Fee Management
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For managing assets throughout the investment horizon, management fees are charged per second proportionally to the ownership in the AUM. For brevity, the fee rate is always shown as an effective annual rate. Note that the management fee is always charged regardless of the fund’s performance.
Charging management fees can be straightforward in traditional finance since the NAV for individual investors can be tracked easily. However, technical challenges such as, fund tokens being fungible and transferable, digital assets being volatile and illiquid, and different investors having uneven investment horizons break down the normal fee calculation procedure. We thus use a price dilution model to track the NAV and calculate the fees accurately.
Performance fees are generally charged once per year based on a high-water mark model i.e. per the highest return that exceeds a base threshold.
Charging performance fees can be straightforward in traditional finance since the entry and exit amounts and dates for individual investors can be tracked easily. Technical challenges, in addition to those present in the management fee calculation, render it impossible to even accurately track the fees. We use an approximation method with a price dilution model to track the NAV and calculate the fees.
All the fees are charged based on a price dilution model, meaning that additional fund tokens are created to devalue the fund token price, in the amount equivalent to charing the fees in the denomination asset. The fee tokens are stored in separate vaults for each investment fund, from which the fund manager can claim at any time. For each fund, the management fee tokens are minted and stored in a management fee vault (MFV) and performance fee tokens correspondingly in a performance fee vault (PFV).
The fee management module may operate independently of other modules. The following steps show how fee management works in general. It should be noted that the order of execution is crucial i.e. management fee calculation must precede performance fee calculation.
performance fee rate (time-independent)
Finally, update the high-water mark.
Recall that fund tokens are fungible and transferable. It is therefore impossible to accurately charge performance fees for individual investors. Consequently, when one party benefits, the others lose. Our performance fee model is designed to track the actual performance by raising the high-water mark at every subscription and redemption. This mechanism gives benefit of the doubt to any new investors, particularly those who invest deeply under the high-water mark, known as free riders. On the optimistic side, fund managers are strongly incentivized to carefully manage the funds at all times in order to strive against the nonchargeable fee.
The price without fees refers to the token price for which no fees are changed since the last fee settlement. This price, therefore, stays the highest among all the other prices. Note that this price is usually not revealed to investors in traditional fund management since the management fee is already included and deducted as an operational cost and may create confusion otherwise.
The price with management fee refers to the token price for which only the management fee is charged i.e. the performance fee, however, is not since the last fee settlement. In traditional fund management, this price is referred to as the gross asset value per token (GAV per token). As time passes by, the management fee gradually builds up, resulting in increasing spreads between this price and the price without fees. This price is used for measuring fund performance with respect to the high-water mark and thus charging the performance fee when settlement occurs.
The price with management and performance fees refers to the token price for which all the fees are charged i.e. the performance fee is additionally charged. This price, therefore, stays the lowest among all the other prices. In traditional fund management, this price is referred to as the net asset value per token (NAV per token).
As the fund outperforms i.e. the price with management fee above the high-water mark, the performance fee gradually builds up, resulting in increasing spreads between this price and the price with management fee. On the other hand, when the fund underperforms i.e. the price with management fee below the high-water mark, the performance fee cannot be charged, resulting in this price overlaying the price with management fee. Note that when settlement occurs i.e. at subscription and redemption, the other prices must instantly converge to this price.
There is a single high-water-mark parameter per investment fund. Subscribers who invest below the high-water mark will enjoy the benefit of a free ride since the performance fee cannot be charged below such a level. To avoid unnecessary confusion, the price reported to investors will have all the fees deducted. Hence, investors can smoothly track the net performance and set realistic expectations.
Thus, we have:
Thus, we have:
Assuming the time granularity in seconds, we thus have:
where:
Since the performance fee depends only on the token price and does not require continuous-time scaling, we simply have:
Although the price dilution model embraces the idea that fee tokens are fund tokens that simply belong to the fund manager and can, in fact, be treated the same way as fund tokens of any investor, one might be particularly concerned that the fees should explicitly be charged only on the AUM that belong to actual investors. An alternative derivation shows both methods are equivalent.
Consider the value of the fee changed on the investor portion and added to the vault:
With some algebraic work, we arrive at the same formula:
Then, the rest of the derivation immediately follows.
management fee rate (in effective annual rate)
token supply i.e. including those in the vaults
time (in seconds) since last fee settlement e.g. at subscription, redemption, fees collection
i.e. time (in seconds) in 1 year
Mint fund tokens in the amount of to the management fee vault. Note that \text{management_fee} already accounts in the unit of fund tokens. The derivation of the formula is shown in a separate section . Finally, update the total supply.
token supply i.e. including the newly minted management fee tokens
fund token price i.e. management-fee-diluted
current high-water mark i.e. since last fee settlement
Mint fund tokens in the amount of to the performance fee vault. Note that already accounts in the unit of fund tokens. The derivation of the formula is shown in a separate section . Now, update the total supply and price accordingly.
net asset value
The graph above illustrates how fees are charged and affect the token price over time. Let be the times at which fund operations occur; regardless of them being subscription or redemption.
Let and be effective annual rates charged in the denomination asset and in fund tokens, respectively.
When the management fee is deducted from the portfolio, the token price is given by
Then, convert the effective annual rate into the continuous rate :
Assuming years elapse since the last fee settlement, the management fee charged is:
Let and be performance fee rates charged in the denomination asset and in fund tokens, respectively. Similarly, we have:
Let be the number of investor fund tokens e.g. stored in the wallets or with custodians, the number of fee tokens already mined and stored in a fee vault, and the number of fee tokens to be minted for dilution.
