Actuarial Glossary :: "The Mother of All Actuarial Glossaries"

R

Rate Interval (A/D)

A period during which an individual has a constant age, according to a precise age definition. Rate intervals are used in mortality investigations to provide a consistent age definition from which to derive mortality rates.

 

Rate on Line (G)

For non-proportional reinsurance, the total premium charged for the reinsurance divided by the width of the layer covered.

 

Rating Basis (G)

In setting premium rates, the values assigned to each of the rating factors used. The term might also be used to refer to the set of rating factors used (ie the rating structure).

 

Rating Factor (A/D)

An item of factual information (eg number of past accidents) used in a premium calculation. The rating factors are used as proxies that reflect the true underlying risk factors, which cannot normally be determined (eg competence of driver).

 

Rating Factor (G)

A factor which is used to determine the premium rate for a policy. The rating factor should be a risk factor or a proxy for a risk factor or risk factors.

 

Rating Structure (G)

The set of rating factors used.

 

Rating (G)

The process of establishing appropriate premium rates.

 

Re-Inforced Policy (N)

A combination of a decreasing term assurance and a basic with-profit endowment or whole life assurance. The sum assured under the term assurance decreases more or less in step with the bonus growth on the basic policy. Thus the total cover remains relatively constant.

 

Real Assets (E)

The normal use of the expression is to describe any asset that tends to hold its real value in times of unexpected inflation. In some circumstances, it can mean physical, tangible assets such as property and gold.

 

Real Rate of Return (E)

The rate of return above inflation.

 

Real Yield (H)

In the context of Subject H, a real yield may refer to the excess of investment return over either salary increases or retail prices increases. It might also be an assumed real yield (eg for the purposes of a valuation) or it might be an actual real yield (eg if you were looking at the experience of a pension scheme).

 

Real (A)

After adjustment to allow for inflation. A real Asset is an asset (eg an Equity or a Property investment) whose value is protected against the effects of inflation.

 

Reciprocity (G)

An arrangement between two insurers who agree to reinsure risks with each other. The expression is commonly used with quota share reinsurance, where effectively the insurers swap some of their business and diversify their overall portfolio.

 

Recoveries (G)

Amounts received by insurance companies to directly offset part of the cost of a claim. Recoveries may be made from several different sources, eg reinsurers, other insurers, salvage, liable third parties.

 

Redeem/Redemption (A)

A loan or fixed interest security is redeemed when the initial capital is repaid. The redemption rate may be greater than or less than 100% ie an amount greater than or less than the capital amount may be repaid. See also: Irredeemable.

 

Redirection Option (F)

A term used in unitised business. A policyholder has a redirection option if he/she can elect that new premiums are allocated to a different unit fund.

See also Switching Option.

 

Refund of Contributions (A/D)

Repayment of a member's contributions to a pension scheme if the member leaves without receiving a pension eg if the member dies before retirement age or changes jobs. In the UK members who withdraw voluntarily with more than 2 years' Service must be given a Deferred Pension , rather than a refund of contributions.

 

Reinstatement (G)

Where a claim uses up some of the insurance cover (eg where the aggregate amount of claims is limited), it may be necessary for the insured to reinstate the cover, possibly with the payment of a further premium (a reinstatement premium). Reinstatements are typically used in excess of loss reinsurance. The basis for reinstatement premiums will be specified in the treaty.

 

Reinsurance to Close (G)

A premium paid when an account under the three year accounting basis is closed. The insurer pays the premium in order to cover outstanding claims from the given underwriting year.

 

Reinsurance (A/D)

Insurance effected by an insurer to provide protection against large claims and catastrophes which might damage the insurer's solvency position. There are specialist reinsurers which write only reinsurance business. Many Direct Insurers also accept reinsurance business.

 

Reinsurance (F)

Reinsurance is the process by which a direct-writing life insurance company transfers part of its risk under a contract to another life insurance company. This may be another direct-writing company or a professional reinsurance company. The reinsuring company may in its turn reinsure some of the risk with someone else.

