# Calculation of a performance fee

Discussion in 'SA7' started by Jozef Minar, Sep 1, 2019.

1. Hi all,

I just went through Assignment X6 model solution, part (i) and I was surprised to see how the performance fee was calculated there.

When I worked out the question, I thought that the performance fee is based on excess return that the manager delivered compared to the benchmark. In the question, we started with the fund value £200m, the benchmark return over the first period was 5%, the fund return was 8% and the performance fee was 10%. Thus, thanks to the manager’s ability we are better off £6m, because the end-of-period fund value is £216m and it would have been £210m if the benchmark return was achieved. I therefore thought that the performance fee should be £600k.

However, according to the model solution the approach above is wrong and the correct answer is £648k. It says that normal way how the performance fees are calculated is to take the end-of-period fund value and calculate the outperformance as the excess return applied to end-of-period fund value. In this case this means that performance fee is 10% of (0.08-0.05) × £216m, thus £648k.

I don’t know how these fees are calculated in practice and I don’t want to argue with the claim that this second approach is the most widespread. However, I would like to point out on the inconsistency present in this second approach, which I will firstly present on a simple example.

Imagine for a moment that the fund in question was some crazy hedge fund aiming for the extreme returns using some highly leveraged (almost casino-like) strategies. Let us start with the fund value £1m, the benchmark return over the first period 0%, the fund return 500% and the performance fee of 20%. Using my approach, we would calculate that we are better off £5m, and thus we can calculate the performance fee to be £1m. However, if we use the approach of the model solution, then we apply excess return (which is 500%) to the end-of-period fund value, £6m. In this case this means that performance fee is 20% of (5-0) × £6m, thus £6m. The whole fund’s value is thus used as the fee to the fund manager and investors lose all their money (if there is also a flat fee component, the investors will be left with a negative balance and will owe another money to the fund manager).

Although the example speaks for itself, I would like to also explain in pure mathematical terms why I consider the first approach to be mathematically robust (unlike the second approach). Let the initial fund value be L, the benchmark return over the first period rb, the fund return over the first period rf (rf > rb) and the performance fee p. The end-of-period fund value (before fees) is (1+rf) × L and would be (1+rb)× L if the benchmark return was achieved. Using my approach, the outperformance in absolute terms is (rf - rb) × L and the performance fee (rf - rb)× L × p. The end-of-period fund value (after fees) would thus be
(1+rf) × L - (rf - rb)× L × p = L × [1 + (1 – p) × rf + p × rb].​
This is a very nice mathematical expression, because achieved return (after performance fee) is the weighted average of fund return (before performance fee) and the benchmark return with weights used 1 – p and p respectively. This corresponds to my expectation of how the performance fee should affect the net return. However, using the normal way (as per model solution) we get that the performance fee equals p × (rf – rb)× (1+rf)× L. The end-of-period fund value (after fees) would thus be
(1+rf) × L - p × (rf – rb)× (1+rf)× L = L × [1 + (1 – p) × rf + p × rb - p × rf × (rf – rb)].​
The achieved return (after performance fee) thus contains a second-order term p × rf × (rf – rb). This term does not fit well with the result for me and can create awkwardness, such as in the example above.

2. ### Colin McKeeActEd TutorStaff Member

Hi, You have indeed come up with an odd example which does seem to make the method ridiculous. This example in the Assignments is actually taken from a SA6 past paper question and I have changed the numbers (but not the methodology). I dont have personal experience of how performance fees are calculated, and therefore had to assume that the way the exam calculated it was common. Your exanmple is very extreme, so it is possible that the method is still correct, but is just not designed with such an extreme situation in mind. I am afraid that I cant really add any more as I dont know what the answer is. It may be that another student reading this post and doing the assignments can shed light on the most common approaches. However I can confirm that the assignment calcs do mirror the past paper calcs.

3. Interesting problem. I used the same method as Jozef when attempting the assignment.

I'm not sure how performance fees are calculated in reality, however the acted method does seem susceptible to extreme movement whereas Jozef's method works as one would expect under all circumstances.

Colin, in case we do get a performance fee calculation question in the exam, would you advise using the method from the assignment, despite the inherent flaw?

Additionally, does anyone know when the Apr 2019 SA7 paper and mark scheme will be released?

4. ### Colin McKeeActEd TutorStaff Member

The method in the assignment uses the method used by the examiners in the past paper question, so if they were to ask a similar question, they would have to give you full marks if you used this method.