Measuring Longevity Risk: An Application to the Royal Canadian Mounted Police Pension Plan

• Published date: 01 March 2014
• Date: 01 March 2014
• Author: M. Martin Boyer,Lars Stentoft,Joanna Mejza
• DOI: http://doi.org/10.1111/rmir.12018

Risk Management and Insurance Review

C

Risk Management and Insurance Review, 2014, Vol.17, No. 1, 37-59

DOI: 10.1111/rmir.12018

FEATURE ARTICLES

MEASURING LONGEVITY RISK:ANAPPLICATION TO THE

ROYAL CANADIAN MOUNTED POLICE PENSION PLAN

M. Martin Boyer

Joanna Mejza

Lars Stentoft

ABSTRACT

An employer that sets up a defined benefit pension plan promises to periodically

pay a certain sum to each participant starting at some future date and continu-

ing until death. Although both the future beneficiary and the employer can be

asked to finance the plan throughout the beneficiary’s career, any shortcoming

of funds in the future is often the employer’s responsibility.It is therefore essen-

tial for the employer to be able to predict with a high degree of confidence the

total amount that will be required to cover its future pension obligations. Ap-

plying mortality forecasting models to the case of the Royal Canadian Mounted

Police pension plan, we illustrate the importance of mortality forecasting to

value a pension fund’s actuarial liabilities. As future survival rates are uncer-

tain, pensioners may live longer than expected. We find that such longevity risk

represents approximately 2.8 percent of the total liability ascribable to retired

pensioners (as measured by the relative value at risk at the 95th percentile)

and 2.5 percent of the total liabilities ascribable to current regular contributors.

Longevity risk compounds the model risk associated with not knowing what is

the true mortality model, and we estimate that model risk represents approx-

imately 3.2 percent of total liabilities. The compounded longevity risk therefore

represents almost 6 percent of the pension plan’s total liabilities.

INTRODUCTION

Although we would all like for our life to last as long and be as healthy as possible, we

would also like to maintain a level of consumption that satisfies us. Consequently, we

would prefer not to run out of cash once we are old and gray. Lacking financial resources

is, however, one of the pernicious effectsstemming from longevity risk, which we define

as the risk that a population lives longer than anticipated. Obviously, longevity risk

M. Martin Boyer is the CEFA Professor of Finance and Insurance, and CIRANO Fellow at

HEC Montr´

eal; e-mail: martin.boyer@hec.ca. Joanna Mejza was a graduate student in Financial

Engineering at HEC Montr´

eal. Lars Stentoft is an Associate Professor of Finance and member

of CIRP´

EE at HEC Montr´

eal, and Visiting Professor of Finance and member of CREATES at

the Copenhagen Business School. This research is financially supported by CIRANO and by the

Social Science and Humanities Research Council of Canada. This article was subject to double-

blind peer review.

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38 RISK MANAGEMENT AND INSURANCE REVIEW

greatly affects the profitability of institutions that offer lifetime pensions, but longevity

risk also consistently affects all levels of society, from individuals to organizations and

governments.

One element that highlights the importance of longevity risk is the systematic histor-

ical underestimation of the survival rates at older ages (see, e.g., Oeppen and Vaupel,

2002; Turner, 2006). For example, Turner(2006) reports that in the past 100 years, life ex-

pectancy has systematically been underestimated by about 18 months for each decade.

Clearly, the decrease in the mortality rate has important consequences on the viabil-

ity of pension funds since underestimating life expectancy after retirement will lead

to insufficient accumulations before retirement. The importance of longevity risk and

some organizations’ exposure to it has recently been recognized by the international

accounting standards board, which has begun to tackle the problem of how to disclose

longevity risk in financial statements of publicly traded corporations (see Fujisawa and

Li, 2010). Another important particularity of aggregate longevity risk is its systematic

and undiversifiable nature (see Milevsky et al., 2006).

In this article, we consider one Canadian defined benefit pension plan and stress the

impact of adequate mortality forecasting on actuarial liabilities.1Any shortcoming of

funds in an employer-sponsored pension plan is often the employer’s responsibility. It

is thus essential for the employer to be able to predict with a high degree of confidence

the total amount that will be required to cover its obligations to the future retirees. To

do so, several assumptions must be made, such as the rate of return on the assets before

they are liquidated, the amount of the periodic payments, and the number of years

employees are expected to live after retirement. All these factors have sizable impacts

on the actual cost of the pension plan and on its solvency ratio.

To be specific, we implement the two-factor stochastic mortality model of Cairns et al.

(2006) (the CBD model hereafter) using the Canadian mortality tables, and measure

the longevity risk associated with issuing immediate and/or deferred annuities for the

pension plan of the Royal Canadian Mounted Police (RCMP, 2008). The present value of

the expected future benefits (i.e., the plan’s actuarial liability) is also calculated using the

projected mortality rates as forecasted by the Office of the Chief Actuary (OCA hereafter)

of Canada and these are compared to the results obtained with the CBD model. Given

the CBD results, we then run Monte Carlo simulations to obtain the plan’s value at risk

(VaR) to emphasize the uncertainty about the future. Our approach allows us to show

that the longevity VaR varies depending on the age group of the participants as well as

on the type of the annuity (immediate vs. deferred), and we estimate that to compensate

for longevity risk alone, pension funds should increase their reserves by 6–9 percent,

depending on the pension plan’s maturity, composition of beneficiaries, structure and

level of certainty needed.

The next section presents the key features of the CBD mortality model and gives a broad

outlook of Canadian mortality trends. In the section titled “An Application to the RCMP

Pension Plan,” we apply the CBD model to the RCMP pension plan. It reveals how the

1See Ambachtsheer (2008) for an analysis of the general issues surrounding the pension debate

in Canada and Antolin (2007) for the case in the Organisation for Economic Co-operation and

Development (OECD).