CASE: LARA TOOLS S. A.

CASE: LARA TOOLS S. A.                Part A: RISK RETENTION

LARA TOOLS S. A. –known as LATOSA by the local residents—is a medium sized company manufacturing all types of instruments and tools used in the repair and maintenance of industrial equipment. The company has been operating for over 25 years now and has experienced moderate—but sustained—growth.

The table below summarizes the loss and claim experience including accidents and financial losses due to damage and theft, from the last five years along with general data illustrating the growth of LATOSA.

Table 1: Claim information and general data concerning the firm.

[pic 1]Note: All information in this table is evaluated at 12/31/X5. Amounts ($) are rounded to the nearest thousand.

Note how losses increased considerably in year ´X2. This forced the company to hire a risk manager to formalize the risk management process of the firm, i. e., to identify, quantify, control, and monitor the risks to which LATOSA is exposed.

The former risk manager retired one month ago and you are hired to substitute him. Your first assignment is to quantify ($) and predict (“forecast” would be a better term) the operational risks for next year, X6, and provide top management with the relevant information to make a decision about how much risk should be retained and managed with internal cash flow, and how much should be transferred to an insurance company, for example.

You started enthusiastically looking for historical data concerning loss events like accidents, theft, fire—and other damages, product liability lawsuits, etc., but the only relevant data you found is the information presented in table 2.

The data presented in table 2 correspond to a partially completed analysis elaborated by your predecessor to evaluate an All Risk Insurance Policy with several deductible options. The insurance agent presented an offer, including the following five deductibles: $500, $1,000, $5,000, $10,000 y $25,000 per loss event, along with the corresponding reductions in payable insurance premiums.

Table 2: Stratified loss data for different deductibles.

[pic 2]

Notes:

1. The data presented here are for years X1 to X5 inclusive, where X5 is the most recent (i.e., the year that just finished). All information is valued at date 31/12/X5. 

2. Claims with a value of $0 are omitted from quantitative analysis. They correspond to unjustified claims (not valid) or that correspond to completely depreciated equipment, etc.

3. Data presented in the last column correspond to the information contained in Table 1.

4. In your analysis you may assume that all loss data are completely developed and amounts are completely indexed for inflation. For more information about how to develop loss data and how to index the corresponding amounts ($), see part B of this case.  

This historical information allows us to Project our loss history to the near future, i.e., next year (X6). When you have a long loss history, i.e., many observations from many years, you could use linear regression to project this experience into the future. However, in this case with relatively few observations we will have to make do with simpler tools and procedures.

As stated above,

YOUR GOAL: is to project and cuantify ($) the operational risks to which LATOSA is exposed for next year (X6) and to supply the necessary “elements” (information) to the owners so they can make an optimal decision about how much risk to retain and how much to transfer.

In your analysis you may assume: 

• That the frequency and the severity of adverse events are independent^[1].
• That the frequency distribution of losses follows a normal distribution (note: for the frequency distribution this is a reasonable assumption especially when there are many observations). Compute the mean and the standard deviation from the simple, and use the standard normal distribution to find the probabilities of finding more tan X losses, etc. 
• That the information from Table 2 is already completely developed and indexed.

You are asked to:

1. Calculate an “Operational Value at Risk (OpVaR)” with a 95% confidence level. (Note: to make this really the “worst possible loss next year at the 95% confidence level under normal circumstances”), we must have that at the very least either the frequency and/or the severity or both are at least 95%. Probably best is to take both at the 97.5% level such that: 1 – (0.975)2 > 95%.

2. Now, suppose that your insurance broker presents a proposal for the renewal of LATOSA´s All Risk Policy with the following five deductibles: $500, $1,000, $5,000, $10,000 y $25,000 per loss event. The corresponding premium reductions are: $35,000, $45,000, $100,000, $150,000 y $200,000, respectively. According to your analysis, which of the following deductibles appear most attractive and why?

You may use both qualitative as well as quantitative arguments to defend your answers. Remember, the absence of abundant, high quality data is the rule rather than the exception. Even under these circumstances you will have to make decisions!

3. Discuss the most important factors determining the level of risk retention vs. the level of risk transfer.

Rúbrica de Evaluación para el Caso LARA TOOLS S.A. parte A:

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