The Theoretical Aspects of How Much Insurance Should One Have

It is difficult to put a price tag/value on anyone’s life. However to buy insurance you have to first answer the question of how much insurance should one have. So to put a price to your life, it is important to know your Human Life Value (HLV).

Huebner (1964) postulated that the optimal sum assured for a working individual should be equal to the displacement cost of his life to his family/dependents.  The HLV of a working individual is therefore measured by the discounted present value of expected future earnings over the residual working life minus his own consumption needs.

There is a vast literature that discusses, refines and prescribes it.

The advantages of the HLV concept

Firstly, the idea is borrowed from property insurance and is based on the principle of indemnity.  It therefore seems consistent with insurance precepts.

Secondly, it gives a more or less objective and precise yardstick to quantify the sum assured.

Thirdly, it protects the standard of living of survivors, something that every insured is concerned about.

Having said this, it is possible to raise a number of issues on which the HLV approach provides no guidance.

The critics of the HLV concept

  1. Firstly, any individual’s earning and consumption profile would fluctuate from year to year unless he is in a job like government employment where predictability is high. Should the individual change the amount of insurance as the earning/self maintenance undergo a change?  For example if he falls ill and his medical hospital expenses increase should he reduce the sum assured as the HLV equation above predicts?  Surely no one would do that!  On the contrary, he may be induced to increase his insurance!
  2. Secondly, as his life progresses and his residual working life diminishes so would his human life value. Should he then go on reducing the amount of life insurance in such a way that on retirement he has no life insurance whatsoever because his HLV is zero?  Most customers simply don’t do this.
  3. Thirdly, even granting that a customer’s HLV should equal sum assured, the HLV approach gives no guidance with respect to which life insurance policies should the customer buy; term, endowment, money back? We may tacitly suppose that HLV prescribes the pure term assurance plan, it being the cheapest.  Yet the fact is that in most countries this plan does a miniscule proportion of business.
  4. Fourthly, the HLV approach seems entirely to ignore the fact that customers view life insurance as a vehicle of saving for the future in addition to providing protection. In other words, they attach an opportunity cost to the premiums that they pay.  Yet formula (1) considers only the opportunity cost associated with the net income stream of the individual, not the premiums that he pays and the benefits that he receives under the life insurance policies.

To put it in the words of Borch (1977), “ the idea of Huebner has its origin in property insurance, the real problem in this field is not to evaluate property but to decide if the owner should carry some of the risk himself.  Clearly this decision will depend on the cost of the insurance cover and calls for an economic analysis.  As life insurance is a form of saving it will have to compete with other forms of saving.  The growing interest in portfolio theory over the last two decades has brought much attention to insurance.  Life insurance policies obviously should have a place in the optimal portfolio.  How prominent this place should be will depend on the nature of alternative investments”.

  1. Fifthly, and this point is closely related to the point just made, the HLV approach does not consider the payment capacity of the individual. Can he really afford policies whose sum assured equals HLV after meeting other needs?  Will insurance companies be willing to write these policies?  Although not strictly criticisms of the HLV approach questions like these help to draw attention to the fact that in most societies the actual sum assureds that are bought and sold are much lesser than the human life values.

Therefore, HLV concept must be suitably adjusted :

  • To account for notable changes in income & consumption levels
  • To sync with reducing working life span.
  • To match type of product to specific needs.
  • To take into account that buyers often view insurance as an investment product also.
  • To suit the payment capacity of the individual

See the examples of calculating HLV


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Measurement of Risks and the tradeoff with Returns

The risk return trade-off is based on the principle that potential return rises with an increase in risk. Low levels of uncertainty (low-risk) are associated with low potential returns, whereas high levels of uncertainty (high-risk) are associated with high potential returns.

According to the risk-return tradeoff, invested money can render higher profits only if it is subject to the possibility of being lost.

Fluctuation in returns is used as a measure of risk. Therefore, to measure risk, generally the periodic returns are first worked out, and then their fluctuation is measured. The fluctuation in returns can be assessed in relation to itself, or in relation to some other index. Accordingly, the following risk measures are commonly used.

Variance

Suppose there were two schemes, with monthly returns as follows:

Scheme 1: 5%, 4%, 5%, 6%. Average=5%

Scheme 2: 5%, -10%, +20%, 5% Average=5%

Although both schemes have the same average returns, the periodic (monthly) returns fluctuate a lot more for Scheme 2. Variance measures the fluctuation in periodic returns of a scheme, as compared to its own average return. This can be easily calculated in MS Excel using the following function:

=var(range of cells where the periodic returns are calculated)

Variance as a measure of risk is relevant for both debt and equity schemes.

Standard Deviation

Like Variance, Standard Deviation too measures the fluctuation in periodic returns of a scheme in relation to its own average return. Mathematically, standard deviation is equal to the square root of variance.

