A LINEAR PRICING MODEL FOR LIFE INSURANCE POLICIES

A LINEAR PRICING MODEL FOR LIFE INSURANCE POLICIES Mihir Dash Anju Ann Verghese School of Business, ALLIANCE University ABSTRACT Life insurance products are priced according to two reciprocal requirements. As finacnial products, they must yield returns to investors, but decreasingly so with increased risk exposure. On the other hand, they must be priced to reflect the providers risk exposure. Thus, the pricing and returns of life insurance products depend on the underlying risk exposure. This study proposes a linear model for the pricing of life insurance policies. The proposed model provides an approach for comparing different types of life insurance products, enabling investors to choose between products. Keywords: life insurance products, risk exposure, premia. INTRODUCTION Life is fraught with tensions and apprehensions regarding the future and what it holds for the individual. Despite all the planning and preparation one might make, no one can accurately guarantee or predict how or when death might result and the circumstances that might ensue in its aftermath. So it is essential to plan for the future. The chances for a fatality or an injury to occur to the average individual may not be particularly high, but then no one can really afford to completely disregard his or her future and what it holds. Insurance is system by which the losses suffered by a few are spread over many, exposed to similar risks. Insurance is a protection against financial loss arising on the happening of an unexpected event. Insurance policy helps in not only mitigating risks but also provides a financial cushion against adverse financial burdens suffered. Insurance policies are usually based on certain principles 1 : - Uncertainty of time and occurrence - Predictability of level of loss - Loss must be significant de minimis. - The loss must not be catastrophic insurer must not be insolvent. Life insurance is a contract that pledges payment of an amount to the person assured (or his nominee) on the happening of the event insured against. The contract is valid for payment of the insured amount during: the date of maturity, or specified dates at periodic intervals, or unfortunate death, if it occurs earlier. Among other things, the contract also provides for the payment of premium periodically to the insurance provider by the policyholder. Life insurance is 1 http://www.irda.gov.in/ Electronic copy available at: http://ssrn.com/abstract=1988813

universally acknowledged to be an institution which eliminates risk, substituting certainty for uncertainty, and comes to the timely aid of the family in the unfortunate event of death of the breadwinner. By and large, life insurance is society s partial solution to the problems caused by death. Life insurance, in short, is concerned with two hazards that stand across the life-path of every person: that of dying prematurely leaving a dependent family to fend for itself, and that of living till old age without visible means of support. Key Features of Life Insurance Nomination: When one makes a nomination, as the policyholder you continue to be the owner of the policy and the nominee does not have any right under the policy so long as you are alive. The nominee has only the right to receive the policy monies in case of your death within the term of the policy. Assignment: If your intention is that your policy monies should go only to a particular person, you need to assign the policy in favour of that person Death Benefit: The primary feature of a life insurance policy is the death benefit it provides. Permanent policies provide a death benefit that is guaranteed for the life of the insured, provided the premiums have been paid and the policy has not been surrendered. Cash Value: The cash value of a permanent life insurance policy is accumulated throughout the life of the policy. It equals the amount a policy owner would receive, after any applicable surrender charges, if the policy were surrendered before the insured's death. Dividends: Many life insurance companies issue life insurance policies that entitle the policy owner to share in the company's divisible surplus. Paid-Up Additions: Dividends paid to a policy owner of a participating policy can be used in numerous ways, one of which is toward the purchase of additional coverage, called paid-up additions. Policy Loans: Some life insurance policies allow a policy owner to apply for a loan against the value of their policy. Either a fixed or variable rate of interest is charged. This feature allows the policy owner an easily accessible loan in times of need or opportunity. Conversion from Term to Permanent: When in need of temporary protection, individuals often purchase term life insurance. If one owns a term policy, sometimes a provision is available that will allow her to convert her policy to a permanent one without providing additional proof of insurability. Disability Waiver of Premium: Waiver of Premium is an option or benefit that can be attached to a life insurance policy at an additional cost. It guarantees that coverage will stay in force and continue to grow. The Benefits of Life Insurance Risk cover: Life Insurance contracts allow an individual to have a risk cover against any unfortunate event of the future. Tax Deduction: Under section 80C of the Income Tax Act of 1961 one can get tax deduction on premiums up to one lakh Rupees. Life Insurance policies thus decrease the total taxable income of an individual. Loans: An individual can easily access loans from different financial institutions by pledging his insurance policies. Electronic copy available at: http://ssrn.com/abstract=1988813

