# How much risk can your company stand?

Each year risk managers must choose an appropriate retention level
for their risk financing program. But finding the right level is like
walking a tightrope because premium cost savings must be cautiously
balanced against the risk of financial loss. As with the acrobat, this
balancing act can be highly profitable for the risk manager if there is
enough thorough preparation.

There is more than straightforward financial analysis involved in setting the right retention level. The evaluation of an organization's risk-bearing capacity should also include a close look at the nature of the businesses conducted by the organization and management's tolerance for risk. Furthermore, risk managers must ensure that their activities do not impair the organization's objectives, and perhaps even further them. They must also ascertain whether sufficient resources are available to implement the desired risk financing program.

Traditional Methods

A common method used to evaluate risk retention capacity involves taking the weighted average of different components of a company's resources such as assets, working capital and shareholders' equity. However, this method is incomplete because it does not respond to changing business conditions. Furthermore, the approach can be trivialized by a seemingly random application of weights. For example, is a 14 percent weighting for working capital more appropriate for one company than a 10 percent weighting? Should the same percentage be used for all organizations so that no allowance is made for their different operations?

Even if these weightings reflect the level of corporate resources available for risk financing, this approach is still flawed because measures of liquidity, profitability and financial strength should be viewed as separate constraints to risk retention instead of measures mixed in some haphazard financial alchemy. Retention levels would then be determined by optimizing the financial return given a set of constraints.

Another approach uses utility functions in which the appropriate retention level maximizes an agreed upon utility function using predetermined variables and constraints. However, this more sophisticated approach has one fundamental drawback: It is good in theory but impractical to use. To describe a utility function in mathematical terms, one must do three things: identify the variables, make assumptions about their probability distributions and determine constraints. Generally, the more assumptions that are made, the less valid the output. Furthermore, there is always the problem of identifying all the relevant variables and constraints.

A Practical Approach

The Self Insurance Retention Analysis Method (SIRAM) is a practical three-step approach developed by the authors to determine an appropriate retention level. It entails applying investment analysis techniques to risk retention decisions, which involve improved cash flow but increased risk.

A risk manager investigating the desirability of a higher retention would no doubt consider the tradeoff between premium savings and increased self-insured losses and risk at higher retentions. This characteristic is illustrated in the Loss Analysis graph shown above.

Therefore, the analysis starts by determining the required minimum premium discount, which is the break-even premium savings required to adequately compensate the company for changing its retention level. This break-even discount consists of two components; the net present value (NPV) of the change in expected losses and an adjustment for the change in risk.

The NPV of expected losses is used because the full effect of the increase in expected costs is not felt, since funds are retained by the organization until they are paid out in claims and, hence, can be used for income-generating activities. Therefore, the premium savings should at least be equal to the NPV of the change in expected self-insured losses.

One must also consider the change in risk, which increases with higher retentions. While risk is defined here as the difference between losses under a worst-case scenario and expected losses, the increase in risk can also be viewed as the amount of additional capital the company has exposed by increasing its level of self insurance. To compensate the company for assuming greater risk, a further reduction in premium is necessary.

What is an adequate return on the company's exposed capital? The authors believe that a reasonable measure of return is a risk premium factor equal to the difference between the company's return on investment and its cost of capital. This ensures that the company will earn the same return on the capital at risk as it earns on other investments.

This risk premium factor, instead of other financial measures such as the return on investment, is applied to the excess of worst case over expected losses because, although capital is not being used, it is nevertheless exposed. That is, capital must be available to finance retained losses above the expected level of losses. The ratio of pretax earnings to equity is sometimes used as a proxy for a company's pretax return on investment. The net of this ratio and the company's cost of capital, what has been referred to as the risk premium factor, is the percentage applied to the increased risk of adverse loss experience.

This calculation is added to the change in the NPV of expected self-insured losses to arrive at the required minimum premium discount. The Required Discount graph on page 86 illustrates this concept. For example, in evaluating an increase in retention from a $250,000 retention to a $500,000 retention, the required minimum premium discount is $552,076. This calculation is based on the following pretax assumptions: (1) expected losses of $1,605,000 and $2,153,000 at the $250,000 and $500,000 retentions, respectively. Simple subtraction would yield an increase in self-insured losses of $548,000 as a result of the increased retention; (2) "worst-case" scenario losses (defined as the level of losses that occur once in 20 years) of $2,515,000 and $3,614,000 at the two retentions. Subtracting these adverse scenarios from the expected losses would yield a risk of $910,000 and $1,461,000 at these retentions. This implies that increasing retentions would cause self-insured risk to increase by $551,000; (3) a risk premium factor of 8 percent based on the difference between an 18 percent return on investment and a 10 percent cost of capital; (4) a payout schedule of 70 percent in the first year and 30 percent in the second year (the effect is that NPV of losses is 92.7 percent of the actual magnitude). The effect of the payout schedule is more pronounced with longer tailed coverages.

