The Influence of Demographic and Economic Factors on the Widow’s Reverse Annuity Benefits in Coronavirus Pandemic

A reverse annuity is a type of equity release contract. It is a sales model aimed at older people. The contract is based on the transfer of property to a company that is interested in acquiring it, in exchange for a lifelong monthly benefit. ⁽¹¹⁾, ⁽¹²⁾ The transferral of property to the company takes place after signing the contract, but the senior person can live there until their death. This right is guaranteed in section four of the Mortgage Register.

The yearly benefit of the reverse annuity contract for a person aged x, who pays a financial sum at the beginning of each year, as long as they are alive, is calculated as follows, ⁽¹³⁾ (1) b¨x=α⋅Wa¨x, {{\ddot b}_x} = {{\alpha \cdot W} \over {{{\ddot a}_x}}}, where W is the real value of the property, αis the percentage of W, α∈(0%,100%] and ä_x – represents the actuarial value of individual whole life annuity for a person at age x.

The actuarial value ä_x is calculated as follows, ⁽¹⁴⁾ (2) a¨x=∑k=0∞vk⋅kpx, {{\ddot a}_x}\sum\limits_{k = 0}^\infty {{v^k} \cdot {\;_k}{p_x}} , where v denotes the discounting factor and _kp_x is the probability that a person of age x will live at least k years.

The discounting factor v is determined by using the following formula, (4) v=11+i, v = {1 \over {1 + i}}, where i is the interest rate.

As can be seen from the above, the reverse annuity benefits depend on the value of property W, interest rate i, and the expected lifetime of a person of age x.

Increase in the proportion of seniors observed in recent decades is a consequence of several demographic processes, the most important of which are the lengthening of human life expectancy and the simultaneous decline in fertility (drop in birth rates) below the level ensuring the continuation of generations. The elderly population, due to its constant growth, is characterised by an increasing internal diversity (e.g., in terms of age, gender, education, place of residence, health status), which will further intensify in the face of the so-called double ageing (i.e., a very dynamic increase in the proportion of people aged 80 and over in the population). In particular, a pronounced feminisation and singularisation of ageing can be observed.

An important measure taken into account when estimating actuarial values is life expectancy at birth. In Poland, since the 1960s, a systematic extension of the average life expectancy has been observed, both in the populations of men and women. Many factors influence this phenomenon, including improvement in nutrition, development of medicine, increased detection and treatment of diseases, advancement of the quality and access to medical services, and social changes related to improved living conditions and hygiene. The decrease in the value of life expectancy in 2020–2022 was the result of the pandemic from the SARS-CoV-2 virus, causing COVID-19. Life expectancy values in the years 1960–2022 in male and female population are presented in Figure 1.

Figure 1:

Life expectancy at birth in Poland in female and male populations (1960–2022)

Source: authors’ elaboration based on GUS data

Increase in average life expectancy causes a growing population of elderly people, with a particularly dynamic growth in the group aged 80 and over. Additionally, the phenomenon of feminisation and singularisation of ageing can be observed among seniors.

The feminisation of ageing is due to a higher population of women than men, which increases with age and is especially observable in older age groups. In Poland, in the entire population, the percentage of widows is almost five times higher (13.7%) compared to the percentage of widowers (2.9%), and increased male mortality rates occur in the group of people over 50 years of age. ⁽¹⁵⁾ The feminisation rate varies not only according to age but also to place of residence. It increases with age and is higher in cities, except for the group of people aged 85 and over. The coefficient values for 2021 are presented in Figure 2.

Figure 2:

Feminisation rate in Poland in 2021

Source: authors’ elaboration based on GUS data

However, the singularisation of ageing is characterized by a high percentage of older people living in single-person households. According to forecasts, in 2030, just over half (53.3%) of households in Poland will be run by people over 65 years of age, including 17.3% by people aged 80 and over, and due to the feminisation of old age, women are much more likely to stay in single-person households. ⁽¹⁶⁾ The increase in the percentage of older people in society has not only economic but also health and social consequences.

