Actuarial Science: Unit Linked Contracts

In this article, we will understand what unit-linked contracts are. Have you wished for earning a profit on the premium you pay for your insurance cover? Did you think you could invest in securities while actually buying yourself insurance?

What if I tell you I have a product that invests your premium in stock market?

You will probably think the stock market involves risk, you might end with very less and insufficient sum during the claim and so the product is not useful. But, what if I tell you I have a product that gives you the benefit of investment in securities(chosen by you), protection of your Sum Assured and insurance cover? Would it intrigue you?

Here is the deal, I put a unit-linked contract on the table.


Let me break-down unit-linked contracts ,for you , in the article below,

Firstly, insurance contracts are simply contracts between two parties wherein one party transfers its risk to another party for a price. For general people, it is a way of removing their exposure to risk. People are risk-averse and are ready to pay some amount to transfer their risk, because of which insurance companies exist.

Insurance companies take a bunch of uncorrelated risks together which reduces the probability of risk for them due to which they make a profit and continue the business. Insurance can be Life and Non-Life (health, motor, etc.).

Life Insurance companies offer various types of policies like whole life cover, endowment benefit, and term assurance cover. In these policies, the policyholder (insured) pays a premium and receives a death benefit on death during the term of the policy or maturity benefit on surviving the term of the policy, whichever applicable.

Unit Linked Insurance Plan is a life insurance product, which provides risk cover for investments such as stocks, bonds or mutual funds. In this policy, the insured does not receive a fixed amount when the benefit is payable .The premium that the insured pays are invested in an investment fund chosen by the policyholder.  The investment fund is divided into units which are priced continuously.

The value at the date of death or survival (i.e.  At the time of claim) of the cumulative number of units purchased is the sum assured under the contract.  A minimum guaranteed sum assured is specified in the terms of the contract to ensure that the policyholder avoids any difficulties arising from particularly poor investment performance. The insurance company holds reserves to meet the claims timely and ensure its survival.


Investment Options available for policyholders:

ULIP offers investors the option to invest in equity and debt. Investors can choose their investment fund as complete equity, complete debt or balanced (50% each), according to their risk appetite. An aggressive investor can pick equity oriented fund option whereas a conservative one can go with debt option.

Benefits of having a ULIP

You get market-linked returns as the sum assured. While traditional insurance plans offer 4% to 6% returns, ULIP can offer you double-digit returns if you are invested in equity funds, says Deepak Yohannan, CEO of

 Unit-linked plans offer the twin benefits of life insurance and savings at market-linked returns. Thus, you have the opportunity to invest your money to earn higher returns, while taking care of your protection needs.

Unit Linked Plans offer you a wide range of flexible options such as the option to switch between investment funds to match your changing needs, the facility to partially withdraw from your fund, subject to charges and conditions.

Structure Of The Contract

Allocation percentage:  A certain proportion of premium, taken from the policyholder, is deducted for the company’s expenses. The remaining premium is invested to purchase units.

Bid-Offer spread:  The policyholder buys units with his premium at the offer price and at maturity the company buys those units back from the policyholder at the bid price. The bid price is lower than the offer price. This bid-offer spread goes to the company’s fund.

Charges: The company charges certain expenses to cover its administration cost like policy fee, fund management charges and other charges to allow for the withdrawal of policy or switching investment funds during the term of the contract.

The unallocated premium amount, bid-offer spread and other charges are recorded in the company’s non-unit fund which is maintained for tracking its profit on policies. A unit fund is maintained for the policyholder. The heads in the respective funds can be understood very well through the diagram.

Unit linked policies are relatively complicated compared to traditional insurance products. It is difficult to use the traditional actuarial approach for evaluating the premiums and the reserves of these contracts. Instead, profit testing is a plausible and popular approach for evaluating premiums and the reserves for it.

Let’s understand profit-testing with an example,
In the question, mortality rates are taken from a tabulated AM92 ULTIMATE table, tabulated for UK and interest rate for discounting is assumed to be 6%. Indian mortality rates are tabulated in CMI Tables (Continous Mortality Investigation). Every insurance company has a record of age-wise mortality rates and interest rate is chosen by them according to their policy.

We will perform the operation on excel, it can be done on other software also like R programming. The formula to be used in the calculation is as follows:

For unit fund
Premium allocation= premium received * allocation percentage

Fund at start= fund value at end

Interest = (fund at start + premium allocated – B/O spread)*0.05

Management charge = 0.01*(fund at start+ premium allocated-B/O spread +interest)

Fund value at end  = fund at start+ premium allocated- b/o spread + interest – management charge

For Non-unit fund
Interest = (unallocated premium + B/O spread – expenses)*0.03

Extra death cost = max (12000- fund value at end) * age mortality
Extra maturity cost = fund value at end of 3rd year *(1-mortality at age 22)

End of year cf= unallocated premium + B/O spread – expenses+interest – extra death cost – extra maturity cost + management charge

The sum assured is maximum of 12000 and the fund value at time of claim.

In the non-unit fund, the end of year cash flow is the profit per policy for the company. The expenses of the company are administration cost and death benefit and maturity benefit also pose some cost to the company. The cost of maturity to the insurance company is just 10% of the fund value at the end of year 3.

We create a profit vector with profit values.

Profit vector = (341.79, 771.76, -799.95)

Profit signature = profit vector multiplied with the probability of surviving the year

Profit margin = (present value of profit signature)/ present value of premiums received

Now, companies decide a profit margin for a set of policies. The profit margin is the profit % the company expects to earn from a policy to continue surviving.  Once a profit margin is chosen, companies vary the premiums. Certain assumptions are made during the test. The company runs tests varying their assumptions and profit margin and reaches an appropriate premium level.

This sums up the premium calculation process and working of unit-linked contracts. ULIP is an innovative product that strikes a balance between investment and insurance and balance is determined by personal goals and risk factors. There can be innovations in ULIP, few instances are:

  • a regular premium product offering a guaranteed sum assured on death, to give an endowment assurance;
  • a single premium product offering a return of premium on death to give a pure savings bond;
  • a regular premium contract offering an annuity payment during periods of disability or unemployment; or,
  • a single premium product offering an annuity payment until death.

Download the Excel Used above

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