredReturn-(PassiveWeight*(BmReturn-Fees)))/ActiveWeight)+Fees

That total return subtract the benchmark return is the excess return required.

There is a clear relationship between Active Weight and Return required, as the weight increases the return required goes down.

I’ve plotted decreasing fees from 2% to 0.5% in decreases of 0.1% (Top circle is 2% bottom one is 0.5%).

I assumed the benchmark will go up 10% over the period, when computing these numbers.

Excess Returns vs Active Weights

What is interesting here is it’s much easier to increase the active weight and generate performance than it is to lower fees.  A product that hugs close to the benchmark and charges high fees will very rarely outperform which is clear here as the skill required is very large which is unlikely.

The take home for managers is that it is very hard to beat a benchmark if you do not have a “high” active weight, and for investors to avoid investing in products that have low active weights unless the fees are comparably low as the skill required to outperform is very unlikely. In a later post I will explore how to quantify the probability that a manager trading randomly could outperform.

 

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