The Covid pandemic has deepened the phenomena of feminisation and secularisation. Figure 3 shows death rate (i.e., the number of deaths per 1,000 people) in the population of seniors aged 60 and over in 2010–2021, taking into account the division of the population by gender.

Figure 3:

The death rate in Poland of senior populations (above 65 years old)

Source: authors’ elaboration based on GUS data

The analysis of the mortality structure shows that the high mortality of the male population, especially in older age groups in Poland, has increased.

The impact of the pandemic on mortality in the population can be seen while analysing the cause of deaths. In Figure 4, the structure of deaths in the Polish population in 2019–2021 is presented. The data allow a conclusion that the COVID mortality rate reached its highest value in 2021, causing almost one fifth of deaths. The pandemic has increased the so-called health debt, thus revealing weaknesses related to the accessibility of the health care system, and negligence in the prevention and treatment of serious and chronic diseases.

Figure 4:

The causes of death of populations in Poland (in percentages)

Source: authors’ elaboration on the basis of GUS data

Figure 5 shows the values of the COVID mortality rate measured by the number of deaths due to COVID per 100,000 inhabitants by age groups and gender. It can be seen that this rate increased with age and was at least one and a half or twice as high in the male population in almost all age groups. The disproportion in COVID mortality in the populations of men and women is caused by the so-called health inequalities in the male population. Men are generally in worse health, for a variety of reasons, from negligence in prevention to the burden of numerous, untreated chronic diseases.

Figure 5:

Covid mortality rate in the elderly population in 2020

Source: authors’ elaboration based on GUS data

It is necessary to point out that extending the life of the population does, however, have economic and social consequences, as well as a certain impact on the average health status of the population. Researchers note that living longer is not the same as living in good health (i.e., without disability and chronic diseases). Increasing rates of human diseases and accompanying disabilities, common in ageing societies, prompt the opening question of whether living longer means living with a disability. ⁽¹⁷⁾ A population with a relatively high life expectancy is not necessarily healthier. ⁽¹⁸⁾ From a societal point of view, a long life is a desirable value, but only if it is accompanied by health, and therefore also by a good quality of life and the absence of limitations in the performance of daily activities.

The Healthy Life Years (HLY) indicator (also known as Disability Free Life Expectancy (DFLE)) is nowadays one of the primary indicators used to assess the health status of a population.

In Poland, the HLY rate is lower in the female population than in the male population. This means that women live longer, but the consequence is that they are more likely to experience chronic diseases that worsen their health. An indicator defined as the percentage of life duration in good health [%HLY] illustrates this well. This indicator is defined as the percentage of life expectancy that a person of age x will live in good health and is calculated as the healthy life expectancy divided by the average life expectancy for a population. In Figure 6, the values of the indicator in female and male populations are shown. It is clear that, regardless of age, men live longer in better health and further implies that women experience more disabilities and chronic diseases, which often require expensive treatment.

Figure 6:

Percentage of life duration in good health [%HLY]

Source: authors’ elaboration based on GUS data

The interest rate plays an important role in determining benefits. During the coronavirus pandemic, governments responded very quickly and comprehensively to economic policy by reducing interest rates. ⁽¹⁹⁾ As a result of the Covid-19 pandemic, interest rates practically declined to zero, before rising rapidly in July 2022. This paper considers the 3m WIBOR rate and the long-term interest rate, determined by the European Central Bank (ECB). Monthly data from January 2020 to July 2022 are considered.

The WIBOR is the interest rate on which mortgages are offered in Poland. It is determined based on the reference rate of the National Bank of Poland. The one-month, three-month and six-month WIBOR (1m WIBOR, 3m WIBOR, and 6m WIBOR, respectively) are distinguished. This article takes into consideration the 3m WIBOR. In 2018, the 3m WIBOR was equal to 1.72%. During the pandemic, the interest rate decreased to 0.22%, and it has increased to 7% since September 2021. The 3m WIBOR still remains at a similar level. It can be observed in Figure 7.

