An insight into different pension schemes

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Quite simply an income paid to an individual for rest of his/her life after retirement. It can be of two types as 1) Defined Contributions 2) Defined Benefits.

1.1.1 Defined Contribution Schemes

Defined contribution schemes are much simpler and can be summarized as follows. Here the level of contributions may be defined in absolute term or percentage of salary or earning of employee. The resulting benefits will then be calculated by some actual or notional investment earnings on the contributions. An amount is paid into a scheme for each member. That amount will be determined by market forces (what other companies, competing for the same workers, are paying) and by what a company can afford. Where specific benefit targets are used within defined contribution schemes, they take on some of the characteristics of defined benefit arrangement.

1.1.2 Defined Benefit Schemes

Defined benefit is benefit payable on retirement and it is specified monthly or yearly benefits which are defined in advance on employee's earnings or salary history, tenure of service and age, rather than depending on investment returns. The definition may be based on salary or earnings immediate prior to the commencement of benefit payable which is called final salary other definition can be career average and there are other definitions too.

1.2 How to Fund Defined Benefit Schemes?

These benefits can be either Funded or Unfunded (Pay-As-You-Go), at one extreme, 'Pay-As-You-Go' (PAYG) systems do not involve any prefunding (i.e. the accumulation of funds during employees' working lifetimes) whatsoever. In an unfunded defined benefit pension, no assets are set aside and the benefits are paid for by the employer or scheme as and when they are paid. Pension arrangements provided by the state in most countries in the world are unfunded, with benefits paid directly from current workers' contributions and taxes.

At the other extreme, an immediate lump sum might be set aside, its amount being sufficient (on an appropriate set of actuarial assumptions, which will be discussed later) to meet all future pension outgo. In a funded scheme, contributions from the employer, and sometimes also from scheme members, are invested in a fund towards meeting the benefits. Typically, the contributions to be paid are regularly reviewed in a valuation of the scheme's assets and liabilities, carried out by an Actuary to ensure that the pension fund will meet future payment obligations.

Pension schemes not only provide pensions on normal retirement age (NRA) but also under other circumstances like: -

Early retirement by choice (voluntary retirement)

Early retirement because of ill health

Death in service

Withdrawal (leaving the employer or scheme)

Late retirement (retirement after NRA)

1.3 Valuation and Liability

1.3.1 Liability

The promise to pay certain defined benefit depends on future timing and durations which are not fixed or certain, but dependent on beneficiary. Also the amount of benefit is uncertain (e.g. if it depends on final salary or average salary which is unknown). There will be actuarial involvement from the time of benefit promised till they are actually paid i.e.

when benefits are to be paid (demographic assumption)

the level of benefit to be paid (financial or economic assumptions)

Our objective is to calculate amount of money we need as at present to fulfill promised benefits of past pension liability and to calculate amount of money required to contribute toward fund for the benefits to be paid in future considering certain actuarial assumptions.These actuarial assumptions are discussed later in the chapter.

1.3.2 Valuation

There are two kinds of valuation involved, first valuing liability for accounting purpose and another valuing liability for funding purpose. Valuing liability for accounting purpose, the guidelines are provided in Accounting Standard which uses long term approach (i.e. Assumptions to be used, Method of valuation, etc.). But, valuing liability for funding purpose, the guideline is not provided anywhere but uses market basis i.e. current financial assumptions. There are several assumptions and methods of valuation which actuaries can use to value pension liability for funding purpose discussed later in the chapter.

The need to calculate and make provision for these benefits in advance requires actuarial involvement, to find out the present value of future payments i.e. projecting the amount which is to be held now in order to meet the uncertain commitments in future; this is done by assuming some discounting factor and expected future cash flows.

The full present value of total benefit is not held immediately when the benefit is promised. But, the cost of benefit is recognized gradually over a service period of employee to the employer. This gradual spread can be made in different ways and which again involves actuary in choosing the method of valuation to fund such benefits.

1.3.3 Actuarial Calculations and Decrements

As discussed in section 1.2, there are several other factors which affect the actuarial valuation so we will discuss in particular the following factors which are called decrements and will try to make service table to calculate the probabilities of these decrements.

We consider an active member under DB scheme. There are four cases where this member's pension starts.

Age (i.e. normal) Retirement

Early retirement because of ill health

Death in service

Withdrawal (leaving the employer or scheme)

These cases can be explained in multiple decrement model, in form of multiple state model shown below in figure 1.1

Figure 1.1: Multiple decrement Model for pension scheme.

1.3.4 Actuarial Assumptions

The Actuarial assumptions are divided in two main parts:

Demographic assumptions

Demographic assumptions are required to project when the benefit will be payable. It considers probability factors discussed in section___. It assumes mortality and morbidity, rates of employee turnover (i.e. withdrawal), disability, early retirement due to ill health, and proportions married.

