Teaching introductory concepts of insurance company management: a simulation game.

The article describes the learning objectives and outcomes of a computer game that simulates an insurance market. Students integrate accounting, finance, risk management and insurance, asset management and investment topics. Students experience competitive interaction in the product and bond markets and the intra-firm stresses of marketing, investment and production activities.

Introduction

This article describes an application of student-centered learning using software to simulate the operations of a property-liability insurance company. (1) The application is a decision-making game used in Risk Management and Insurance classes. The game simulates the operations of a property-liability insurance company and the competition of firms in the insurance market. Students develop an appreciation for the interaction of the decisions of insurance company managers operating under the simulated uncertainty of market and economic conditions.

Learning Objectives

Students develop an appreciation for the complexity of financial management decisions in the context of the ongoing operations of an insurance company. The game develops a feel for the interaction of management decisions and market stress. While it is not industry-specific, some insurance concepts are developed as part of the game -- and the game is more easily understood by those with an interest in the financial services industry.

Students develop an appreciation for the interaction between management forecasts of economic performance and firm-level investment outcomes. Students predict the stock market's performance in the following week in order to develop their current investment strategy. Bad forecasts may be penalized through the competitive nature of the game.

Students develop an appreciation for the interaction between intra-firm decisions affecting investment risk levels, product (underwriting) risk levels and product pricing. A firm that chooses extreme, but opposite, risk levels may perform well through luck, but a system shock may induce financial distress. However, a firm that "plays it safe" in balancing risk levels may not be able to compete effectively on product price.

Students develop an understanding of how managerial decisions affect a firm's performance in a multi-period setting. For example, firms that do not invest in advertising may achieve short run profit gains but will lose market share in later periods. Similarly, choosing a low price may attract a higher market share, but some of the losses (product expenses) will be paid in later time periods and will undermine future profitability.

The game is based on play by competing firms. Each firm makes strategic decisions that impact the values of the other firms through competition in the market for a homogeneous product, homeowners insurance. (2) The decision variables include product pricing, employee compensation schemes, advertising strategy, investment mix and risk strategy, and underwriting strategy. In each of the five weeks of the game, teams submit their selections (see Exhibit 1) and the rationale for their strategy. Their reasoning should reflect an understanding of interactions among variables and their expectation of the next week's stock market performance. Both firm investment returns and the aggregate level of market demand for homeowner's insurance policies are affected by stock market performance. Game results are a function of the selections made by the teams and the week's stock market performance.

Feedback to students consists of:

* a summary of the simulated annual results for the "industry," and

* program output reporting a simulated balance sheet and income statement for each firm.

Each week, teams also receive a relative ranking of selected performance variables and the team's points earned through that week (see Exhibits 2 and 3). Points earned by a team are a weighted average of selected performance variables from which deductions are made to recognize the firm's opportunity costs. Sufficient information is provided to permit each team to assess the strategic behavior of other teams. Though the instructor may assign a grade primarily on the outcome of the game, the authors suggest the grade also reflect the instructor's evaluation of the expected strategy reports submitted by students.

This article begins with an overview of the game structure. This discussion is followed by sections that provide greater detail about insurance operations, investment strategy, regulatory influences and, finally, a description of game scoring.

Game Structure

The game is organized around the two major functions of an insurance company:

* insurance operations and

* investments.

Each week, students select the values of six decision variables that affect insurance operations:

* sales promotion

* advertising

* price

* new business commission rate

* old business commission rate, and

* the choice of underwriting level (the primary determinant of the insurance company's operational risk level).

The firm's investment decisions involve the management of the stock-bond-cash mix and the risk levels of the insurance company's investment portfolio. The investment portfolio consists of three assets: cash, bonds, and common stocks. The impact of each variable on market share is determined by its value relative to the sum of the variable for all firms.