Retirement Planning: What had provided protection against the financial consequences of premature death may now be used to help them enjoy their retirement years. Moreover the cash value can be used as an additional income in the old age. Educational Needs: Similar to retirement planning the cash values that flow from ones life insurance schemes can be utilized for educational needs of the insurer or his children. Life Insurance versus Savings Contract of Insurance: A contract of insurance is a contract of utmost good faith technically known as uberrima fides. The doctrine of disclosing all material facts is embodied in this important principle, which applies to all forms of insurance. At the time of taking a policy, policyholder should ensure that all questions in the proposal form are correctly answered. Any misrepresentation, non-disclosure or fraud in any document leading to the acceptance of the risk would render the insurance contract null and void. Protection: Savings through life insurance guarantee full protection against risk of death of the saver. Also, in case of demise, life insurance assures payment of the entire amount assured (with bonuses wherever applicable) whereas in other savings schemes, only the amount saved (with interest) is payable. Aid To Thrift: Life insurance encourages 'thrift'. It allows long-term savings since payments can be made effortlessly because of the 'easy instalment' facility built into the scheme. (Premium payment for insurance is either monthly, quarterly, half yearly or yearly). For example, the Salary Saving Scheme (popularly known as SSS) provides a convenient method of paying premium each month by deduction from one's salary. In this case the employer directly pays the deducted premium to LIC. The Salary Saving Scheme is ideal for any institution or establishment subject to specified terms and conditions. Liquidity: In case of insurance, it is easy to acquire loans on the sole security of any policy that has acquired loan value. Besides, a life insurance policy is also generally accepted as security, even for a commercial loan. Tax Relief: Life Insurance is the best way to enjoy tax deductions on income tax and wealth tax. This is available for amounts paid by way of premium for life insurance subject to income tax rates in force. Assessees can also avail of provisions in the law for tax relief. In such cases the assured in effect pays a lower premium for insurance than otherwise. Money When You Need It: A policy that has a suitable insurance plan or a combination of different plans can be effectively used to meet certain monetary needs that may arise from timeto-time. Children's education, start-in-life or marriage provision or even periodical needs for cash over a stretch of time can be less stressful with the help of these policies. Alternatively, policy money can be made available at the time of one's retirement from service and used for any specific purpose, such as, purchase of a house or for other investments. Also, loans are granted to policyholders for house building or for purchase of flats (subject to certain conditions). Product Range Term Insurance: Term Insurance is a no-frills life insurance plan and covers you for a term of one or more years. It pays a death benefit only if you die in that term. Term Insurance generally offers the cheapest form of insurance. You can renew most Term Insurance policies for one or more terms even if your health condition has changed. Each time you renew the policy for a new term, premiums may climb higher. Electronic copy available at: http://ssrn.com/abstract=1988813

