Introduction

In recent times there has been an almost complete unanimity in the popular media (financial newspapers and financial TV channels), that the purchase of a life insurance policy is compatible with financial investment theory. Comparisons are made between the IRR on life insurance products with that of other financial products and we are told that the IRR on a life insurance product is much lower, thereby making an “investment” in life insurance is unattractive. This sentiment is so strong that one finds even the people selling life insurance believing it.

This article explains why the popular sentiment is scientifically and theoretically wrong and why one should never calculate the IRR on life insurance products, at least in the manner that is currently done.

Systemic and Non-systemic Risk

Starting with a seminal work by Harry Markowitz in the late 1950s where a distinction was made between systemic risk and non-systemic risk in investments, portfolio theory has come a long way to develop the Capital Asset Pricing Model, the Arbitrage Pricing Model and many other models to help investors design their investment portfolios. The fundamental basis of Portfolio Theory is the assumption of the existence of systemic risk and non-systemic or idiosyncratic risk. The existence of these risks affects the performance of the assets held in a portfolio.

Systemic risk is exogenous to the portfolio and cannot be diversified. Non-systemic risks or idiosyncratic risks are risks are endogenous to the portfolio components and can be diversified to attain risk optimisation for maximizing returns. Systemic risk covers the risks posed by events such as, earthquakes and other natural calamities, shifts in consumption patterns, falling incomes, recession, fiscal policy, regulations, etc. For an individual policy holder in life insurance that contains a life-risk cover for example, death is a systemic risk. The portfolio manager in other words can do little to mitigate the risks posed by such events. On the other hand non-systemic risks can be statistically identified thus allowing the portfolio manager to diversify the risks. Examples of this are seasonal fluctuations of prices, product life cycles, etc.  Portfolio managers, using statistical modelling, can estimate such risks with a defined range of probabilistic outcomes.

The expected return on a given investment is the sum total of the risk-free rate of return and the return that comes from the degree of risk on the investment. Risk is the existence of a set of possible outcomes that have varying degrees of probabilities distributed around the mean of the expected return. The higher the range of the distribution around the mean, the greater the risk.

The objective of portfolio investments is to maximize returns, within his or her risk class, by diversifying the non-systemic risks. That is every investor tries to maximize his or her returns by balancing the portfolio with respect to the risks involved in various financial instruments of varying degrees of risk, in the fond hope that if the risk factors play in his or her favour, the investor will get more returns as compared to a situation where the portfolio is not diversified.

As with any body of knowledge, portfolio theory too is constructed on the pillars of a few assumptions. This article is not a complete critique of portfolio theory, however we shall discuss some of the relevant assumptions here, since they are relevant to the main arguments of this article.

Some of the Assumptions in Investment Theory

1. The timing of the cash inflows and the cash outflows is known.
2. The period for which the investment is to be held, the time horizon is known
3. Systemic risks, that is, risks not in the control of the investor, cannot be diversified. They are outside the control of the investor.

Characteristics of a Life Insurance Product

We shall now see the characteristics of a life insurance product and assess their consistency with the assumptions of investment theory. A life insurance product has amongst others the following characteristics:

1. A life insurance endowment product is a joint product. It produces two outcomes for a single payment – the death benefit and the maturity benefit.
2. There is no unique method of apportioning the costs of the joint products between the two outcomes.
3. The timing of the maturity benefit in a life insurance product is known, but the timing or duration of getting the death benefit is not known.

The characteristics listed above have a direct impact on what we can do (or cannot do) with the cash flows arising out of a life insurance policy.

3. When a person buys an endowment product the policy holder is buying a joint product with joint costs giving the policy holder two products; any calculation of returns or yield should take into account both the products and not just one product, say the maturity benefit. In other words, we must consider death benefit as well as maturity benefit (in the case of an endowment product) or only death benefit (in the case of a term assurance plan).
4. While considering the death benefit the period or duration is not known, hence yield cannot be calculated on the benefit a policy holder enjoys by having a life insurance cover.
5. The Apportionment Muddle: The purchase of a life insurance product creates a joint product. That is one payment creates many potential outcomes. Death benefit and maturity benefit being the main outcomes. In the creation of the joint product, there are also joint costs, e.g. marketing and distribution costs, underwriting costs, policy maintenance costs and so on. A common problem in costing is the apportionment of joint costs to joint products. In life insurance for example what part of the distribution costs can be apportioned to death benefit and what part to maturity benefit. Cost accountants who face this problem in manufacturing enterprises have developed various statistical methods to apportion costs in the case of joint products.

Statistical methods have a limitation. There are many methods of apportionment. The method of apportionment determines the profit earned on each of the joint products, for there is no unique method for such apportionment. For example if Rs. 1000 is paid to the sugarcane farmer for procuring sugarcane in a sugar factory, and the factory also produces bagasse for sale, the cost of Rs.1000 has to be borne by both sugar and bagasse. By one method it Rs.600 may be apportioned to sugar while Rs.400 to bagasse. With another method Rs.800 may be apportioned to sugar and Rs.200 to bagasse. Obviously, this results in different prices and profits for sugar and bagasse. For the sugar factory however, it is total price realized, and total profit earned.

In life insurance policy for a buyer, this is not so. The policy holder does not get a total monetary benefit which is the sum of death benefit and maturity benefit. And for the purposes of calculating the IRR on the policy the two benefits can neither be clubbed together nor seen in isolation of each other. So, the assumption that future cash flows inflows and outflows can be uniquely identified does not hold for life insurance products.

• 6. The Discounting Muddle: Life insurance cash flows can be discounted but IRR cannot be calculated: Death is certain, but the timing is uncertain. The main reason why death and maturity benefits can neither be clubbed nor seen in isolation is that the timing of death is uncertain. As mentioned earlier, in order to calculate IRR, we need to know the period for which to calculate. Since the timing of death is uncertain, we cannot calculate IRR, unless some ridiculous statistical assumptions are built in.
• 7. The Diversification Muddle: Death is a systemic risk; it cannot be diversified away, which is the purpose of portfolio theory. Adding or removing death benefit from the portfolio in no way helps the investor to maximize profitability of investments by risk-return optimisation. Just as for example we cannot introduce a proxy for government regulations in portfolio theory, we cannot introduce death benefit in portfolio theory.

Calculating IRR of an endowment product is unscientific

IRR calculation is a rigorous scientific process. It is a theory that is replete with postulates, axioms and proof. The conditions for which the theory can be used is defined within the body of the theory itself. Using the theory for any other purpose is a fallacy and gives many misleading conclusions.

The conclusion, for example, that the return on a life insurance product is lower than that of say mutual funds is misleading to say the least. At worst it is an outright fraud. In reality we cannot calculate the IRR of a life insurance product for the method of calculation of IRR does not permit us to do so. The science of IRR allows us to calculate the IRR on a mutual fund or a bank deposit, since they fully fit into the body of the science of calculating the IRR. To put it in plain terms, we do not know the IRR of a life insurance product. We cannot take death benefit and maturity benefit as one product, since they have different characteristics and also have different time horizons. In addition, in the case of the death benefit, even the timing is not known. And death benefit is not an investment outcome as we understand investments, so return on investment on death benefit cannot be calculated.

The flip side of all the arguments stated above is that life insurance professionals should explain the uniqueness of the life insurance product and not fall into the trap laid by finance professionals who are mis-leading the public with their unscientific calculations. Life insurance is the only product that allows a person to save and protect the risk of living too long or dying too early. There is no other financial product that gives this benefit. There is no need to talk about returns or yield in order to sell life insurance. This is the task of financial analysts not insurance professionals.