Case Study General Findings
Using the same charts as previously, we can make a few judgments about the options presented. For this example, let's assume the company does not want to lose more than $20 million in a fiscal period. This would be considered its risk appetite and is roughly equivalent to maximizing utility for a corporation. By
Exhibit 25.10 Combined Portfolio Modeled Options
Exhibit 25.11 Given Insurance Premiums
Current 
Option #1 
Option #2 
Option #3 
Option #4 
Option #5 

EQ WC GL 
$2,941,765 $ 288,796 $1,359,385 
$2,353,412 $1,098,994 $ 696,302 
$3,618,371 $ 607,957 $ 261,277 
$4,942,165 $ 116,861 $ 68,436 
$6,008,556 $ 64,051 $ 26,041 
$2,941,765 $ 40,630 $ 696,302 
selecting a program that puts the $20 million or more at risk, there is potential for breaching that corporate goal.
Note that the models assume that insurance is recoverable for the risk analyzed. This may not always be the case, so it is important to review coverage and ensure that the model is reflective of the coverage provided and that the insurance carrier's ability to pay is also reviewed.
The numbers and options have been chosen to reflect realistic scenarios. The results are typical of what we see in the insurance and corporate landscape.
Findings on the earthqгake simulation are (see Exhibit 25.12):
• We have a wide variety of options and a wide variety of risk levels.
• The slope of the efficient frontier is very steep as a result.
• The options all lie close to the frontier, resulting in many efficient options.
• If the organization is using a risk appetite for only earthquake risks, then it would look at the efficient frontier below the $20 million tail value at risk level. (Options #3 and #4 qualify.)
Exhibit 25.12 Efficient Frontier on Earthquake Options
Exhibit 25.13 Efficient Frontier on Workers' Compensation Options
Findings on the workers' compensation simulation are (see Exhibit 25.13):
• We have a similar wide variety of options, but a much tighter range of risk levels.
• The slope of the efficient frontier is very shallow as a result.
• The options all lie close to the frontier, resulting in many efficient options.
• If the organization is using a risk appetite for only workers' compensation, then it would look at the efficient frontier below the $20 million tail value at risk level. All options qualify.
• Because workers' compensation risks are relatively stable, the model has only modest differences between options and all options are reasonable.
• To change the options to give a greater range of results, one could be more extreme on the options (assuming the insurance market is willing to provide such options to the corporation).
Findings on the general liability simulation are (see Exhibit 25.14):
• We have a similar wide variety of options, and a modest range of risk levels.
• The slope of the efficient frontier is shallow as a result.
• The options all lie close to the frontier, resulting in many efficient options.
• If the organization is using a risk appetite for only general liabi lity, then it would look at the efficient frontier below the $20 million tail value at risk level. (All options qualify.)
• Similarly to workers' compensation, different options can be substituted here for a wider range of outcomes.
Exhibit 25.14 Efficient Frontier on General Liability Options
The portfolio shown in Exhibit 25.15 is simply the annual events for all three lines added together, again with no correlation assumptions (i.e., independence). Portfolio option #1 is the sum of each of the respective lines Option #1, with no aggregate insurance limitations assumed. The framework certainly allows for aggregations and correlations; we have not provided them here for simplicity.
Exhibit 25.15 Efficient Frontier on the Combined Portfolio Options
Findings on the portfolio simulation are (see Exhibit 25.15):
• The portfolios no longer follow the efficient frontier, as some of the options lie considerably above the efficient frontier line.
• The slope of the efficient frontier is somewhat steep, and follows the risks that contribute to the portfolio (earthquake in this instance is driving the steep curve).
• If the organization is using a risk appetite for the entire portfolio, then it would look at the efficient frontier below the $20 million tail value at risk level. (Only option #4 qualifies.)
We can now see how the efficient frontier insurance framework utilizes the information provided, combines a complex set of insurance structures, and uses a risk appetite to select the best portfolio option. This framework facilitates a company's ability to make factbased decisions, using realtime information. The organization no longer has to wonder if it is getting the best deal or if there were other options that might have provided a better bang for its buck.