Financial / Economic assumptions

Financial assumptions are required to project amount of the benefit will be payable. It considers interest rate for discounting future cash flow, rate of salary increase, salary scale (promotional) and price inflation, rate of increase in pension payment.

Mostly all future benefit payments are discounted using specific interest rate to find present value and will be invested to attract additional income before the actual payments.

There is no necessity to use the same actuarial method and assumptions for funding and valuing liability, but there are obvious advantages. As regards to funding & valuing, the selection of method and assumptions is more difficult to answer, simply because assumptions can be used to manipulate the results. For example, a high discount rate and a weak mortality table can make a plan appear to be better funded than is really the case…and vice versa.

Demographic assumptions:

Mortality: Mortality assumptions are required both before and after retirement. Employer need to know how many people are likely to reach retirement age to access eventual pensions. Most schemes use published actuarial tables as their mortality assumptions. Generally, the assumption of lighter mortality implies that more pensions will be paid and will be paid for longer, this increases pace of funding.

Withdrawal Rates: Schemes expects to profit from members leaving service. This situation might occur where the benefit to the person who leaves were subject to price inflation while normal retirement benefits were subject to (higher) salary inflation. These withdrawal rates reflect industry experience and they are higher at younger ages and lower at older ages. The inclusion of withdrawal rates normally reduces the pace of funding.

Ill Health Retirement: Where enhanced benefits are payable on Ill Health Early Retirement, an assumption will be required to assess the amount of Ill Health Early Retirement benefit to be paid. Ill Health Early Retirement pensioners experience heavier mortality tan "normal" pensioners. Higher assumed Ill Health Early Retirement rates will normally increases pace of funding, although the impact is offset through the assumption of heavier mortality.

Proportions married: Where Spouse's benefits are provided, an assumption is normally made regarding the proportion of members who will be married at retirement, leaving, or death. Higher proportions imply faster funding but the impact of this assumption is not significant.

Financial or Economic assumptions:

Investment Return/Interest Rate: This is the level of return expected to be achieved on fund before members retire. The choice of rate will be determined by yields available from scheme's current and expected asset mix. A starting point might be to look at risk free yields available on government bonds. As the rate of investment is used to discount future benefits, a higher rate will lead to lower value being placed on future benefits, hence slower pace of funding through lower contribution rates. Sometime different yield on investment is considered for postretirement, i.e. the interest rate expected on insurance company's annuity rates when member come to retire.

Price Inflation: Benefits are often linked to price inflation (both pre and post retirement), so projected benefits will depend on level of inflation assumed for the future. Future price inflation can be obtained from the difference between yields from index - linked bonds and government bonds. The higher the rate of price inflation implies higher projected benefits, hence faster funding.

Salary Inflation: This assumption will determine projected benefits, where they are linked to final salary either on retirement or on exit from scheme or on death. The assumption is likely to be based on the used for price inflation, with an addition of 1% or 2% to reflect historical experience. Such addition will vary from industry to industry. The higher the rate of price inflation implies higher projected benefits, hence faster funding.

1.4.1 What makes a good funding method?

We are taught the need for following main four factors to be considered within any acceptable method of funding (Lee E M, 1986):





However, the relative importance of these and other issues affecting the rate at which funds are put aside to meet future liabilities varies from case to case.


It is generally accepted that an employer will look for Stability. Fluctuating cash flows are considered unacceptable. These factor covers stability of payments under assumed condition and under deviations from the assumed conditions.


Only expected present value of future income is greater than expected present value of future outgo is not sufficient condition. Any funding method must ensure there is enough money available for the fund to pay the promised benefits. This includes benefits on leaving, death or retirement (as discussed in section 2.3.1). There should not be excessive assets tied up in pension fund, if the funding method results in assets which are more than sufficient, it is unlikely to be the best use of money.


Any funding scheme is secured if sufficient fund is built up to make future liabilities payments. However, as Lee (Lee E M, 1986) says "the mere existence of fund separate from the assets of the employer obviously does not in itself guarantee pension rights. The size of the fund in relation to its liabilities is crucial." Security is measured by level of funding (i.e. ratio of value of assets to value of accrued liabilities).


Basically it is special case of stability, it is required to deal with changing structure, without becoming unstable. In extreme case, it is measured as if the scheme is closed for new entrants and by considering the effect of closure on employer contributions.

1.4.2 Funding Methods

After calculation of liabilities considering actuarial assumptions, we will look now the available methods of funding to fund required to meet future liabilities. The term "funding method" is used to refer to the way of determining the amount and timing of contributions made to meet the future liabilities. As a consequence of this spreading of cost most methods also define a "fund" that should be held at a particular point in time.