When an insurance company issues a policy, some of the associated expenses -- taxes, agent commissions, administrative expenses -- are charged immediately against the company's income. This charge decreases surplus at once while the premium collected is set aside in an unearned premium reserve to be recognized as income over the life of the policy. This statutory accounting procedure is an artifact of solvency regulation, however an implication is that as an insurance company writes more business, expenses must immediately be paid from surplus -- reducing the company's ability to write additional business. Companies experiencing rapid expansion are particularly susceptible to this regulatory solvency constraint created by the timing mismatch of expenses (which must be debited immediately) and income (which must be credited over time). These regulatory concerns aside, when a firm sells policies the premium income is available to service the various expenses of the firm and to generate investment income.

Insurance loss costs are determined by a combination of frequency (how many claims per unit), severity (average cost of each claim) and the total number of units insured. Insurers set aside loss reserves for claims which have been incurred but not reported (IBNR). As claims are reported to the company, these reserves are reduced. The game captures the uncertainty of actual versus expected losses by introducing a random error component in actual losses while reserves are calculated based on a fixed expected loss ratio derived from "historical" averages.

Insurance Operations

Homes can be statistically grouped into cohorts that experience similar within-cohort losses (frequency and severity of losses) but different between-cohort losses. The difference between the average losses of different groups occurs because people have different behavioral characteristics and homes have different construction and location characteristics. The game captures this underwriting-level effect with some simplifying assumptions by estimating the number of homes lost at different underwriting levels. (3)

Losses, Loss Adjustment Expenses and Pricing. The student selects a desirable underwriting level with knowledge of the expected loss and loss adjustment expenses associated with each underwriting level. The expected loss ratio ranges from 58 percent (level 1) to 90 percent (level 9) with incremental increases of four percent Actual losses have a random component that allows actual losses to range from 2 percent below to 3 percent above the expected loss ratio for that underwriting level. Thus, by chance a looser underwriting level could have better performance than the next underwriting level; this is demonstrated in Exhibit 4 which lists the expected loss ratio, actual loss ratio range, and expresses the expected loss ratio as a percentage of the number of policies. (4)

The loss ratio generally is the larger of two ratios, the loss ratio and the expense ratio -- the sum of which is called the combined ratio. The combined ratio is a standard industry measure of approximate firm operating profitability. The loss ratio is usually calculated as the ratio of losses incurred, including the expenses of settling loss claims, to premiums earned. The expense ratio is usually calculated as the sum of underwriting expenses incurred, including commissions, state premium taxes and overhead expenses. (5) In this game, the firm starts with an underwriting level of 7 and other values that suggest the firm requires 105.65 percent of premiums to cover its losses and underwriting expenses. (6) Though there are limitations in correctly interpreting the combined ratio, the 105.65 ratio value suggests that the firm with an underwriting level of 7 will lose $5.65 on each $100 policy written. Investment returns must be high for such a firm to both cover these losses and offer a sufficient return to investors.

The game requires simplifying assumptions to highlight understanding of key concepts and relationships. One assumption is that the average loss and loss adjustment expense is $225,000. Another assumption concerns the timing of revenue and expenses. Timing determines the amount of funds available for investment (or the need to obtain external funding). It is assumed that one-fourth of the policies are written each quarter of the year, and commissions are paid when the policy is written. Losses and loss adjustment expenses are paid with a one-quarter lag; underwriting decisions will have a two-year effect and students must consider the lingering losses of past year decisions.

Market Share Determination. The size of the aggregate market for homeowner's insurance is determined by the number of teams playing the game. Each team starts the game with 250,000 policies. The year-to-year change in the aggregate demand for homeowners insurance policies is determined by a random growth variable (set between -1 and +2 percent) and a value determined by the stock market performance. The aggregate market is distributed among firms in a multi-step process using a formula with six arguments:

* price

* commissions -- new

* commissions -- renewal

* underwriting level

* marketing effort, and

* financial rating.

For example, at the start of a game with three teams, if the price of each team is $100 the relative price effect for each team is 0.3333. The market share of the firm is the weighted average of these relative factors with weights that give greater importance to the price, commission, and underwriting level choices.

