Diversification is a risk management technique that mixes a wide variety of investments within a portfolio. The rationale behind this technique contends that a portfolio of different kinds of investments will, on average, yield higher returns and pose a lower risk than any individual investment found within the portfolio.
Diversification strives to smooth out unsystematic risk events in a portfolio so that the positive performance of some investments will neutralize the negative performance of others. Therefore, the benefits of diversification will hold only if the securities in the portfolio are not perfectly correlated.
Pooling simply refers to the spreading losses incurred by the few over the entire group so that the average loss is substituted for actual loss. This is the situation where the actual role of underwriters and actuaries can be seen.
We see that the loss of an individual in spread across the entire group. Through insurance and diversification of the portfolio one can reduce the risk levels.
Pooling Arrangements
Basic Idea
Replace your loss with the average loss of a group
Issues
What happens to each person's
Expected loss
Standard deviation of loss
Maximum probable loss
How do these results change with
More participants
Correlation in losses among the participants increases
There are certain assumptions we have to take:
The Pool consists of a group of risks that are:
Relatively homogenous
Losses to which the group is subjected are accidental, not intentional
Costs of Pooling Arrangements
Pooling arrangements reduce risk, but they involve costs:
Adding Participants
marketing
underwriting
Loss adjustment expenses
Verifying Losses
Collecting Assessments
The contracting costs incurred when an insurer investigates and attempts to determine the value of loss claim made against the risk-pool are called loss adjustment expenses.
Two Person Pooling Arrangements
This is the type of risk division where losses of one are borne by another also. Here the losses are divided among two people.
Risk sharing or pooling arrangements are at the base of insurance. Here a number of individuals, each carrying a certain risk Yi, will agree to enter their risks into a pool with a total risk Y = ∑iYi, and the i'th individual will in exchange receive a share of the pool as illustrated in the figure given below. If we assume that the pool transfers the risk to another insurer then the pool will pay a premium exceeding the expected value E(Y). We assume the (re)insurer calculates the premium according to a premium principle of the form:
π = EY + αC(Y)
where C is some risk measure.
The essence of this assumption is that the premium is calculated from the distribution of the total risk Y. Now the premium is to be paid by the individuals participating in the pool according to some allocation scheme. From the expression we see that since the expected value is linear, this comes down to finding a way to share the loading αC(Y) between the participants in the pool. The individual premiums πi will then be given by:
Πi = EYi + αA(YijY1; : : : ; Yn );
where A(YijY1; : : : ; Yn) is the risk allocated to individual i from the group consisting of risks Y1; : : : ; Yn.
From the above the analogy between the allocation of premium loading and the allocation of Economic Capital is obvious. In an EC framework the reinsurer is the owner of the company asking for some return proportional to the EC. The actuarial safety loading _ is the "market price of risk" charged by the owners for taking on the risk of having capital in the company. By calculating the contribution to the pool by using the above equation the individual risks are therefore charged with the same price per unit of allocated risk.
For this we can look at an example:
Question
Two people with same distribution
Outcome Probability
Rs. 2,500 0.20
Loss =
$0 0.80
Assume losses are uncorrelated
So we need to find the Expected value and the Standard deviation
Solution
Pooling Arrangement changes distribution of accident costs for each individual
Outcome Probability
Rs. 0 (.8)(.8) = .64
Cost = Rs. 1,250 (.2)(.8)(2) =.32
Rs. 2,500 (.2)(.2) = .04
Therefore Expected Cost = (1250 * .32) + (2500*.04) = Rs. 500
Effect on Expected Loss
w/o pooling, expected loss = Rs. 500
with pooling, expected loss = Rs. 500
Effect on Standard Deviation
w/o pooling, standard. deviation = Rs. 1000
with pooling, standard. deviation = Rs. 707
Pooling Arrangements with Many People
The pooling arrangement can be done with many people also where the losses are divided or spread through more than 2 people.
Below in this graph we can see the distribution of losses with 4 participants and also for 20 participants.
