Estimating the Return Impact of Fund Management Fees
Summary
The document examines how to quantify the effect of a management fee on investor returns when two funds have otherwise identical performance. It contrasts discrete and continuous fee calculations and proposes accounting for fees at frequent intervals as the fund value changes. The central distinction is between fees recorded as cash outflows and the economic cost of the returns that capital could have earned if fees had remained invested.
It argues that the relationship between these measures depends on market path and convexity: in a rising market, fees removed earlier can forgo later growth, while the effect reverses under the opposite convexity. The author says this makes it difficult to separate fee effects from style drift and asks about suitable approximations and statistical significance. No empirical results or recommended estimation procedure are supplied. A response suggests clarifying the fee deduction schedule and comparing ending fund wealth with total fees collected.
Key ideas
- Management fees can be modeled as deductions at discrete or continuous intervals.
- Frequent deductions make the fee impact depend on the path of fund value.
- Accounting fees and the opportunity cost of removed capital are distinct measures.
- Market convexity can change the relationship between recorded fees and foregone returns.
- The document does not establish a preferred estimator or significance test.
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Full text
# How to quantify the impact of management cost on return?
# How to quantify the impact of management cost on return?
Suppose funds X and Y are the same but X has 0.25% higher management cost. Suppose we are analyzing a 2 year interval. The simple models with discrete/continuous interval -assumptions are not really right below. I will get more specific in the end.
- discrete intervals `0.9975**2`
- continuous intervals $e^{0.0025*2}$
- $\sum_{0}^{days} a_{i} 0.0025^\frac{t_{i}}{t_{total Days}}$, where $a_{i}$ is amount of capital invested.
This is not really right, as the prices change frequently. Let $P_{1}=P_{0}r_{1}$, $P_{N}=P_{N-1}r_{N}=P_{0} \prod_{0}^{t}r_{i}$ and now to charge the customer we could take charge with as small intervals as possible:
- $C_{0} = 0$, $C_{1} = P_{1} pp_{1}$ and $C_{N} = P_{N} pp_{N}$,
where $pp_{N}$ is a charging function. It is a function because the economic cost to the investor is not really just day-adjusted cost but the foregone opportunity to invest into the fund. Now the sum of such costs differ with convexity. If we have a rising market, the accounting cost is less than the economic cost according to Jensen (note that the accounting cost is just taken from the end result while the economic cost of each single CF):
$EC = \sum^{n}_{i=1} p_{i} pp(x_{i}) \geq pp( \sum_{i=1}^{n} p_{i} x_{i}) = AC$,
It is opposite for the opposite convexity. Because of changing convexity, I have found it very hard to track the impact of cost on the return. Its impact does change over time as described.
How can I quantify the impact of management cost on return? What kind of approximations do you use and how do they differ with different convexity? It is very hard for me to separate the impact of management cost from other issues such as style-drifting. I need to find some proper ways with proper significance levels to investigate this issue. Any paper about this?
## Answer by Tal Fishman (score 1)
https://quant.stackexchange.com/a/1560
Is the management fee deducted daily or annually? Or perhaps are you trying to quantify the difference between the two? If annually, are fees in this example deducted based on average daily balance, or ending balance?
I think you are also confusing yourself regarding economic vs. accounting cost. Look at how much money is left in the fund after fees under different scenarios versus how much the manager collected in fees.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.