This can be easily calculated in MS Excel using the following function:

=stdev(range of cells where the periodic returns are calculated)

Standard deviation as a measure of risk is relevant for both debt and equity schemes.

Beta

Beta is based on the Capital Assets Pricing Model, which states that there are two kinds of risk in investing in equities – systematic risk and non-systematic risk.

Systematic risk is integral to investing in the market; it cannot be avoided. For example, risks arising out of inflation, interest rates, political risks etc.

Non-systematic risk is unique to a company; the non-systematic risk in an equity portfolio can be minimized by diversification across companies. For example, risk arising out of change in management, product obsolescence etc.

Since non-systematic risk can be diversified away, investors need to be compensated only for systematic risk. This is measured by its Beta.

Beta measures the fluctuation in periodic returns in a scheme, as compared to fluctuation in periodic returns of a diversified stock index over the same period.

The diversified stock index, by definition, has a Beta of 1.  Companies or schemes, whose beta is more than 1, are seen as more risky than the market. Beta less than 1 is indicative of a company or scheme that is less risky than the market.

Beta as a measure of risk is relevant only for equity schemes.

Risk-adjusted Returns

Relative returns comparison is one approach to evaluating the performance of the fund manager of a scheme. A weakness of this approach is that it does not differentiate between two schemes that have assumed different levels of risk in pursuit of the same investment objective. Therefore, although the two schemes share the benchmark, their risk levels are different. Evaluating performance, purely based on relative returns, may be unfair towards the fund manager who has taken lower risk but generated the same return as a peer.

An alternative approach to evaluating the performance of the fund manager is through the risk reward relationship. The underlying principle is that return ought to be commensurate with the risk taken. A fund manager, who has taken higher risk, ought to earn a better return to justify the risk taken. A fund manager who has earned a lower return may be able to justify it through the lower risk taken. Such evaluations are conducted through Risk-adjusted returns.

There are various measures of risk-adjusted returns. This workbook focuses on three, which are more commonly used in the market.

Sharpe Ratio

An investor can invest with the government, and earn a risk-free rate of return (Rf). T-Bill index is a good measure of this risk-free return.

Through investment in a scheme, a risk is taken, and a return earned (Rs).

The difference between the two returns i.e. Rs – Rf is called risk premium. It is like a premium that the investor has earned for the risk taken, as compared to government’s risk-free return. This risk premium is to be compared with the risk taken. Sharpe Ratio uses Standard Deviation as a measure of risk. It is calculated as (Rs minus Rf) ÷ Standard Deviation. Thus, if risk free return is 5%, and a scheme with standard deviation of 0.5 earned a return of 7%, its Sharpe Ratio would be (7% – 5%) ÷ 0.5 i.e. 4%. Sharpe Ratio is effectively the risk premium per unit of risk. Higher the Sharpe Ratio, better the scheme is considered to be. Care should be taken to do Sharpe Ratio comparisons between comparable schemes. For example, Sharpe Ratio of an equity scheme is not to be compared with the Sharpe Ratio of a debt scheme.

Treynor Ratio

Like Sharpe Ratio, Treynor Ratio too is a risk premium per unit of risk. Computation of risk premium is the same as was done for the Sharpe Ratio. However, for risk, Treynor Ratio uses Beta.

Treynor Ratio is thus calculated as: (Rf minus Rs) ÷ Beta

Thus, if risk free return is 5%, and a scheme with Beta of 1.2 earned a return of 8%, its Treynor Ratio would be (8% – 5%) ÷ 1.2 i.e. 2.5%.

Higher the Treynor Ratio, better the scheme is considered to be. Since the concept of Beta is more relevant for diversified equity schemes, Treynor Ratio comparisons should ideally be restricted to such schemes.

Alpha

The Beta of the market, by definition is 1. An index scheme mirrors the index. Therefore, the index scheme too would have a Beta of 1, and it ought to earn the same return as the market. The difference between an index fund’s return and the market return, as seen earlier, is the tracking error.

Non-index schemes too would have a level of return which is in line with its higher or lower beta as compared to the market. Let us call this the optimal return.

The difference between a scheme’s actual return and its optimal return is its Alpha – a measure of the fund manager’s performance. Positive alpha is indicative of out-performance by the fund manager; negative alpha might indicate underperformance.

Since the concept of Beta is more relevant for diversified equity schemes, Alpha should ideally be evaluated only for such schemes.

These quantitative measures are based on historical performance, which may or may not be replicated.

Such quantitative measures are useful pointers. However, blind belief in these measures, without an understanding of the underlying factors, is dangerous. While the calculations are arithmetic – they can be done by a novice; scheme evaluation is an art – the job of an expert.


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