High‐water mark fee structure in variable annuities

• Published date: 01 December 2021
• Author: David Landriault,Bin Li,Dongchen Li,Yumin Wang
• Date: 01 December 2021
• DOI: http://doi.org/10.1111/jori.12345

J Risk Insur. 2021;88:1057–1094. wileyonlinelibrary.com/journal/JORI

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1057

Received: 12 May 2020

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Revised: 3 May 2021

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Accepted: 5 May 2021

DOI: 10.1111/jori.12345

ORIGINAL ARTICLE

High‐water mark fee structure in variable

annuities

David Landriault

1

|Bin Li

1

|Dongchen Li

2

|Yumin Wang

1

1

Department of Statistics and Actuarial

Science, University of Waterloo,

Waterloo, Ontario, Canada

2

Department of Mathematics, University

of St. Thomas, St. Paul,

Minneapolis, USA

Correspondence

Yumin Wang, Department of Statistics

and Actuarial Science, University of

Waterloo, Waterloo, Ontario, Canada.

Email: y2478wan@uwaterloo.ca

Abstract

This paper proposes a novel high‐water mark fee

structure and investigates its impact on the market-

ability of variable annuities. To evaluate the welfare

effects of holding a variable annuity, we adopt mean‐

variance analysis. By also examining the welfare effects

of holding two alternative investments, we introduce a

quantitative measure, namely a compatible set of risk

aversions, to assess the marketability of the variable

annuity under a certain fee structure. Comparing the

compatible sets and the welfare effects of holding the

variable annuity under the high‐water mark fee

structure with those under a constant and a state‐

dependent fee structure, we find that the high‐water

mark fee structure improves the variable annuity's

marketability in two aspects: First, it makes the vari-

able annuity preferable to the alternative investments

for a broader range of policyholders. Second, when the

variable annuity is preferred over the alternative in-

vestments, it produces the highest welfare for the

policyholder.

KEYWORDS

compatible set of risk aversions, high‐water mark fee structure,

marketability, policyholder welfare, variable annuity

© 2021 American Risk and Insurance Association

1|INTRODUCTION

Variable annuities (VAs) are equity‐linked insurance products issued by insurance companies.

Their flexible investment options, favorable tax‐deferral treatment, and stable long‐term

guarantees have made them one of the most prevalent investment/savings vehicles over the last

two decades. In a typical VA contract, a policyholder (PH) pays a lump sum initial premium to

an insurer who invests the sum into a basket of preassigned mutual funds (often referred to as

the policy fund) by setting up an investment account to track the performance of the policy

fund. Payouts under the VA contract are often subject to some minimum guarantees which

kick in when the performance of the policy fund is poor. To fund these guarantees, the insurer

periodically depletes the investment account by charging insurance fees. The PH is also given

the option to surrender the VA contract before maturity, subject to some predetermined sur-

render penalty. In light of the above, a standard VA contract with minimum guaranteed

payouts offers the PH protection against bearish market conditions while allowing the PH to

gain (financially) from bullish market movements.

Nevertheless, even with the seemingly great advantages to PHs, the VA market has ex-

perienced dwindling sales over the past half decade (see Bernard & Moenig, 2019). Many

reasons have been evoked to explain this trend, most notably unfavorable fee structures as-

sociated with VA products. Therefore, the sluggish market highlights the importance of fee

structure design for VAs.

The most prevalent fee structure for VAs is the so‐called constant fee structure which termly

levies a fixed percentage of the investment account as insurance fees. This time‐invariant and state‐

invariant fee structure suffers from a number of drawbacks, which served as the main catalyst for a

number of researchers to look into alternative (and possibly more favorable) fee structures in VAs.

For instance, to deal with the high insurance fees, Bernard and Moenig (2019)proposeatime‐

dependent fee structure where the insurance fee decreases after a certain time threshold. This fee

structure is shown to reduce insurance fees while keeping the VA contract profitable to insurers. To

manage the volatility risk, Cui et al. (2017) consider a volatility index (VIX)‐linked fee structure in a

Heston‐type stochastic volatility setting. It is demonstrated that, compared to the constant fee

structure, the VIX‐linked fee structure lowers the sensitivity of insurers' liabilities to market volatility.

To contain the surrender risk, Bernard et al. (2014) introduce a state‐dependent fee structure that

charges a constant fee only when the value of the investment account is below a certain threshold.