The two most important types of reinsurance in life assurance business are risk premium and original terms reinsurance. Catastrophe reinsurance is also quite important.

 

Reinsurance (G)

Insurance purchased by an insurance company in relation to their insurance liabilities.

 

Reinsurer (A/D)

An insurer that offers insurance to another insurer.

 

Reinsurer (G)

An insurer providing reinsurance cover. Some reinsurers do not write direct insurance business.

 

Renewable Term Insurance (N)

Term insurance which can be renewed at the end of the term, at the option of the policyholder and without evidence of insurability, for a limited number of successive terms. The rates increase at each renewal as the age of the insured increases.

 

Renewal Date (A)

A policy anniversary. Under an annual premium policy, premiums are payable on the renewal dates.

 

Renewal (Expenses) (A/D)

Expenses which are incurred, other than the Initial Expenses.

 

Reopened Claims (G)

A claim which had formerly been deemed closed, but which subsequently needs to be reopened because further payments may possibly be required. Insurers should hold reserves to cover the potential liability of closed claims being reopened.

 

Replacement (G)

Short for "replacement as new". It refers to policies where the insurer provides for the replacement with new items on the loss of old items. Compare with indemnity.

 

Repo Agreement (E)

A sale and repurchase agreement under which a security (eg a gilt or a Treasury bill) is sold with an agreement to buy it back on an agreed date at an agreed price. It is, in effect, a form of secured borrowing.

 

Required Minimum Margin of Solvency (EU) (G)

The minimum level by which an insurance company's assets should exceed its liabilities according to EC (and UK) legislation. Often taken to be approximately 20% of net written premiums. Precise calculations vary by class and amount of business, and relate to both gross incurred claims and gross written premium with a limited adjustment for reinsurance. Also referred to as the Statutory minimum solvency margin and occasionally colloquially as SMSM.

 

Required Solvency Margin (RSM) (F)

Life offices are required to keep some extra assets in addition to the reserves for policies. There are detailed rules for calculating this required margin. The rules specify the degree to which admissible assets (market value) need to exceed the DTI statutory value of liabilities and the degree to which less tangible assets (eg future profits) can also be used to cover some of the RSM.

In life assurance contexts, this required solvency margin is also often referred to simply (and not strictly correctly) as the solvency margin. (This is different from Subject G, where the phrase "solvency margin" is used to mean the excess of assets over liabilities).

 

Requirement For Capital (F)

On a per contract basis, the requirement for capital is the amount of finance a company needs in order to be able to write that contract. This can be extended to the whole company where its requirement for capital is the finance it needs in order to be able to carry out its new business plans.

Mathematically, the requirement for capital of a policy at a particular time is the amount by which its published mathematical reserves plus RSM exceed the asset share of the policy. If at all times the asset share exceeds the reserve plus RSM, the requirement for capital is zero.

This capital can be supplied by:

 

1. free assets as they appear in the DTI returns
2. external finance

 

Reserve (A/D)

The expected net present value of receipts minus outgo to an insurer under an insurance policy. Reserves may be calculated retrospectively or prospectively. Reserves may be calculated on a basis different from the premium Basis. See also: Policy Value.

 

Reserve (F)

A reserve is money you decide you need to hold now in order to meet your future liabilities. It can be calculated in one of three ways:

 

1. cashflow gross premium: by calculating an amount now such that any future office net negative cashflows will be eliminated
2. formula gross premium: by assessing the value of what you need to pay out in benefits and expenses less the value of future office premiums. There are other elements to the calculation, but benefits, expenses and premiums are enough for the moment.
3. formula net premium: by assessing the value of what you need to pay out in benefits less the value of future net premiums.