Selecting an appropriate risk premium factor is a flexible process. The idea is to use a measure that adequately reflects the company's risk return profile. The risk premium factor should be adjusted to reflect other characteristics of the organization, its industry and the self-insured coverages. For example, if the company is highly leveraged, the ratio of earnings before interest and taxes to equity may be used as a proxy for the return required by the corporation, instead of the more commonly used ratio of pretax earnings to equity.

To summarize, the required minimum premium discount is the sum of (1) the difference in expected losses between the proposed and current retention levels, discounted at the organization's cost of capital, and (2) the difference between worst case and expected losses (the risk) at the proposed retention minus the difference at the current retention, multiplied by the risk premium factor. This is the minimum premium savings the organization would need for the new retention level to cost effectively balance the trade-off between cost savings and increased risk.

Risk management expenses can also be included in the cost of risk at various retention levels. The inclusion of such expenses makes the analysis more complete but is not essential since the major portion of risk management expenses is fixed.

The second step in the SIRAM approach is to compare the premium discounts implicit in actual market quotations for alternative retention levels to the required minimum premium discounts. The difference is the market-offered real discount for moving to a higher retention level. Using the previous example of a company analyzing the cost effectiveness of changing from the $250,000 retention to the $500,000 retention, a market offered premium savings of $499,000 should be compared to the required minimum premium savings of $522,076. Using the SIRAM approach, the real premium discount is a negative $53,076. That is, it is not cost effective to choose the $500,000 retention with the hypothetical market quote. A positive real premium discount would have implied that it would be cost efficient for the company to assume the proposed retention.

A company can select any retention level for which there is a positive SIRAM risk-adjusted saving, since the firm will earn an adequate return on the exposed capital.

The final SIRAM step involves comparing the savings with the change in risk. This step is only necessary if there are positive real premium savings at more than one proposed retention. The real discount is compared to the increased risk of adverse loss experience associated with moving to a higher retention as shown in the Actual and Required Discounts graph on page 88.

Although one could argue that the retention level with the greatest dollar savings is the most appropriate, it could also be argued that the retention level with the highest ratio of real savings to increase in risk is the optimal level because it has the shortest payback period. The question boils down to whether a large dollar savings with a marginal rate of return is better than a small dollar savings with a high rate of return on change in risk. The decision-maker would have to judge these differences based on how sensitive the analysis is to the underlying assumptions contained in the market quotes and discount rates.

Implementation

Once the right retention level has been identified, the risk manager should evaluate the financing requirements, which will be compared to alternative projects to determine the best use of company resources. The company's overall financial performance is modeled using pro forma projections for the coming year combined with information from past years. This facilitates assessing the impact of different loss scenarios on the company's financial performance and enhances financial planning to meet project cash flow needs.

Management is thus able to evaluate loss projections and their inherent uncertainty in light of budgets and key financial ratios. They may also able to compare the company's projected financial performance with that of its competitors. Rarely is the risk retained under a risk financing program so great that it jeopardizes these financial ratios.

Like other analytical methods, SIRAM has been developed to simplify the actual risk return situation by providing a quantitative result on which a decision may be taken regarding risk retention in the majority of situations. SIRAM relies on actuarial loss projections and, therefore, is affected by factors that make actuarial loss forecasting less reliable. Two circumstances impacting the reliability of all risk retention decisions are loss exposures with low frequency characteristics and catastrophic incidents, such as earthquakes, that cause simultaneous losses across several lines of coverage. Although beyond the scope of this article, the authors have developed techniques which may be used in conjunction with SIRAM to make the necessary adjustments to the risk retention decision.

SIRAM is different from standard investment decision techniques because the risk component is isolated from the expected loss component. The expected cost is discounted at the organization's cost of capital, which is normally the cost of borrowing, while the risk of adverse losses is multiplied by a rate equivalent to the net of the company's return on investment and its cost of capital. Therefore, the full exposure of capital is considered although there is no cash outflow at the expected case.

In contrast, in most investment decision techniques, the discount rate is increased to allow for increased risk and applied to all anticipated cash flows. This often leads to underestimating the impact of future cash outflows because they have been discounted at a higher rate. The effect of increasing discount rates to adjust for increased risk implies a more favorable picture than is really the case.

The authors believe that the core elements of SIRAM-the calculation of a required minimum premium discount, the use of a risk premium factor to adjust for increased uncertainty and the use of the real market-offered premium savings-represent a practical, easy-to-use tool for identifying the appropriate retention level. While there is no doubt that improvements can be made to the analysis, this approach is applicable in most circumstances.