MacKay et al. (2017) later show that, in a complete market, the state‐dependent fee structure can

render surrender behavior fully suboptimal by imposing a certain marketable surrender penalty.

Moreover, Moenig and Zhu (2018) find that the state‐dependent fee structure offers the best potential

remedy for lapse‐and‐reentry in VAs.

Although each aforementioned paper focuses on improving one aspect of the constant fee

structure's deficiencies (e.g., reducing high insurance fees, lowering the volatility risk, or dis-

couraging PH surrender behavior, etc.), little is known about the impact that the corresponding

newly proposed fee structures may have on PH welfare. Examining the impact of fee design on

the welfare effects of holding a VA helps determine whether fee design can improve VA

marketability in comparison to alternative investments, and possibly address the issue of

dwindling sales in the VA market. However, by merely focusing on risk management im-

plications of the proposed fee structures from the insurer's perspective, the analysis fails to fully

address the issue of declining demand.

In light of the above, the goal of this paper is twofold. First, we propose a VA with a novel high‐

water‐mark fee structure and evaluate the welfare effects of holding the VA. This high‐water mark

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(HWM) fee structure

1

is assumed to have a blend of features, from a state‐dependent constant fee to a

pure HWM fee. More specifically, in addition to a constant fee charged when the investment account

isbelowacertainthreshold,theHWMfeestructureisdesignedtoalsoapplyanHWMfeeonthe

increase in the record highs of the investment account above the threshold. This fee structure can be

considered as a generalization of both the constant and the state‐dependent fee structures, and it will

be shown to reduce the uncertainty of the VA payout.

Second, we introduce a quantitative measure, namely a compatible set of risk aversions,

to assess the marketability of a VA under a certain fee structure. For the fee structure, the

compatible set is defined as a collection of risk aversions where, for any level of risk

aversion within this set, the PH's welfare of holding the VA is higher than that of holding

either of two alternative investments, namely a risk‐free bond and a pure fund. The com-

patible set offers a benchmark to compare the impact of different fee structures on VA

marketability. By definition, a wider compatible set indicates better marketability of the

corresponding fee structure as it makes the VA preferable to the alternative investment

options for a broader range of PHs. We also conduct sensitivity analysis on compatible sets

under various parameter settings to investigate VA marketability under different fee

structures in various market conditions.

By comparing the compatible sets and the welfare effects of holding the VA under the

HWM fee structure with those under the constant and the state‐dependent fee structures, we

find that the HWM fee structure improves VA marketability in the following two aspects. First,

the HWM fee structure generates the widest compatible set under various parameter settings.

Second, when the VA is preferred over the alternative investment options, the HWM fee

structure produces the highest welfare for the PH.

As for the analysis, we first adopt the risk‐neutral pricing approach to determine the fair

insurance fees

2

for the VA with the HWM fee structure. This is the conventional approach to

price VAs in the literature; see for example, Milevsky and Salisbury (2001), Milevsky and

Salisbury (2006), Bauer et al. (2008), Dai et al. (2008), Huang and Kwok (2016), and references

therein. Within the risk‐neutral pricing framework, the insurer assumes that the PH aims to

maximize the expected present value (EPV) of the VA's future cash payouts.Corresponding to

insurers' worst‐case liabilities, this assumption has important risk management implications

as it renders that insurers can, at least in theory, hedge every possible cash outflow with

no risk.

Next, from the PH's perspective, we examine the welfare effects of holding the VA con-

tract under the HWM fee structure. We carry a comparative analysis by also considering PH

welfare under the constant and the state‐dependent fee structures. In a complete and fric-

tionless market, it is opportune for PHs to maximize the EPV of the VA's future payouts (see

Bauer et al., 2017 for more details). However, for PHs, the life insurance market is neither

complete nor frictionless, and they might deviate from maximizing future payouts. Therefore,

we evaluate PH welfare by a mean‐variance (MV) preference model in a potentially in-

complete market. More specifically, the PH is assumed to maximize their welfare quantified

by an MV objective function.

1

The HWM fee structure is frequently applied in the hedge fund industry where a Two‐and‐Twenty fee scheme (2% constant fee for asset under management

and 20% HWM fee for newly created HWM) is widely accepted. The impact of the HWM fee on investors and fund managers in the hedge fund has been well

documented; see for example, Guasoni and Obłój (2016) and references therein.

2

The fair fee is also called the break‐even fee. It is the fee that equates the expected present value of PHs' future cash payouts to their initial premiums.

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