Setting price cannot be made with reference to competition alone -- the relationship between price and the underwriting level is critical. However, teams must recognize traditional competitive relationships. If one team lowers its price relative to the others, it will acquire a higher market share and, consequently, higher losses, loss adjustment expenses, commissions and state premium taxes. If the net effect of the price reduction is that aggregate premiums exceed these higher expenses, operational profits increase. Otherwise, the cash flow generated from this strategy must yield investment returns sufficient to cover the operational losses. Teams are free to change the price on their first decision, but a team wishing to change its price by more than 20 percent must obtain the consent of the commissioner/instructor by submitting a price request justification.

Teams with relatively high commission rates obtain market share advantages, and the game reflects the reality that insurers differentiate between old business and new business commission rates. The new business commission rate represents the commission on new policies sold by the firm's agents. Teams start with a new business rate of 22 percent and an old business rate of 11 percent. While the old business commission rate has little effect on new sales, it is the dominant factor in controlling the firm's retention of old clients. Higher retention rates are desirable since old business has a higher profit margin than new business.

The relative effect of marketing efforts is somewhat more complicated because advertising expenditures have a diminishing three period effect and sales promotion/bonuses have a more significant impact that is limited to one period. (7) The marketing effort effect is complicated by the need to adjust for rating effects (described in the regulatory section). First, a temporary firm market share is determined. It is a weighted average of the ratios computed for price, new and renewal commissions, underwriting level and advertising/bonuses. However, firms with a low rating are penalized to 80 percent of this temporary market share. The released market shares from low-rated firms are distributed to high-rated firms using the ratio of their temporary market share to the sum of this value for all high-rated firms.

Investment Strategy

The next set of decisions that a team must consider represents its investment strategy. Investment strategy consists of

* the proportion of a firm's assets that it targets to invest in cash, bonds or stocks, and

* the level of risk it desires in its bond and stock portfolios.

A firm may place from zero dollars to an amount equal to surplus in common stocks and may place unrestricted amounts in bonds. Some money, usually 3-5 percent of total assets, must be left in cash to meet liquidity needs. It is conceivable that a firm could have 5 percent in cash and 95 percent in bonds. A firm's ability to transfer funds from bonds to stock and vice versa is unrestricted except for a transfer cost. It costs one half of one percent of the amount transferred to move funds. These costs are paid at the beginning of the year.

The firm also must determine the level of investment risk it is willing to take on its investment portfolio. A team's investment return on bonds depends on the other teams' bond investment decisions, as will be explained below. There are five risk levels for common stocks and two for bonds. The higher the risk level the greater the potential for profits or losses. The return a team earns on its investment in stocks is determined by an index for common stocks to be selected by the instructor. In making its risk level selection for stocks, a firm has five choices. Exhibit 5 describes the risk levels associated with each of the five common stock investment choices.

Suppose the index being used is the Dow Jones Industrial Average (DJIA). If a team chooses level D, it will earn a rate of return on its common stock portfolio equal to six times the past week's percentage change in the DJIA. Assuming that the index declined 2 percent the last week, then a firm that chose a risk level of D would have earned -12 percent. This would cause a $40,000,000 portfolio to decline to $35,200,000. The data on stock market performance is drawn from the "Money and Business" section of the Sunday New York Times. (8)

A team's bond investment return is a function of the other teams' decisions in the bond market A team choosing strategy A obtains a guaranteed 8 percent return before taxes. Teams choosing strategy B will earn an uncertain return, higher or lower than 8 percent If four or more teams choose strategy B, that strategy earns less than 8 percent (see Exhibit 6).This relationship shows the effect of supply and demand for investment funds. That is, the class creates its own bond market

Regulatory Influences

In addition to specific rules that limit firm actions, regulatory influences include government taxation. The game mimics specific regulatory rules that affect firm behavior in the areas of price, investments and sales (net premiums written). The game also mimics an impact of a quasi-government activity -- the impact of insurer ratings.

