LMT Calibration for Open Ended AIFs - Example of methodology

One of the current hot topics in the management of Alternative Investment Funds (“AIF”) is the rising popularity of real assets and private equity for retail investors. Historically, these investors did not have access to these asset classes, and with a keen interest from the fund managers to expand their fundraising abilities, a “democratization” effort has been underway for the last few years.

This rise of interest and the road ahead was discussed extensively during this year’s Cross-Border Distribution Conference [1], and has definitely led to new challenges for risk managers, especially in the area of liquidity risk.

With a more varied investor base unlocked by this “democratization” comes different liquidity expectations, which may be seen to be at odds with alternative asset classes. For example, real assets such as real estate properties or infrastructure projects (wind farms, airports, railways, power plants and others) require an amount of capital to be locked in the investment for a considerable amount of time spanning from several years to decades. On the other side of the balance sheet however, investors will be expecting to be able to redeem their shares on a regular basis.

As a result, a fund manager aiming to provide access to alternative asset classes will generally opt for a fund-of-fund structure, providing liquidity to its investors via distributions made by the underlying funds and/or liquid investment pockets, with liabilities that can be controlled thanks to adequate liquidity management tools.

Liquidity management tools (“LMT”)

The last few months have been accompanied with a lot of discussions about liquidity management tools, as both the revised UCITS Directive and AIFMD (2024/927) introduce more details on their availability and use, following guidance from standard setting bodies such as FSB [1] and IOSCO [2].

In its latest consultation paper on the topic [3], ESMA divides the liquidity management tools available to UCITS and open-ended AIF managers into three distinct categories:

• Anti-Dilution Tools (“ADT”), which are tools which aim to adjust the price at which investors redeem shares (resp. subscribe to shares), in order to avoid passing the cost of asset sales (resp. purchases) to the remaining (resp. existing) investors;
• Quantitative LMTs, which are non-ADT liquidity management tools that are quantitative in nature; and
• Other LMTs, which include the available LMTs that do not fall in the other two categories.

While Anti-Dilution Tools (“ADT”) are generally more suitable for open-ended funds invested in more traditional asset classes, the quantitative LMTs available to AIFMs, such as redemption gates and extension of notice periods, can be calibrated on the basis of the projected liquidity profile of the fund.

Management companies and AIFMs need to set adequate processes for the selection of these liquidity management tools, their calibration, as well as their activation. This calibration process has to account for the projected liquidity profile of the fund, and need to prove adequate in avoiding future liquidity mismatches (in a way not dissimilar to the Liquidity Stress Testing exercise).

For example, in the context of the calibration of redemption gates, ESMA lists:

Managers should calibrate the activation threshold in order to ensure that it operates effectively and in the best interest of investors at all times. In calibrating such threshold, managers should give due consideration to the NAV calculation frequency, the investment objective of the fund and the liquidity of the underlying assets and should ensure that investors are able to redeem their units or shares under normal market conditions.

The use of redemption gates should not be restricted in terms of the maximum period over which they can be used (maximum duration of redemption gates), or the maximum number of times that redemption gates can be activated (maximum use of redemption gates), as long as it remains temporary in nature. These matters should be determined by the manager on a case-by-case basis.

Modelling projected liquidity

The calibration of liquidity management tools involves making informed projections on the liquidity availability in order to determine how much liquidity can be offered by the fund manager to the fund’s investors. In addition, the same elements used for informing these productions will be used for determining the appropriate methodologies necessary for the liquidity stress-testing for the fund.

A simple model for building these liquidity projections is the one proposed by Takahashi and Alexander (2001) (hereafter referred to as the Takahashi-Alexander or TA model), which is based on historical data, and can be summed up as:

• Contributions are heavily concentrated over the first few years of the fund’s life, then decline geometrically;
• Distributions vary over the fund’s life, start at 0, grow and reach a maximum around the fund’s half-life, and then decline steadily to 0 at the fund’s maturity; and
• The Net Asset Value of a fund grows at a constant growth rate over time (after removing contributions and distributions).