Term policies cover only the risk during the selected term period. If the policyholder survives the term, the risk cover comes to an end. A Term plan is a pure risk cover plan, meeting the needs of people who are initially unable to pay the larger premium required for a whole life or an endowment assurance policy, but they hope to be able to pay for such a policy in the near future. Money Back Life Insurance Policy: Money back policies are quite similar to endowment insurance plans where the survival benefits are payable only at the end of the term period,plus the added benefit of money back policies is that they provide for periodic payments of partial survival benefits during the term of the policy so long as the policy holder is alive. An additional and important feature of money back policies is that in the event of death at any time during the term of the policy, the death claim comprises full sum assured without deducting any of the survival benefit amounts. The insurance premium of Money Back Policies are higher than Term Insurance Policy because in Term Insurance there is no survival benefits after the expiry of the insurance period. Money Back Policies are good for people who want to Insure their life and also want to some return from their investment's at a later date. The return from investments in Money Back Policies would range between 5% to 8% annually depending on the interest rate movements. Endowment Insurance Policy: Endowment insurance are policies that cover the risk for a specified period and at the end the sum assured is paid back to the policyholder along with all the bonus accumulated during the term of the policy. The Endowment insurance policies work in two ways, one they provide life insurance cover and on the other hand as a vehicle for saving. They are more expensive than Term policies and Whole life policies. Normally the bonus in calculated on the sum insured but the only draw back is that the bonuses are not compounded. Endowment insurance plans are best for people who do not have a saving and an investing habit on a regular basis. Endowment Insurance Plans can be bought for a shorter duration period. Whole Life Insurance Policy: A whole life policy continues as long as the policyholder is alive. In whole life insurance plan the risk is covered for the entire life of the policyholder, that is the reason they are called whole life policies. The nominee of the beneficiary are paid the policy monies and the bonus only upon the death of the policyholder. The policyholder is not get any money during his or her own lifetime, that means there is no survival benefit to the policy holder. Unit Linked Insurance Policy: Unit-linked insurance plans (ULIPs) are a special kind of insurance policies which have a benefit of life insurance and which also serve as an investment tool. In a unit linked insurance plan there are two parts in the premium a client pays, the first part of the premium goes into covering the life of the policy holder and the second part goes into investments. Almost all insurance companies give their customers a choice to select the investment mix. They can go for 100% equity funds or 100% debt funds or a mixture of both. In a unlit linked insurance plan the customers are also given choice to switch from one fund to another. The returns from the insurance policy are directly related to the performance of the funds. The only drawback of unit linked insurance plans is its charges for first few years, which varies from 5% to 70% of the premium. Children's policies: The nominee receives a guaranteed amount of money at a pre-determined time and not immediately on death of the insured. On survival the insured receives money at the same pre-determined time. These policies are best suited for planning children's future education and marriage costs.

Annuities/Pension schemes: These are policies that provide benefits to the insured only upon retirement. If the insured dies during the term of the policy, his nominee would receive the benefits either as a lump sum or as a pension every month. METHODOLOGY This study proposes a linear model for the pricing of life insurance policies: P SA. q, where P/SA is the premium as a percentage of the sum assured, q is the probability of nonsurvival of the individual during the term of the contract. The intercept parameter α is the limiting premium as the probability of non-survival of the individual during the term of the contract tends to zero. The slope parameter β represents the rate of increase in the premium with increased risk of non-survival during the term of the contract. The model thus relates the pricing of life insurance policies with the underlying risk exposure of the contract, viz. the risk of nonsurvival of the individual during the term of the contract. The study does not address the returns of a life insurance contract. The data for the study was collected pertaining to the life insurance policies of various private sector insurance companies in India, including Bharti Axa life Insurance Company Ltd 2., Bajaj Allianz Life Insurance Company Ltd 3., Birla Sun Life Insurance Company Ltd 4., SBI Life Insurance Company Ltd 5, MetLife India Insurance Company Ltd 6., and Reliance Life Insurance Company Ltd 7. The variables considered for the study are the premium as a percentage of the sum assured, and the probability of non-survival of the individual during the term of the contract. These have been calculated from the premium for each policy across age group 20-60 years, with an assumed maturity period of ten years for each policy, and the sum assured varied for different policies. The probability of non-survival of the individual was obtained using the following expression: (k ) q j pk pk 1... pk j 2 (1 pk j 1 ) =, viz. the probability that a person i 0 aged k will survive j-1 years but not j years, and where pi is the probability that a person aged i will survive for age i+1 (i.e. the age-specific survival rate). The age-specific mortality rates used in this calculation were obtained from standard life tables. j 2 = p k i 1 p k j 1 ANALYSIS The graphs in Figures 1-6 below relate the premium as a percentage of sum assured the probability of non-survival for different insurance policies. 2 http://www.bharti-axalife.com/ 3 http://www.bajajallianz.com/corp/index.jsp 4 http://www.birlasunlife.com/ 5 http://www.sbilife.co.in/sbilife/content/home 6 http://www.metlife.co.in/ 7 http://www.reliancelife.com/rlic/index.aspx