The game is played under a hybrid prior approval rating system. Under this system companies must have the commissioner's approval to raise rates above certain levels, although prices may be lowered without permission. The second specific regulatory constraint concerns investment policy. No firm is allowed to have a common stock-to-surplus ratio greater than one. The firm is prohibited from investing its policyholders' money in stock -- only the corporation's funds (surplus) are allowed to be invested in common stocks. This constraint was added to prevent students from investing all their funds in stocks during a bull market because too large of an investment in common stock is unrealistic and may not be a good management practice. During normal economic conditions, most property-liability companies have a stock-to-surplus ratio less than one.

The third regulatory constraint concerns a firm's sales. The upper limit on sales is four times the firm's surplus. While this restriction may be severe, it provides order to the game and makes teams quite conscious of the need to have adequate surplus to support a given level of sales (net premiums written).

Teams may violate the second and third regulatory constraints - knowingly or unknowingly -- but when this happens the firm's rating deteriorates. There are two ratings A and B. If a firm has an A rating, it has a market potential equal to all firms playing the game. if a firm has a B rating, it has a market potential equal to 80 percent of all firms in the game. This rating system recognizes the fact that lower-rated firms tend to have smaller markets. Mortgagees, for instance, are required to deliver a highly rated homeowner's policy on or before the day of the closing. The mortgagee requires a highly rated insurer because such insurers are presumed to have a lower probability of default Thus, one would expect the B-rated insurers to face less demand for their products than the A-rated insurers.

The B rating is applied for the period following the violation of constraints 2 or 3. There is no effect on future sales if the firm corrects its financial situation. Once within the regulatory constraints of the game, a firm's A rating is restored and it can operate just like any other firm.

Tax Determination. Though insurance corporations are liable for federal corporate income taxes, the bulk of taxation of insurance companies is primarily at the state level where a premium-based tax of approximately 2 percent is applied in most jurisdictions. Half of this tax is paid mid-year and at year-end. For ease of computation, a federal rate of 33 percent of net income before taxes is applied to determine the federal tax liability which is paid at the end of the year.

Game Scoring Outcomes for Students and Instructors

The most profitable team is usually the winner, but game performance is measured by the following formula:

3 x Surplus + Total Assets + Net Premiums Written -- $137,695,250- (Risk-free Rate x [Surplus.sub.t-1])). (9)

In this formula, surplus is heavily weighted to stress its importance to shareholders and as a proxy signal of quality to those making insurance purchasing decisions. By focusing on the desirability of earning profits that enhance surplus, instructors can extend the discussion of the tradeoff between providing a cash flow to shareholders, which reduces surplus and demand for the firm's product; and providing a financial safety cushion which, in financial service firms, attracts more customers. The game can be made more realistic by tying students' grades to the firm's ability to gain market share.

Two subtractions are made in the scoring formula. The first subtraction ($137,695,250) is the sum of the initial firm value of surplus, assets and net premiums written. This sum is subtracted to isolate the impact of the team's decisions on the firm's values. The second value subtracted from the score is obtained by multiplying surplus at the end of the previous period ([Surplus.sub.t-1]) by the risk-free rate (the T-bill rate for that week). This subtraction forces students to be aware that they incur an opportunity cost when using the firm's funds and must earn a competitive return. Instructors can enhance the discussion by questioning the reasonableness of using the risk-free rate as a proxy for the firm's opportunity cost. Furthermore, if an opportunity cost is applied to prior period surplus, should it be applied to other firm resources, such as working capital?

Learning Outcomes

Instructors are able to develop in students an understanding of risk management as an enterprise-wide activity because success m the game requires an appreciation of the interaction between underwriting level choice, price choice and investment choices.

Also, instructors can use the game to develop the merits of alternative business strategies. For example, given the short time horizon of the game, it is possible that a team can succeed with either a profit maximizing or size maximizing strategy. Size maximization teams tend to have low underwriting profits and high sales. A firm that grows rapidly produces substantial positive cash flows. These firms have large amounts of funds to invest. If a size maximization team cannot produce a greater rate of return on investments than a profit maximization firm, it cannot expect to win the game. The size maximization strategy tends to work best when there is a period of both increasing size of the product market and the value of the stock market is rising.