We cover each element of the model in the sub-sections below.

Contributions

Contributions over time C(t) are defined via a Rate of contribution applied on the undrawn commitments, i.e. CC-PIC(t), where CC represents the total committed capital and PIC(t) represents the total paid-in capital at time , i.e.

The risk manager’s input into this part of the model is to determine the appropriate rates of contribution for each year of the life of the target fund. The model usually assumes different rates of contributions on the first two years, in order to account for the usually larger contributions required at the beginning of a fund’s life.

An assumption could be that, in the first year, 25% of the total commitment will be called, and another 25% in the second year, while any subsequent year would see a 50% rate of contribution. This translates into:

For a total commitment of EUR 1M, the contribution profile would look like the following:

Technically, the model user is not constrained by this shape of the contribution term structure, although it is the one generally observed on historical data.

Distributions

Distributions are determined via a constant Rate of distribution , determined through three model parameters, i.e.

where Y represents the minimum distribution level (the yield), L represents the maturity of the target fund (i.e. the expected time to exit at inception, in years), and B represents the Bow parameter, which represents the rate at which the distributions are expected to increase as the fund approaches maturity.

We display below the impact of the Bow parameter on the distribution rate over time below (using a 20-year maturity to make differences more obvious):

The calibration of this Bow parameter remains a complex task, and is generally quite assumption-driven. For usage in liquidity stress-testing, the parameter can be updated on a yearly basis based on the actual distributions made by the fund.

Based on that rate of distribution, the actual distribution on any given year can be derived as:

where NAV(t)  is the Net Asset Value of the fund at time t and G is the Projected growth rate for the NAV of the fund.

Finally, the evolution of NAV can be defined in terms of this growth rate and accounting for contributions and distributions as:

Example of a single fund

To illustrate the model and its use, let us consider a single infrastructure fund with the following characteristics:

We plot the results of the model below:

As displayed in Figure 4, the expected yearly liquidity generation for the sample fund becomes sufficient to fund the expected capital contributions after four years of life, thus indicating that a lock-up period of at least four years should be consider in order to ensure that investor redemptions could be honored via the distributions generated by the fund’s investments.

In addition, the level of projected distributions will inform the level of gating applied to the fund once the lock-up period has elapsed.

Example for an open-ended fund of funds

A similar approach can be employed for a portfolio of alternative funds with different expected capital call and distribution schedules. Let us consider the following prospective mixed portfolio:

Based on an analysis of the current investment environment and peer funds, the following assumptions are made:

Applying the model to these funds yields the following contribution/distribution schedules:

The final projected liquidity profile can then be obtained for the fund by comparing the values for contributions and distributions, i.e.

Conclusion

The Takahashi-Alexander model remains a simple approach that has its drawbacks in its current form. For use in risk management, extensions to the model are generally considered, such as the addition of a calibrated uncertainty on the Bow parameter as well as on the Rate of contribution. Similarly, a liquidity stress-testing exercise would also include adverse performance scenarios (i.e. on the assumed growth rates) in order to consider the impact on projected liquidity ability.

These topics and other pragmatic approaches to liquidity modelling will be explored during our upcoming Deloitte Quantitative Masterclass, which will take place on November 28th. For more information and registration, please consult our dedicated website, or contact Sylvain Crepin , Martin Reinhard or myself for more information.

[1] Revised Policy Recommendations to Address Structural Vulnerabilities from Liquidity Mismatch in Open-Ended Funds

[2] Anti-dilution Liquidity Management Tools – Guidance for Effective Implementation of the Recommendations for Liquidity Risk Management for Collective Investment Schemes

[3] Consultation Paper - Guidelines on Liquidity Management Tools of UCITS and open-ended AIFs

[1] https://en.paperjam.lu/article/asset-allocation-panel-alterna