All the methods used can be considered prospective in that they are based on future liabilities and future contributions. The valuation of liabilities are always based on current employees of pension scheme but projecting the benefit payments to employees is also projected, for some methods will involve the projection of future new entrants to the pension scheme.

Whichever the method we use, the main objective is always the same, the contributions made need to be sufficient to ensure that promised benefits are paid on time.

There are different methods of funding which are either "fund based" methods where the aim is to maintain certain level of funding, which then defines the contribution required for e.g. Current Unit method and Projected Unit Method or "contribution based" methods where the aim is to define certain level of contribution, which the defines the level of funding at specific point in time for e.g. Entry Age Method, Attained Age Method and Aggregate Method.

But we will discuss the following three methods for funding:

Entry Age Method

Attained Age Method

Projected Unit Credit Method (Projected Unit Method)

Under the methods mentioned above we need to define the following:

Standard Fund

This is the amount of liabilities to be recognized (theoretical value of fund that should be held) as on valuation date.

Standard Contribution Rate

This is the amount of contribution required as derived by the method used. It assumes that "fund" held equals the standard fund. In this context the "fund" may be taken to be the value of asset held in pension fund. The contribution derived may be defined as an absolute amount or percentage of salary. Contributions are only normally payable in respect of members accruing benefit i.e. active members of pension scheme.

1.4.3 Actuarial Methods

Entry Age Method


To establish the level of contribution rate that, when payable over the active lifetime of the employees, is sufficient to meet the benefits being provided.


Standard Fund = the expected present value of total future benefits - the expected present value of future standard contribution.

Attained Age Method


To establish for active members of the pension scheme the level of future contribution rate such that, the future contributions will sufficient to provide future accruals of benefits.


Standard Fund = the expected present value of accrued benefits.

Projected Unit Credit Method (Projected Unit Method)


To maintain a fund equal to the value of accrued benefits, by taking in to consideration projected amount to date of payment.


Standard Fund = the expected present value of projected benefits on valuation date based on projected earnings.

1.5 Morality Assumption and available Mortality Tables.

Benjamin Franklin wrote, "In this world nothing can be said to be certain, except death and taxes", but while death might be a certainty, its timing is far from certain.

As with any actuarial calculation, technical provisions require assumptions to be made about the future course of all those factors affecting the cost of providing the benefits. These assumptions must be chosen prudently. Key assumptions will include inflation, investment return and how long scheme beneficiaries are expected to live (longevity). A mortality rate refers to the assumed probability of dying within a year whereas longevity usually refers to the future expected lifetime derived from any particular set of mortality rates. There have also been significant new developments in the field of mortality relevant to pension scheme funding, particularly those highlighted by the Continuous Mortality Investigation (CMI) of the actuarial profession.

We should bear in mind that mortality has the following features:

wide variability is observed between individuals;

there is variability year-on-year in the whole population;

long-term trends can be observed in age specific mortality of whole populations; and

historically, experts have usually underestimated the rate at which mortality will reduce (longevity increase).

Evidence has shown for many years that mortality is steadily reducing, so that the expectation of life (longevity) is increasing. Evidence also shows that there is significant variation in pensioner mortality by amount of pension. There is evidence to suggest that socio-economic circumstances and lifestyle choices such as smoking, drinking and exercise habits have an impact on mortality. However, it is not likely that these factors can be accessed directly.

An analysis of a scheme's own mortality experience will usually provide relevant evidence. However, with a small membership, random fluctuations could make this unreliable as a sample from which to draw inferences about the future. In the case of small schemes, it may not be worthwhile to undertake this analysis, instead relying on more general factors such as industry, occupation or pension size or use of the standard tables.

There are two basic decisions trustees need to take on mortality assumptions:

the base table (including any adjustment) to reflect the scheme's current mortality experience; and

the allowance for future improvement.

We are available with many pensioners standard table some older ones are:

Life Office Pensioners, Female, Amounts (PA) 90f.

Life Office Pensioners, Male, Amounts (PA) 90m.

Pensioners, Female, Amounts (PFA) 92.

Pensioners, Male, Amounts (PMA) 92.

Latest are:

Pensioners, males, Normal, Amounts (PNMA00)

Pensioners, females, Normal, Amounts (PNFA00)

All pensioners (excluding dependants), Female, Lives (S1PFL)

All pensioners (excluding dependants), Female, Amounts (S1PFA)

All pensioners (excluding dependants), Female, Amounts, Light (S1PFA_L)

All pensioners (excluding dependants), Female, Amounts, Heavy (S1PFA_H)

All pensioners (excluding dependants), Male, Lives (S1PML)

All pensioners (excluding dependants), Male, Amounts (S1PMA)

All pensioners (excluding dependants), Male, Amounts, Light (S1PMA_L)

All pensioners (excluding dependants), Male, Amounts, Heavy (S1PMA_H)