Student interest in this simulation game is consistently high, and semester-to-semester word-of-mouth guarantees that these alternative strategies are widely discussed. Student learning can be enhanced through classroom presentations that highlight and summarize the concepts developed in this game. Through use of this simulation, students are engaged and entertained -- and they learn! EXHIBIT 4 UNDERWRITING LEVEL RELATIONSHIPS Underwriting Expected Loss Ratio Expected Loss Ratio

Level Loss Ratio Range Policy Equipment %

1 .58 .56 - .61 0.02577778

2 .62 .60 - .65 0.02755556

3 .66 .62 - .69 0.02933333

4 .70 .68 - .73 0.03111111

5 .74 .72 - .77 0.03288889

6 .78 .76 - .81 0.03466667

7 .82 .80 - .85 0.03644444

8 .86 .84 - .89 0.03822222

9 .90 .88 - .93 0.04000000 EXHIBIT 5 RISK LEVELS FOR COMMON STOCK INVESTMENT Risk Level Return

A 2.0 times weekly percent

change in stock index

B 3.0 times weekly percent

change in stock index

C 4.5 times weekly percent

change in stock index

D 6.0 times weekly percent

change in stock index

E 7.0 times weekly percent

change in stock index EXHIBIT 6 LEVEL B BOND RETURNS Number of Teams Bond Rate

1 15 percent

2 10 percent

3 7 percent

4 4 percent

5 or more 2 percent

Endnotes

(1.) This game is inspired and modeled on a DOS-based game developed by R. Hoyt and J. Trieschmann in the early 1990s; we use the framework of their game but developed independent competitive formulae and conditions. The software is made available as shareware with a suggestion that those who find it useful make a contribution to St. John's University where the game is tested in the Risk Management classes. The programming was performed by M. D. Lewis, Inc. and part of the funding for the project was supplied by a grant from the Kemper Foundation.

(2.) A "firm" is a team that may contain any number of students; the game permits operation by any number of teams.

(3.) The value of the homes at different underwriting levels also would be different but the current version of this game treats all homes as of equal value regardless of the underwriting level and holds the loss adjustment expense per home constant.

(4.) The program works off the policy equivalent value to avoid the unrealistic possibility that could occur if actual losses were based on total revenue. That is, a loss formula based on revenues could have the wrong result that a firm facing an elastic demand curve could lower price and thereby lower both revenue and losses although the number of homes insured, and logically the actual losses, would increase.

(5.) Williams, Risk Management and Insurance, provides a detailed description of these ratios and their interpretation.

(6.) Underwriting level seven has an expected loss ratio of 82 percent and an expense ratio of 23.65 percent At a price of $100 per policy and 250,000 polices, expected losses are $20,500,000 or 91.11 times the $225,000 value of an average home. The firm is expected to retain 85 percent of its policies and 15 percent are new business; together with commission rates of 22% for new business and 11% for renewal business, this retention percentage determines the new and old commissions paid by the firm. The state premium tax rate is 2 percent of premiums, or $500,000. Finally, the firm is spending $1 million on advertising, $500,000 on promotion expenses, and $750,000 in overhead expenses. The sum of these loss and underwriting expenses, $20,500,000, is 0.0364444 percent of the total insured value of the 250,000 policies in force at the start of the game (that is, $225,000 times 250,000 times 0.000364444).

(7.) Teams start with an existing firm that has been spending $1 million a year on advertising.

(8.) Because investment results are affected by the actual performance of the stock market, students develop an awareness of current economic conditions and appreciate the interaction between economic conditions and business decisions.

(9.) The overall score weights the results of the first two weeks by 15 percent, 20 percent weights are assigned for weeks 3 and 4, and week 5 is weighted by 30 percent The intent of the weighting structure is to reduce the impact of learning curve errors in the early rounds and to provide time for the development of the team's long-run strategy.

(10.) Reinsurance will be included in a future version of the game but is not used in the current version