There is more than straightforward financial analysis involved in setting the right retention level. The evaluation of an organization's risk-bearing capacity should also include a close look at the nature of the businesses conducted by the organization and management's tolerance for risk. Furthermore, risk managers must ensure that their activities do not impair the organization's objectives, and perhaps even further them. They must also ascertain whether sufficient resources are available to implement the desired risk financing program.

Traditional Methods

A common method used to evaluate risk retention capacity involves taking the weighted average of different components of a company's resources such as assets, working capital and shareholders' equity. However, this method is incomplete because it does not respond to changing business conditions. Furthermore, the approach can be trivialized by a seemingly random application of weights. For example, is a 14 percent weighting for working capital more appropriate for one company than a 10 percent weighting? Should the same percentage be used for all organizations so that no allowance is made for their different operations?

Even if these weightings reflect the level of corporate resources available for risk financing, this approach is still flawed because measures of liquidity, profitability and financial strength should be viewed as separate constraints to risk retention instead of measures mixed in some haphazard financial alchemy. Retention levels would then be determined by optimizing the financial return given a set of constraints.

Another approach uses utility functions in which the appropriate retention level maximizes an agreed upon utility function using predetermined variables and constraints. However, this more sophisticated approach has one fundamental drawback: It is good in theory but impractical to use. To describe a utility function in mathematical terms, one must do three things: identify the variables, make assumptions about their probability distributions and determine constraints. Generally, the more assumptions that are made, the less valid the output. Furthermore, there is always the problem of identifying all the relevant variables and constraints.

A Practical Approach

The Self Insurance Retention Analysis Method (SIRAM) is a practical three-step approach developed by the authors to determine an appropriate retention level. It entails applying investment analysis techniques to risk retention decisions, which involve improved cash flow but increased risk.

A risk manager investigating the desirability of a higher retention would no doubt consider the tradeoff between premium savings and increased self-insured losses and risk at higher retentions. This characteristic is illustrated in the Loss Analysis graph shown above.

Therefore, the analysis starts by determining the required minimum premium discount, which is the break-even premium savings required to adequately compensate the company for changing its retention level. This break-even discount consists of two components; the net present value (NPV) of the change in expected losses and an adjustment for the change in risk.

The NPV of expected losses is used because the full effect of the increase in expected costs is not felt, since funds are retained by the organization until they are paid out in claims and, hence, can be used for income-generating activities. Therefore, the premium savings should at least be equal to the NPV of the change in expected self-insured losses.

One must also consider the change in risk, which increases with higher retentions. While risk is defined here as the difference between losses under a worst-case scenario and expected losses, the increase in risk can also be viewed as the amount of additional capital the company has exposed by increasing its level of self insurance. To compensate the company for assuming greater risk, a further reduction in premium is necessary.

What is an adequate return on the company's exposed capital? The authors believe that a reasonable measure of return is a risk premium factor equal to the difference between the company's return on investment and its cost of capital. This ensures that the company will earn the same return on the capital at risk as it earns on other investments.

This risk premium factor, instead of other financial measures such as the return on investment, is applied to the excess of worst case over expected losses because, although capital is not being used, it is nevertheless exposed. That is, capital must be available to finance retained losses above the expected level of losses. The ratio of pretax earnings to equity is sometimes used as a proxy for a company's pretax return on investment. The net of this ratio and the company's cost of capital, what has been referred to as the risk premium factor, is the percentage applied to the increased risk of adverse loss experience.

This calculation is added to the change in the NPV of expected self-insured losses to arrive at the required minimum premium discount. The Required Discount graph on page 86 illustrates this concept. For example, in evaluating an increase in retention from a $250,000 retention to a $500,000 retention, the required minimum premium discount is $552,076. This calculation is based on the following pretax assumptions: (1) expected losses of $1,605,000 and $2,153,000 at the $250,000 and $500,000 retentions, respectively. Simple subtraction would yield an increase in self-insured losses of $548,000 as a result of the increased retention; (2) "worst-case" scenario losses (defined as the level of losses that occur once in 20 years) of $2,515,000 and $3,614,000 at the two retentions. Subtracting these adverse scenarios from the expected losses would yield a risk of $910,000 and $1,461,000 at these retentions. This implies that increasing retentions would cause self-insured risk to increase by $551,000; (3) a risk premium factor of 8 percent based on the difference between an 18 percent return on investment and a 10 percent cost of capital; (4) a payout schedule of 70 percent in the first year and 30 percent in the second year (the effect is that NPV of losses is 92.7 percent of the actual magnitude). The effect of the payout schedule is more pronounced with longer tailed coverages.

