A Hybrid Equity Release Plan for Retirement Financing

Koon-Shing Kwong; Yiu-Kuen Tse; Junxing Chay

doi:10.1515/apjri-2019-0028

Article

A Hybrid Equity Release Plan for Retirement Financing

Koon-Shing Kwong , Yiu-Kuen Tse and Junxing Chay

Published/Copyright: August 31, 2020

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From the journal Asia-Pacific Journal of Risk and Insurance Volume 15 Issue 1

Abstract

There are two main equity release plans for retirement financing: reverse mortgage plan and home reversion plan. Both plans entitle the homeowners not only to release cash from their properties but also to allow them living there for life. In the lease buyback scheme (LBS) recently introduced in Singapore, the home owner sells the tail-end of the property lease to the government in exchange for a cash payment upfront. Unlike the two main equity release plans, the LBS only allows the owner to stay in the property for the front part of the lease but not for life.

In this paper, we propose a hybrid home equity release plan that incorporates features of the home reversion plan and the LBS. We provide an actuarial framework to analyze the pricing of the hybrid plan, as well as the LBS and home reversion plan. Some numerical illustrations are presented to show the actuarial values of the plan under different choices of plan parameters, such as the lease period and the portion of property value sold. The hybrid plan provides enhanced flexibility to plan takers to meet their retirement needs.

Keywords: reverse mortgage; lease buyback scheme; equivalence principle; mortality risk

Corresponding author: Koon-Shing Kwong, School of Economics, Singapore Management University, Singapore, E-mail: kskwong@smu.edu.sg

Funding source: Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1

Award Identifier / Grant number: C244/MSS17E007

Funding source: Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 3

Award Identifier / Grant number: MOE2013-T3-1-017

Funding source: Housing and Development Board Singapore

Acknowledgments

The authors would like to thank the three anonymous referees for valuable comments and suggestions to improve an earlier version of this paper.Kwong’s research was supported by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant (17-C244-SMU-002). Tse’s research was supported by the Singapore MOE AcRF Tier 3 Official Grant Number MOE2013-T3-1-009.

Appendix

We take expectation of the square of the future loss random variable, Y2, to obtain

E(Y2)=∑k=nω−x−1∑j=011v2n(1−vk−n+(j+1)/12d(12))2× npx× k−n+j/12|112qx+n=∑k=nω−x−1∑j=011v2n(1−2vk−n+(j+1)/12+v2[k−n+(j+1)/12][d(12)]2)× npx× k−n+j/12|112qx+n=2v2n npxd(12)∑k=0ω−n−x−1∑j=011(2(1−vk+(j+1)/12)−(1−v2[k+(j+1)/12])2d(12))× k+j/12|112qx+n=2v2n npxd(12)[a¨x+n(12)−(1−d(12)24)∑k=0ω−n−x−1∑j=011((1−v2[k+(j+1)/12])2d(12)×(1−d(12)/24))× k+j/12|112qx+n]=2v2n npxd(12)[a¨x+n(12)−(1−d(12)24)× 2a¨x+n(12)]

With the result of E(Y) given in Section 4.1, we evaluate the standard deviation of Y, σY and then calculate the standard deviation of L as σL=12Rαϕ×σY, based on Equation (4).

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Received: 2019-09-25

Accepted: 2020-05-26

Published Online: 2020-08-31

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Articles in the same Issue

https://doi.org/10.1515/apjri-2019-0028

Keywords for this article

reverse mortgage; lease buyback scheme; equivalence principle; mortality risk