Figure 1: premium vs. probability of non-survival for Bharati Axa policies Figure 2: premium vs. probability of non-survival for Bajaj Allianz policies Figure 3: premium vs. probability of non-survival for Birla Sun Life policies

Figure 4: premium vs. probability of non-survival for SBI Life policies Figure 5: premium vs. probability of non-survival for MetLife policies Figure 6: premium vs. probability of non-survival for Reliance Life policies

The graphs in Figures 1-6 indicate a linear relationship between the premium as a percentage of sum assured the probability of non-survival for most of the policies considered. The exceptions to this pattern include Bharati Axa Life Safe Confident, Bharati Axa Aajeevan Anand, Bharati Axa Future Camps, which indicate a piecewise-linear (linear spline) relationship between the premium as a percentage of sum assured the probability of non-survival; and SBI Life Smart Shield, which indicates an inexplicable change in the relationship (beyond a cut-off age), but which may still be piece-wise linear. Almost all the policies show edge effects at lower probability of non-survival (i.e. for lower age groups), particualrly Reliance Whole Life Plan and Met 100 Non Par. These non-linearities could reflect a reduction of premia in order to attract younger customers. The regression results are presented in Table 1 below. Table 1: regression results insurance provider insurance policy intercept (α) slope (β) Bharti Axa Life Insurance Co Ltd. Life Elite Secure 0.63% 0.5431 Life Secure Confident 0.14% 0.0733 Life Family Income 0.48% 0.2777 Life Save Confident 11.13% 0.2056 Life Aajeevan Anand 12.60% 0.0529 Life Future Camps 8.13% 0.1562 Bajaj Allainz Life Insurance Co Ltd. Term Care 0.81% 0.3983 Invest Gain 11.69% 0.1863 Protector 0.20% 0.0881 Super Saver 13.55% 0.0640 New Risk II 0.10% 0.0860 Cash Gain 10.24% 0.3095 Birla Sun Life Insurance Co Ltd. Protector Plan 0.22% 0.0371 Protect Plus Plan 0.07% 0.0311 SBI Life Insurance Co Ltd. Smart Shield 0.08% 0.0261 Saral Shield 0.06% 0.0675 MetLife Insurance Co. Ltd. 100 Non Par 1.44% 0.2112 Suraksha Trop 0.61% 0.2006 Suvidha Endowment Non Par 8.53% 0.0444 Suraksha Plus 0.05% 0.0607 Reliance Life Insurance Co. Ltd. Super Five 25.64% 0.2414 Connect to Life Plan 6.69% 0.1144 Whole Life Plan 4.85% 0.3525 Cash Flow Plan 12.63% 0.1462 The intercepts varied considerably, the lowest being 0.05% (for MetLife Suraksha Plus), and the highest being 25.64% (for Reliance Life Super Five). Similarly, the slopes varied considerably, the lowest being 0.0261 (for SBI Smart Shield), and the highest being 0.5431 (for Bharati Axa Life Secure). In fact, three clusters of policies can be identified. The first cluster can be described as low priced, with α < 0.25% and β < 0.10, comprising the policies: Bharati Axa Life Secure Confident, Bajaj Allianz Protector, Bajaj Allianz New Risk II, Birla Sun Life Protector Plan, Birla Sun Life Protector Plus Plan, SBI Life Smart Shield, SBI Life Saral Shield, and Met Suraksha Plus.