Selecting an appropriate risk premium factor is a flexible process. The idea is to use a measure that adequately reflects the company's risk return profile. The risk premium factor should be adjusted to reflect other characteristics of the organization, its industry and the self-insured coverages. For example, if the company is highly leveraged, the ratio of earnings before interest and taxes to equity may be used as a proxy for the return required by the corporation, instead of the more commonly used ratio of pretax earnings to equity.

To summarize, the required minimum premium discount is the sum of (1) the difference in expected losses between the proposed and current retention levels, discounted at the organization's cost of capital, and (2) the difference between worst case and expected losses (the risk) at the proposed retention minus the difference at the current retention, multiplied by the risk premium factor. This is the minimum premium savings the organization would need for the new retention level to cost effectively balance the trade-off between cost savings and increased risk.

Risk management expenses can also be included in the cost of risk at various retention levels. The inclusion of such expenses makes the analysis more complete but is not essential since the major portion of risk management expenses is fixed.

The second step in the SIRAM approach is to compare the premium discounts implicit in actual market quotations for alternative retention levels to the required minimum premium discounts. The difference is the market-offered real discount for moving to a higher retention level. Using the previous example of a company analyzing the cost effectiveness of changing from the $250,000 retention to the $500,000 retention, a market offered premium savings of $499,000 should be compared to the required minimum premium savings of $522,076. Using the SIRAM approach, the real premium discount is a negative $53,076. That is, it is not cost effective to choose the $500,000 retention with the hypothetical market quote. A positive real premium discount would have implied that it would be cost efficient for the company to assume the proposed retention.

A company can select any retention level for which there is a positive SIRAM risk-adjusted saving, since the firm will earn an adequate return on the exposed capital.

The final SIRAM step involves comparing the savings with the change in risk. This step is only necessary if there are positive real premium savings at more than one proposed retention. The real discount is compared to the increased risk of adverse loss experience associated with moving to a higher retention as shown in the Actual and Required Discounts graph on page 88.

Although one could argue that the retention level with the greatest dollar savings is the most appropriate, it could also be argued that the retention level with the highest ratio of real savings to increase in risk is the optimal level because it has the shortest payback period. The question boils down to whether a large dollar savings with a marginal rate of return is better than a small dollar savings with a high rate of return on change in risk. The decision-maker would have to judge these differences based on how sensitive the analysis is to the underlying assumptions contained in the market quotes and discount rates.

Implementation

Once the right retention level has been identified, the risk manager should evaluate the financing requirements, which will be compared to alternative projects to determine the best use of company resources. The company's overall financial performance is modeled using pro forma projections for the coming year combined with information from past years. This facilitates assessing the impact of different loss scenarios on the company's financial performance and enhances financial planning to meet project cash flow needs.

Management is thus able to evaluate loss projections and their inherent uncertainty in light of budgets and key financial ratios. They may also able to compare the company's projected financial performance with that of its competitors. Rarely is the risk retained under a risk financing program so great that it jeopardizes these financial ratios.

Like other analytical methods, SIRAM has been developed to simplify the actual risk return situation by providing a quantitative result on which a decision may be taken regarding risk retention in the majority of situations. SIRAM relies on actuarial loss projections and, therefore, is affected by factors that make actuarial loss forecasting less reliable. Two circumstances impacting the reliability of all risk retention decisions are loss exposures with low frequency characteristics and catastrophic incidents, such as earthquakes, that cause simultaneous losses across several lines of coverage. Although beyond the scope of this article, the authors have developed techniques which may be used in conjunction with SIRAM to make the necessary adjustments to the risk retention decision.

SIRAM is different from standard investment decision techniques because the risk component is isolated from the expected loss component. The expected cost is discounted at the organization's cost of capital, which is normally the cost of borrowing, while the risk of adverse losses is multiplied by a rate equivalent to the net of the company's return on investment and its cost of capital. Therefore, the full exposure of capital is considered although there is no cash outflow at the expected case.

In contrast, in most investment decision techniques, the discount rate is increased to allow for increased risk and applied to all anticipated cash flows. This often leads to underestimating the impact of future cash outflows because they have been discounted at a higher rate. The effect of increasing discount rates to adjust for increased risk implies a more favorable picture than is really the case.

The authors believe that the core elements of SIRAM-the calculation of a required minimum premium discount, the use of a risk premium factor to adjust for increased uncertainty and the use of the real market-offered premium savings-represent a practical, easy-to-use tool for identifying the appropriate retention level. While there is no doubt that improvements can be made to the analysis, this approach is applicable in most circumstances.

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Author: | Scott, David; Sathianathan, Raghavan |
---|---|

Publication: | Risk Management |

Date: | Jun 1, 1991 |

Words: | 2073 |

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