Some students think that a positive reserve is needed when premiums in the past have exceeded past benefits and expenses. This is very wrong! A reserve is a calculation of what you need, not what you have. In Subject 3 (or A and D) terms, we are looking at a prospective calculation, not a retrospective calculation. These are not equal in practice since experience will not follow the assumptions in the premium basis. In Subject F terms, a retrospective assessment of what you have is only sensibly calculated on the actual experience ie the asset share. It may be larger or smaller than the reserve, the amount you need to meet liabilities.

Reserves can be calculated on a variety of bases which might give substantially different answers.

 

Reserving (A/D)

The process of calculating and setting up Reserves.

 

Reserving (G)

The process of estimating or calculating amounts to be set aside to cover outstanding claims and unexpired risks.

 

Resilience Test Reserve (F)

The UK regulations relating to the valuation of a life insurance company's liabilities specify that companies must make prudent provision against the effects of possible future changes in the value of the assets on their adequacy to meet the liabilities as valued in accordance with the regulations. The resilience test reserve is one approach to making such provision.

The office can be cashflow matched and still require a resilience test reserve.

 

Retained Benefits (H)

Pension or death benefits to which a person is entitled in respect of a previous period of employment. In many cases, such benefits need to be taken into account in determining the maximum benefits payable from the current pensionable employment.

 

Retention (F)

In the context of reinsurance, a company's retention is the amount of any particular risk that it wishes to retain for itself. It will then reinsure the excess over that retention.

For example, if an office has a retention of 300,000 and the sum assured is 1,000,000, it will reinsure 700,000.

 

Retention (G)

With reference to reinsurance, the retention is the amount (or proportion) of risk retained by the direct writer.

 

Retirement Annuity (N)

A contract providing for the payment of a regular pension after retirement. Incorporates valuable tax saving facilities as premiums rank with pension contributions for deduction from taxable income.

 

Retroactive Date (G)

Date on which a direct writer commences cover and to which subsequent faculatative reinsurance arrangement.

 

Retrocession (G)

Risks passed on by a reinsurer, ie reinsurance of reinsurance business.

 

Retrospective Earned Asset Share (REAS) (F)

See Asset share.

 

Return Commission (G)

A commission paid by a reinsurer to the ceding company for proportional reinsurance business to recompense the cedant for acquisition expenses.

 

Return of Premiums (A)

Repayment of the premiums paid by a policyholder. Many life assurance policies include a return of premiums (payable to the policyholder's estate or designated beneficiary) to give the appearance of providing value for money in all circumstances. The amount of premiums returned may be calculated without interest, with simple interest or with compound interest.

 

Return on Capital (F)

This arises in the context of product pricing. A company will usually need to provide capital in order to write new business. The return on that capital will influence whether or not the company writes particular types of business and the price at which it will write them. The level of return required will depend on the levels available from other uses of the company's capital.

The return on capital shown by a policy is the interest rate at which the present value of the profit test cashflow output is zero. Also known as the internal rate of return of the policy.

If a contract has no capital requirement, the return on capital is not defined (and is not a useful measure).

 

Revaluation (A)

An adjustment (eg a regular increase) applied to the value of an asset or the amount of a benefit to offset the effects of inflation.

 

Revaluation (H)

The process of increasing either:

 

• benefits between a member leaving a scheme and retiring (in which case increases may be discretionary, in line with a particular index, or at a fixed rate, but will be subject to legislative requirements).

  or

   

• earnings between receipt by the member and the time at which they are used in the calculation of the member's scheme benefits.

 

Revenue Account (G)

The account which comprises premiums, claims, commission, expenses and changes in relevant reserves or funds to produce the underwriting result.

The precise form of the items in the account will depend upon whether it is being calculated for one or three year accounts.

 

Reverse Yield Gap (E)

The yield gap turned round, ie long-dated gilt yield minus equity yield.

 

Reversionary Annuity (A/D)

An annuity payable to an annuitant following the death of an assured life.

 

Reversionary Bonus (A/D)

Bonus added to the benefit of a with profit policyholder throughout the life of the policy. The benefit is not guaranteed in advance, but once added to the benefit, it is guaranteed.

