Farmland-based Reverse Mortgages for Aged Farmers

Changki Kim; Seungyoung Jung; Eyunghee Kim

doi:10.1515/apjri-2013-0018

Article

Farmland-based Reverse Mortgages for Aged Farmers

Changki Kim , Seungyoung Jung and Eyunghee Kim

Published/Copyright: April 2, 2014

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From the journal Asia-Pacific Journal of Risk and Insurance Volume 8 Issue 2

Abstract

An ageing population and the resulting income shortage of the aged are pressing problems in many countries across the world. In response, the Korean government set up the Farmland Bank to issue a new reverse mortgage, called farmland-backed annuity (FBA), to liquidize farmland assets and provide living expenses to aged farmers. In this study, we construct a suitable farmland price model for FBA. We also make a few proposals on designing FBA so that it meets the various needs of aged farmers. The results of this research would help the organization in charge of FBA to not only resolve the rural ageing problems but also contribute to strengthening the agricultural economy.

Keywords: farmland-based reverse mortgage; Farmland Bank; longevity risk; annuities; ageing population

Appendix

The present value of premium is calculated as the following.

PV of Premium=Premium×(1+pxav+2 pxav2+3 pxav3…)=Premium×∑k=0k pxavk

where

v=11+i: discount rate
k pxa: probability of survival of a policyholder without accident or illness necessitating LTC from age x to x +k;

The present value of LTC benefit (annuity) is calculated as the following.

PV of LTC Annuity=Annual LTC Benefit×{qxltc×(1+pxbv+2pxbv2+3pxbv3…) + pxaqx+1ltcv×(1+px+1bv+2px+1bv2+3px+1bv3…)+…} =Annual LTC Benefit×∑k=0kpxaqx+kltcvk∑j=0kpx+kbvj

where,

qx+kltc: probability of accident or illness necessitating LTC of a policyholder within a year from age x + k;
kpxb: probability of survival of a policyholder after accident or illness necessitating LTC from age x to x + k;

It is assumed that an accident or illness necessitating LTC occurs at the beginning of the year and LTC annuity is paid out at the occurrence and at the beginning of each year to survivors thereafter.

LTC premium is determined where the PV of premium and the PV of LTC annuities equal. To calculate LTC in the Table 12, we used interest rate 4% and LTC risk rate announced by the Korea insurance development institute, the life insurance risk rate No 2005-0339.

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1
While cash-outflow of Farmland Bank is the present value of expected loss (eq. [1]), cash-inflow of Farmland Bank is the present value of risk premium paid by policyholders (eq. [4]).
2
For more details on the survey, refer to the National Statistical Office (2009b), National Pension Research Office (2005), and National Pension Service (2003).
3
According to the National Statistical Office (2009a), the average living costs are approximately 26 million KRW for farmers aged between 60 and 69, and 17 million KRW for farmers aged over 70.
4
According to the National Statistical Office (2009c), farmlands account for 70% of the fixed assets of farmers.
5
Purcal and Piggott (2008) argued that the bequest motive is the single strongest deterrent to an annuity purchase.
6
Ownership of farmland is assumed to be transferred upon the death of FBA policyholders. Thus, the farmland occupancy term of policyholders is equal to the annuity payment period. If not, a model must be established to reflect the difference between these two terms (Weinrobe 1988).
7
In the case of FBA, as the ownership of farmland is transferred to the government, the government can utilize the farmland for government business instead of liquidating the asset. Thus, we make no additional assumptions regarding costs or the required time to liquidate the farmland.
8
In the first year of the contract, annual risk premium (ARP0) as well as initial risk premium (UP0) are paid at the beginning of the year (at t=0).
9
HECM in the United States, which allows lump-sum payment as well as periodic annuity payments, determines the initial principle limit (IPL) assuming lump-sum payment. If an individual chooses a payment method other than the lump sum, the present value of the total payments cannot exceed the IPL of the lump sum. Refer to Synmanoski (1994) for more details.
10
The price of real estate can be affected by interest rate, economic circumstance, and business cycle of the real estate industry. However, like the previous researches relevant to our study, we used the univariate farmland price model for convenience and due to the insufficient data.
11
The appraised value is often used to compute the price of real estate. Refer to Li et al. (2010) for the pros and cons of using the appraised value compared to the market price.
12
For more detail, refer to Buhlmann et al. (1996), Li et al. (2010), and Chen, Cox, and Wang (2010a).
13
Hamilton (1994) assumed an expected average value of the AR (p) model as follows: μ=ϕ01−ϕ1−⋯−ϕp, where ,yt=ϕ0+ϕ1yt−1+⋯+ϕpyt−p
14
As observed in Table 2, withdrawal and cancellation ratio of FBA is high, but currently the Farmland Bank does not reflect contract expiration other than death in annuity pricing. Hence, we do not consider contract expiration due to withdrawal and cancellation, neither.
15
For convenience of analysis, we assumed that the realized mortality rate is equal to the risk-neutral rate.
16
Currently, the farmland price return assumption of the Farmland Bank is determined as follows:The assumption of farmland price return of Farmland Bank=1n∑t=1nXtXt−1, where Xt=farmland price index at t.
The annuity amount calculated under the assumption of the Farmland Bank is 12~18% bigger than the values in Table 8.
17
In fact, Farmland Bank tries to increase sales of life annuity. The bank plans to reduce sales of term annuities gradually by placing age limits on term annuities (i.e. restricting farmers aged below 75 from signing term annuity) and considers applying different pricing assumptions or different sales margins to term annuity and life annuity.
18
Since the purpose of deferred life FBA is to increase the amount of life annuity benefit, deferred life FBA provides only life annuity (not term annuity).
19
A survey of Korean Life Insurance Association (2006) provides additional details on the current conditions of farmers joining health insurance.
20
For more concrete examples of the illnesses and accidents that farmers are frequently exposed to, see Kim (1993) and Jung, M. (1989) and Bak (1995) and Jung, C. (1989), who studied agricultural accidents caused by agricultural machineries.
21
According to Davidoff (2009), annuities may be attractive only in the presence of LTC, and annuities make LTC coverage more beneficial. Hence, it would be a good idea to combine LTC and annuities.

Published Online: 2014-4-2

Published in Print: 2014-7-1

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Articles in the same Issue

https://doi.org/10.1515/apjri-2013-0018

Keywords for this article

farmland-based reverse mortgage; Farmland Bank; longevity risk; annuities; ageing population