How much to pay your fund manager?

An individual wants to invest his hard earned money in a fund seeking good returns on a long term basis. Now there are different kinds of fee structure that he can opt for including fixed fee, profit sharing or a mixture of both. How to go about evaluating the efficiency of these structures?

A rational client would ideally want his manager to work very hard and do the best he can and at the same time charge no fee at all. Of course the manager would not be so eager to manage the capital of such a client.  Hence the client has to take the manager’s perspective into account while negotiating for the best fee structure.

By altering the fee structure the client attempts at maximizing his net returns (Returns from investment – Fee he pays). At the same time, for a fee structure chosen by the client, manager attempts at maximizing his own returns (Fee he receives - cost of effort he put in).

Mathematically this problem can be formulated as following:

Client’s Perspective:

Find F(R) such that [R-F(R)] is maximized. Here F(R) is the opted fee structure which is a function of returns R. Here R is based on the performance of manager.

Manager’s Perspective:

Find E such that [U(F(R(E)))-C(E)] is maximized. Here E is the efforts put in by the manger. This effort would translate into R, returns on investment for client. Based on these returns the client would pay manager some fee, F. This fee would have some utility, U, for manager. C is the cost of effort the manager is putting in to achieve the returns.  

Following is the sample mappings of these variables.

• The more the effort put in the higher the returns on investment. Here a linear mapping is used for the sake of simplicity.

• The larger the fee received by the manager, the more is the utility for him. Here the utility function of a typical risk-averse agent is used.

• The more effort the manager puts in the higher is the cost of effort. Also as the absolute level of effort increases it becomes harder and harder to do additional effort.

Case 1: Fixed fee structure

Here Kfr is the fixed fee percentage. Typical values are 0.5-5%. After calculating, the optimal effort for the mangers comes out to be zero. Client net returns would be (–Kfr). In real life situations, given a fixed fee structure the manager chooses to do the minimum work required to retain the client. This situation is clearly not favorable for the client.

Case 2: Variable (profit sharing) fee structure

Here Kfr is the profit-sharing percentage. The typical values will lie between 10%-50%. As we can see that in a profit sharing framework there is a nonzero effort the manager would put in. This situation is better for both the client and the manager (for certain values of Kfr) when compared with case 1.

Also we can see that the profit sharing percentage (Kfr) has a significant impact on the net returns of the client.  When the profit sharing percentage is very low (let’s say 5%) the agent does not have enough incentive to work. Hence the effort would be low and so will be the net returns for the client. On the other hand let’s assume that the profit sharing percentage is 95%. Though the manager’s effort increases monotonically with the profit sharing percentage, it does not happen linearly.  Hence the client will end up paying more for the incremental increase in effort.  This means there is an optimal profit sharing percentage at which the client can make the maximum out of the agreement.

Case 3: Fixed + Variable fee structure

This leads to two distinct types of behavior that mangers would exhibit.  The manager either chooses to do no work and still charge the fixed fee component (Kfr*Rlb). Or he chooses to do non zero effort so as to benefit from the variable fee component. The actual behavior depends on the exact value of Kfr and Rlb. 

Conclusion:

Based on the above analysis the client should keep the following points in mind before deciding on the structure:

• A fix + variable fee structure is usually better than a fix fee structure. The profit sharing component gives the manager an incentive to work harder.
• While going for a variable fee structure, both very low and very high profit sharing percentage should be avoided.
• While going for a mix structure, ensure that either returns cut off (Rlb) for profit sharing is sufficiently low (realizable with good efforts) or profit sharing percentage (Kfr) is relatively high. Otherwise there would be no incentive for the manager to work.