 

Reversionary (F)

A term used in the context of bonus. A reversionary bonus is one which will increase benefits payable in the future. Regular bonuses are normally reversionary. Offices also sometimes declare special (one-off) reversionary bonuses.

 

Rights Issue (E)

A temporary option for the existing shareholders in a company to purchase more shares in the company at a specified price. The purpose is for the issuing company to raise more money.

 

Risk Attaching Basis (G)

When reinsurance is provided for claims arising from policies that the cedant incepts during the term of an arrangement. As opposed to a loss- occurring approach.

 

Risk Averse (E)

Being prepared to accept higher risk only if a higher return is expected. An investor who is very risk averse will require a much higher expected return to accept higher risk.

 

Risk Discount Rate (F)

A risk discount rate typically arises when carrying out a profit test of a life assurance product. It represents the risk-free rate of return that the providers of capital demand plus an amount to allow for the risk that the profits may not emerge as expected from the product.

It also arises in the determination of the embedded value and appraisal value of a proprietary life company.

The risk discount rate is often based on the opportunity cost of capital required to support the contract. This can be increased to the extent (if any) that there is any unquantifiable risk in the life assurance project being assessed. (Quantifiable risk can be modelled explicitly.)

 

Risk Excess of Loss Reinsurance (G)

Excess of loss reinsurance which relates to individual losses affecting only one insured risk at any one time.

 

Risk Factor (G)

A factor (or characteristic of the insured) which is thought to influence the risk premium, either by influencing the claim frequency, the average claim amount or both.

 

Risk Group (G)

A subdivision of a class of business. It should contain less heterogeneity than the whole class.

 

Risk Premium (A/D)

The pure premium needed to cover the expected risks. but with no allowance for expenses, commission or contingencies.

 

Risk Premium (F)

This usually refers to a single premium that covers a specific risk for a specific period of time. For example, in pricing unit-linked contracts, a company will usually cost for death or sickness cover by applying a monthly risk premium to the appropriate amount at risk in each month.

The term is also used in reinsurance. Here, the risk premium is the amount required to cover the cost of the death sum at risk. It is basically of the form (SA - V)qx, plus expenses where SA = sum assured, V = reserve and qx = probability of dying for a life aged x.

A form of reinsurance called risk premium reinsurance involves a payment only of the risk premium to the reinsurer, and the payment of the sum at risk to the direct writer on the death of the policyholder.

 

Risk Premium (G)

The amount of premium required to cover the risk, ie average claim amount * average claim frequency.

 

Risk (A/D)

The possibility of a financial outcome worse than its predicted value. In general insurance, risk refers to the insurance of a particular item eg a building or a vehicle.

 

Risk (E)

The possibility of an adverse outcome. Investment risk can be described in many different ways. For the purpose of Subject E, the main form of risk is the risk of investors having insufficient assets to meet their liabilities. In many investment textbooks, risk is measured by the variance or standard deviation of investment return.

 

Risk-based Capital (G)

The assessment of the capital requirement for a general insurer by considering the risk profile of the business written,ie the capital required is a function of actual business written. In the US, the required minimum margins of solvency are determined in this way, where it is also called "dynamic solvency testing".

 

Road Traffic Act (G)

The legislation that requires anyone using a motor vehicle on the road to have insurance to cover their legal liabilities to third parties (including passengers) in respect of personal injury and property damage.

 

RPI (E)

An acceptable abbreviation for the Retail Prices Index (an index of UK consumer prices).

 

Run-off Basis (G)

A valuation basis that assumes an insurer will cease to write new cover, and continue in operation purely to accomplish the payment of claims for previously written policies.

 

Run-Off Table (G)

A tabular process used to project the development (or run-off) of outstanding claims.

 

Run-off Triangle (A/D)

A triangular table in general insurance showing the development of past claims in successive years.

 

Running Yield (E)

The annual income on an investment divided by its current market value. Important examples are the flat yield on gilts, the gross dividend yield on equities and the rental yield on property.