Risk Pooling of Uncorrelated Losses
The Pooling arrangements
do not change expected loss
reduce uncertainty (variance decreases, losses become more predictable, maximum probable loss declines)
distribution of costs becomes more symmetric (less skewness)
Risk Pooling of Correlated Losses
Now allow correlation in losses
Result: uncertainty is not reduced as much
Intuition:
What happens to one person happens to others
One person's large loss does not tend to be offset by others' small losses
Therefore pooling does not reduce risk as much
We can see the effect of positive correlation on the quantum of risk reduction in the diagram below:
har39705_0404
Insurance as a Risk Pooling Arrangement
Insurance company's uses risk pool as a method to control the risk of insuring against catastrophic events or extending insurance to individuals or businesses likely to create sizable claims. If a claim arises from a natural disaster or catastrophic weather event such as a hurricane, the companies spread the losses among all members, and single members of the risk pool are protected from claims so large they would bankrupt the company, leaving their claimants with nothing.
Catastrophic Risk Pools
A Risk pool must be created by all the insurance companies. The risk pool must cover claims in the same category, such as fire or flood, and in a specific geographic area, usually an entire state. In the event of a natural disaster such as an earthquake or hurricane, the insurance companies participating in the risk pool draw on the assets of the pool, in an amount determined by the agreement, and are protected from paying out hundreds or thousands of expensive claims on their own. Many countries have formed public/private risk pools, with tax revenue going to support the viability of the risk pool joined by individual companies. This arrangement helps private insurers to carry out business in the location and provide more competitive premiums to individual customers. This helps the individual clients a lot to reduce the risk.
Auto Risk Pools
In car insurance, high-risk drivers with a record of accidents or traffic violations are sometimes forced to buy insurance (which is required by law) from an assigned-risk pool. By state laws, insurance companies must accept a certain percentage of these high-risk customers. Most of these risk pools are administered by a public office and a board of insurance company representatives. Rates are set by the state's department of insurance and vary according to the age, location and driving record of the individual. After a period of three years, those with clean driving records are allowed to return to the private insurance market.
Health Risk Pools
A health insurance risk pool is a public insurance program created by state legislatures. These programs can be used by people who have a hard time buying conventional health insurance on their own, due to their low income or serious pre-existing medical conditions. A health reform law signed in 2010 allowed for the states to participate in a federal risk pool to benefit the uninsured. In exchange, the central government will provide aid to the states for their public health insurance programs.
Waiting Period
To discourage potential insurance buyers from waiting until they have a serious medical condition to obtain coverage, most health insurance risk pools impose a waiting period for those with pre-existing conditions. A new federal law allows those who have already had group health insurance within the last 63 days to buy coverage from the risk pool without a waiting period.
Costs
Premiums are higher for health insurance purchased from a state-operated risk pool, even though this form of insurance is subsidized by taxes or assessments on private insurers doing business in the state. The laws in each state cap the premiums for risk pool health coverage to a certain percentage, from 125 to 200 percent, of the average premium for private health insurance.
Moral Hazards in Risk Pooling Arrangements
A common element of each of the risk-sharing arrangements mentioned above is that the organizations are effectively owned by their policyholders. That is, the policyholders share their risk exposures through the organization but retain exposure to the risk of the pool through their equity positions. Many of these risk pools are quite small, suggesting that the risk retained through the ownership interest in the pool may be significant. Standard insurance companies use the law of large numbers to dissipate unsystematic risk. If risk pools are small, then unsystematic risk may not be fully diversified away in such pools. Also, capital market theory suggests that the optimal portfolio holding is a value weighted portfolio of all risky assets. Stock insurance companies can spread systematic risk over all investors in the capital market, thus spreading systematic risk in accordance with capital market theory. A risk pool can spread the systematic risk of the pool only across its membership, and thus the pool involves a sub-optional sharing of systematic risk. Consequently, there must be some advantage offered by the risk pooling arrangements to offset their inferior risk-sharing capacity in order for them to be viable institutions. This study considers the role of risk pooling arrangements in controlling problems of moral hazard.
Moral hazard refers to a problem of asymmetric information in which the actions of one or more parties affect the outcome of a particular economic situation and the actions are not verifiable by other members of the economy. In an insurance context, moral hazard refers to a reduced incentive for loss prevention or loss reduction by insured individuals. When monitoring is impractical, the optimal market response to moral hazard is generally partial insurance coverage.