Figure 7:

Reference interest rate and the 3m WIBOR in Poland

Source: authors’ elaboration based on data received from https://uokik.gov.pl/stopa_referencyjna_i_archiwum.php and https://stooq.pl/q/d/?s=plopln3m

According to the EU Solvency II Directive, the actuarial values should be determined based on the European Central Bank’s long-term interest rate, ⁽²⁰⁾ which is designated by using the Svensson model of spot interest. This model has the following form, ⁽²¹⁾, ⁽²²⁾ R0,k=β0+β1τ1k1−e−kτ1+β2τ1k1−e−kτ1−e−kτ1+β3τ2k1−e−kτ2−e−kτ2 {R_{0,k}} = {\beta _0} + {\beta _1}{{{\tau _1}} \over k}\left( {1 - {e^{ - {k \over {{\tau _1}}}}}} \right) + {\beta _2}\left( {{{{\tau _1}} \over k}\left( {1 - {e^{ - {k \over {{\tau _1}}}}}} \right) - {e^{ - {k \over {{\tau _1}}}}}} \right) + {\beta _3}\left( {{{{\tau _2}} \over k}\left( {1 - {e^{ - {k \over {{\tau _2}}}}}} \right) - {e^{ - {k \over {{\tau _2}}}}}} \right) where β₀≥0,β₀+β₁≥0,τ₁,τ₂>0.

The parameter β₀ is the long-term interest rate. This interest rate had been decreasing for a long time to almost zero. However, in 2022, there was an increase to almost 2%, which can be observed in Figure 8.

Figure 8.

Long term interest rate from ECB.

Source: author’s elaboration based on data received from https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_area_yield_curves/html/index.en.html

One of the effects of the pandemic was an increase in housing demand and, consequently, a rise in the price per square meter. This was influenced by a number of factors, as real estate and mortgage markets are a complex, interrelated set of parties that include households, developers, banks, and investors. ⁽²³⁾ Lockdown, social distancing, and quarantine caused people fearing another home lock-in to look for larger apartments and houses with gardens in different locations. ⁽²⁴⁾ Other factors were remote work and extremely cheap mortgages. ⁽²⁵⁾ Low interest rates during the pandemic can be seen in the last subsection in Figures 7 and 8. Cheap credit means an increase in consumerism along with ease of financial obligations. ⁽²⁶⁾ The pandemic also resulted in low returns on deposits, stocks, etc., which did not encourage the accumulation of savings and building of financial security. On the contrary, it urged the purchase of housing. As a consequence of these elements, the rise in the price of a square meter of real estate can be observed. Fiscal and monetary policy interventions during the pandemic contributed to the decline in affordability. ⁽²⁷⁾

A significant increase in property prices is noted, among others, in the United States, the United Kingdom, France, Germany, and Poland. ⁽²⁸⁾ Figure 9 shows average housing prices per square meter. The quarterly data is taken from Statistic Poland from the first quarter (Q1) of 2020 to Q1 of 2022 compared to Q1 of 2018.

Figure 9:

Average price per square meter of property

Source: authors’ elaboration based on data received from https://stat.gov.pl/

Real estate prices are showing an upward trend. The average price of an apartment in Poland increased by more than 27% in the first quarter of 2022 compared to the first quarter of 2018 and by 15% compared to the first quarter of 2020. Between 2020 and 2022, the average price per square meter grew largely by 1.8% every quarter. However, in many cities prices doubled or tripled, which can be seen in Figure 10. These are offer prices for 2018–2022.

Figure 10:

Price per square meter of property in some Polish cities

Source: authors’ elaboration based on offer price reports https://www.bankier.pl

In Gdansk, the price was more than 156% higher than the average price in Poland. The largest increase in the price per square meter of an apartment in the selected cities was noted in Szczecin in May 2022 compared to November 2018. It meant an increase of more than 73.4%. In other cities, the growth was between 45% and 61%.

All the described factors significantly affect the benefit of reverse annuities, particularly for widows.