The second cluster can be described as moderate priced, with 0.45% < α < 1.5% and 0.20 < β < 0.60, comprising the policies: Bharati Axa Life Elite Secure, Bharati Axa Life Family Income, Bajaj Allianz Term Care, Met 100 Non Par, Met Suraksha Trop, and Met Suraksha Plus. The third cluster can be described as relatively high-priced, with 6.5% < α < 14% and β < 0.31, comprising the policies: Bharati Axa Life Save Confident, Bharati Axa Life Aajeevan Anand, Bharati Axa Life Future Camps, Bajaj Allianz Invest Gain, Bajaj Allianz Super Saver, Bajaj Allianz Cash Gain, Met Suvidha Endowment Non Par, Reliance Connect to Life Plan, and Reliance Cash Flow Plan. Two of the policies were considered as outliers. Reliance Whole Life Plan was close to the second cluster, but had too high α. Reliance Super Five had an exorbitantly high α, and also quite high β, and so was far away from all three clusters. In fact, all the policies of Reliance Life Insurance Company Ltd. were very high-priced. This may indicate that they are more aggressive investment instruments. The policies of SBI Life Insurance Company Ltd. and Birla Sun Life Insurance Company Ltd. were all low-priced, relatively straightforward insurance products. Bharat Axa Life Insurance Company Ltd., Bajaj Allianz Life Insurance Company Ltd., and MetLife Indian Insurance Company Ltd. provided a range of all types of insurance products. DISCUSSION Life insurance policies are no longer seen solely as a means of insuring life. Due to many new features introduced by life insurers, they are seen in the new light of serving savings and even investment purposes besides the basic purpose of insuring life. Life insurance products are priced according to two reciprocal requirements. As financial products, they must yield returns to investors, but decreasingly so with increased risk exposure. On the other hand, they must be priced to reflect the providers risk exposure. Thus, the pricing and returns of life insurance products depend on the underlying risk exposure. Further, the pricing must reflect the specific features of the insurance contract. The results of the study suggest that insurance policies can be classified according to their pricing pattern relative to the underlying risk exposure. The study proposes a linear model for the pricing of life insurance policies: P SA. q, where P/SA is the premium as a percentage of the sum assured, q is the probability of non-survival of the individual during the term of the contract. The intercept parameter α is the limiting premium as the probability of non-survival of the individual during the term of the contract tends to zero. The slope parameter β represents the rate of increase in the premium with increased risk of non-survival during the term of the contract. The model can be extended to include other risk factors such default risk and demographics (Chen et al, 1995). A limitation of the study is that it does not address the returns of a life insurance contract. In fact, pricing and returns of life insurance products must be inter-related, as shown by Dash et al (2007). They proposed a linear model for returns of a life insurance contract: r. q, where

r is the (internal) rate of return, q is the probability of non-survival of the individual during the term of the contract. This can further be combined with other approaches to insurance pricing, including the options-based approach (Cummins, 1991; Mao et al, 2004). There is thus much more further scope for pricing and returns modelling for life insurance products. REFERENCES Chen, Y., Hamwi, I.S., and Hudson, T. (1995), Capital asset pricing models with default risk: Theory and application in insurance, International Advances in Economic Research, vol. 9(1), pp. 20-34. Cummins, J.D. (1991) Statistical and Financial Models of Insurance Pricing and the Insurance Firm, Journal of Risk and Insurance, vol. 58, pp. 261-302. Dash, M., Lalremtluangi, C., Atwal, S. and Thapar, S. (2007), A Study on Risk-Return Characteristics of Life Insurance Policies, available at SSRN: http://ssrn.com/abstract=1303350 Mao, H., Carson, J.M., Ostaszewski, K.M., and Shoucheng, L. (2004) Pricing life Insurance: combining economic, financial, and actuarial approach, Journal of Insurance Issues, vol. 27, pp. 134-159.