A principal focus of this analysis is the role of size in a risk pool with moral hazard. While it may be quite intuitive that an increase in the number of pool members would tend to decrease the loss-prevention effort levels of the members, verifying this intuition is not trivial. The results here on the effect of pool size on effort suggest that moral hazard may place constraints on the optimal size of such pools.
Stock Market Pooling through Portfolio
We have often heard of the proverb 'Don't put all your eggs in one basket', which connotes to the fact that diversification had many advantages. If you carry your breakable items in several baskets there is a chance that one will be dropped, but you are unlikely to drop all your baskets on the same trip. Similarly, if you invest all your wealth in the shares of one company, there is a chance that the company will go bust and you will lose all your money. Since it is unlikely that all companies will go bust at the same time, a portfolio of shares in several companies is less risky. This is what we call risk pooling through diversification as the losses can be made up with the profits in other stocks.
Diversified portfolios may produce combinations of risk and return that dominate non-diversified portfolios.
This is an important statement that requires a little closer investigation. That investigation will help to identify the circumstances under which diversification is beneficial. It will also clarify what we mean by the word 'dominate'.
The table below sets out two simple examples. In both there are two assets that an investor can hold, and there are two possible situations which are assumed to be equally likely. Thus, there is a probability of 0.5 attached to each situation and the investor has no advance knowledge of which is going to happen. The two situations might be a high exchange rate and a low exchange rate, a booming and a depressed economy, or any other alternatives that have different effects on the earnings of different assets.
Combinations of risk and return
Situation 1
Situation 2
(i) Returns are negatively correlated
Asset A
10.00%
30.00%
Asset B
30.00%
10.00%
(i) Returns are positively correlated
Asset A
10.00%
30.00%
Asset B
0.00%
40.00%
Assets differ in expected return and variability in returns. Part (i) illustrates the return on two assets in two different situations. Asset A has a high return in situation 2 and a low return in situation 1. The reverse is true for asset B. A portfolio of both assets has the same expected return but lower risk than a holding of either asset on its own. In (ii) both assets have a high return in situation 2 and a low return in situation 1. For the risk-averse investor asset A dominates asset B.
Consider part (i) of the table. In this case both assets have the same expected return (20 per cent) and the same degree of risk. (The possible range of outcomes is between 10 and 30 per cent on each asset.) If all that mattered in investment decisions were the risk and return of individual shares, the investor would be indifferent between assets A and B. Indeed, if the choice were between holding only A or only B, all investors should be indifferent (whether they were risk-averse, risk-neutral, or risk-loving) because the risk and expected return are identical for both assets. However, this is not the end of the story, because the returns on these assets are not independent. Indeed, there is a perfect negative correlation between them: when one is high the other is low, and vice versa.
What would a sensible investor do if permitted to hold some combination of the two assets? Clearly, there is no possible combination that will change the overall expected return, because it is the same on both assets. However, holding some of each asset can reduce the risk. Let the investor decide to hold half his wealth in asset A and half in asset B. His risk will then be reduced to zero, since his return will be 20 per cent whichever situation arises. This diversified portfolio will clearly be preferred to either asset alone by risk-averse investors. The risk-neutral investor is indifferent to all combinations of A and B because they all have the same expected return, but the risk-lover may prefer not to diversify. This is because, by picking one asset alone, the risk-lover still has a chance of getting a 30 per cent return and the extra risk gives positive pleasure.
Lessons from the study
Pooling reduces each participant's risk (i.e., costs from loss exposure become more predictable)
Predictability increases with the number of participants
Predictability decreases with correlation in losses
Pooling arrangements does reduce the risk element but a cost comes with it.
There is a positive correlation on the amount of risk reduction.
Insurance is a good method of risk diversification but comes with costs and moral hazards.
In the stock market through proper portfolio creation one can reduce the risks considerably.
Conclusion
The main economic function of insurance institutions is to provide an efficient mechanism for economizing on contracting costs associated with pooling of losses.
Insurance pools and well diversified stock portfolios are, in principle, nearly similar. Both are mechanisms for reducing risk. Predicting the outcome of a set of pooled (and uncorrelated) risks can be done more reliably than predicting the outcome of a single risk. The larger the number of risks in the pool, the smaller is the variance of expected outcomes.
The amount of risk that can be reduced through pooling arrangements increases as the number of participant's increases, all other factors equal. The expected cost of risk per participant will stay the same.
A lot of costs and other moral hazards exist while doing risk diversification but that can be traded off with the returns from such an exercise. This risk pooling is often done by the risk averse investors.
MCQ's
Which of the following is not a type of contracting cost associated with the creation and operation of pooling arrangements?
distribution costs
underwriting expenses
premiums
loss adjustment expenses
Insurers that rely, to some degree, on exclusive agents to sell their policies are known as:
mutuals
direct writers
independents
brokers
The process of identifying (or estimating) a potential insurance buyer's expected loss is known as:
underwriting
risk management
loss adjusting
insurance distribution
Under what circumstance will a pooling arrangement result in reduced risk (standard deviation) to the participants in the pool
only when losses are perfectly positively correlated
when losses are high
only when losses are negatively correlated
whenever losses are less than perfectly positively correlated
Risk-pooling arrangement
reduce the risk faced by each member of the risk-pool
increase the likelihood of small loss events
are used only for liability exposures
will decrease expected loss for members of the risk pool
ABC Limited and PQR Limited both have the following loss distribution.
Use this information to answer questions 6 through 8.
Loss Possibility
Loss Probability
Rs. 0
.90
Rs. 4,000
.10
If ABC and PQR form a pooling arrangement to share losses, what is the expected loss for each of them after the pool is formed?
$500
$450
$400
$360
If ABC and PQR form a pooling arrangement to share losses, what is the variance of expected losses for each of them after the pool is formed?
$28
$280
$800
$4000
Which one of the following effects occurs when Dresden and Morgan form a risk-pool to share losses?
Their individual expected loss decreases, while the variance increases
Their individual expected loss increases, while the variance decreases
Their individual expected loss stays the same, while the variance increases
Their individual expected loss stays the same, while the variance decreases
The formation of risk pools by insurers is the same, in principle, as:
reducing expected losses through the use of safety equipment
creating a well-diversified portfolio of stock shares
using the futures markets to hedge against fluctuations in the exchange rate of a particular foreign currency
agreeing to an assessment premium
The contracting costs incurred when an insurer investigates and attempts to determine the value of loss claim made against the risk-pool are called
distribution costs
premiums
underwriting expenses
loss adjustment expenses
The main (economic) reason for the existence of insurance companies is:
individuals need to diversify risk
insurers' ability to predict individual losses
insurers' ability to form efficient risk pools with minimal contracting costs
individuals inability to determine expected loss
Which of these is not part of insurance risk pools?
Health
Auto
Travel
Catastrophe
MCQ Key
1
2
3
4
5
6
7
8
9
10
11
12
SHORT ANSWER QUESTIONS
What do we mean by pooling?
What are the different issues in pooling arrangements?
What are the costs of pooling arrangements?
Suppose that L is a random variable equal to property losses from a hurricane and that L has the following probability distribution:
Loss
Probability
Rs. 90000
0.01
L =
Rs. 10000
0.05
Rs. 0
0.94
What is the expected value of hurricane losses?
What is risk pooling of correlated losses?
What are the costs in insurance risk pooling arrangements?
How does portfolio diversification help in risk pooling?
LONG ANSWER QUESTIONS
Assume that property losses for XYZ company have the following distribution:
Loss
Probability
Rs. 3000000
0.005
Loss =
Rs. 1500000
0.01
Rs. 800000
0.025
Rs. 0
0.96
What is the expected value of property losses?
Assume that XYZ company determines that its liability losses have the following distribution:
Loss
Probability
Rs. 5000000
0.002
Loss =
Rs. 1500000
0.015
Rs. 500000
0.04
Rs. 0
0.943
What is the expected value of liability losses?
Do you think that XYZ company's property losses are independent, positively correlated, or negatively correlated with its liability losses?
In insurance what are the different types of risk pools?
What are the advantages and disadvantages of risk pooling arrangements?
