Increasingly, firms are finding that the simultaneous use of tools and techniques from insurance and finance can greatly enhance the value of their risk management efforts. A number of books have been written about the subject of integrated risk management, including Doherty's book "Integrated Risk Management" (2000, McGraw-Hill).
You are CRO (Chief Risk Officer) of a non-financial firm that is exposed to two types of risk:
1. Price and volume risk (market risk) – depending on average temperature during the year.
2. Risk for accidents (operational risk)
Currently, your company does not hedge for the market risk, nor has insurance against the operational risk. You are asked to evaluate the following options:
1. Do nothing;
2. Hedge against all the price risk;
3. Take insurance against all accidents;
4. Combine both.
As the goal of this example is to illustrate some of the methods used in integrated risk management and their value added, the examples are kept fairly simple. However, even though a real world example would be more complicated and likely involve more factors, the same techniques, methods and tools would apply.
Average per year
Average loss per event
The expected sales volume is 125,000 with a standard deviation of 10%, which we can model as Lognorm(125000, 12500).
Market risk - Price and Cost per unit of product
Both sales price and costs per unit of product depend on the average temperature of the year, which is assumed to be minimum 15, most likely 20 and maximum 25 Celsius. The related sales price and costs per unit are shown in the figure above. A linear relationship is assumed between the average temperature during the year and the sales price and costs per unit of product (in reality, there would be uncertainty about this relationship which, for simplicity reasons, we ignore here).
Recent independent research has revealed that the expected number of fires occurring per year is an increasing function of the average temperature for that year. In addition, the losses per fire (event) increase with the average temperature during the year. Again, a linear relationship is assumed between the average temperature during the year and the number and size of the fires.
You are asked to evaluate whether the company should hedge against the price risk, obtain insurance against the fire risk or do both. Your bank has quoted a price of $25,000 to hedge against the price risk. In addition, you can assume that the yearly cost of insurance is equal to the expected losses per year, and that the coverage is 90% of your losses. .
The model Integrated Risk Management provides a solution to the problem.
There are several issues in this model that require special attention:
The expected number of fires per year (lambda) is a rate. The actual number of fires in any one year can therefore be modeled with a Poisson distribution, with lambda equal to the expected number of fires given a certain average temperature over the year.
From the input data we can see that both risks have actually some correlated effect. In other words, with high temperatures we have bigger margins on our products, but we also have on average more fires that are also on average larger.
In this example, we assume that the risk premium is equal to the expected losses (i.e. the insurance company makes an expected 10% profit, as they only pay out 90% of the losses). To do this, a simulation is run which calculates the total cost of fires; the mean value is then placed in its cell and the model run again.
The figure below shows the outcome distribution for all four scenarios (do nothing, get insurance, hedge or do both).
This figure shows that hedging against the price risk by itself actually increases the uncertainty (width of the distribution) of next year's net profits!! Insurance only does reduce the uncertainty of the net profits of next year only in the totally left of the distribution. If the company does not take any insurance nor hedges, the negative (indirect) correlation between the market and operational risk already levels out a lot of the risks, as shown by the distribution when neither insurance nor hedging is purchased. The combination of insurance and hedging provide us with a very narrow distribution of profits, but will cost us quite some money (expected profits of this scenario are about $1,74,000 lower).
From the Figure above it seems that insurance against the largest losses only would provide the company with about the same uncertainty distribution but for much lower costs. Therefore, in addition to the above four options, a strategy was simulated in which the company obtained fire insurance with a $1,000,000 deductible. The results of that scenario are shown in the figure below.
How do you think the results would look if the company obtained an insurance policy with a $1,500,000 deductible?
In conclusion, this very simplified example shows that it is important to consider all risks related to a company in an integrated way. Ignoring the relationships between risks can result in making wrong decisions as shown above with the hedging strategy. Finally, there are additional ways to determine the optimal insurance and hedging scenario, but these go beyond the scope of this illustrative example.
The links to the Integrated Risk Management software specific models are provided here:
Why does a corporation actually need capital? The answer is all to do with risk! The required capital for a firm can be considered the sum of three components (see Shimpi, 2001 - "Integrating Corporate Risk Management" for a discussion):
First, a certain amount of capital the firm will need in every future scenario; this is the "operational capital". The second type of capital is to cover the financial consequences of risk due to all the corporate activities. This capital is the "risk capital" and its size depends on the risk tolerance of the firm. Risk capital can be defined as that capital needed to keep the firm's probability of ruin below some defined level (e.g. 1%). The sum of the operational and risk capital is called "economic capital". The third and final form of capital is called "signalling capital", and the purpose of signalling capital is to satisfy outsiders such as investors, suppliers, regulators, rating agents and analysts with the adequacy of the firm's capital. In other words, it assures outsiders that the firm is indeed as strong as the managers know it to be.
In this example, we will determine the required capital of a firm by simulation. The example firm has two main risks, exchange risk and risk of liability suits. By simulating the capital requirements for many scenarios, we can estimate the distribution of the capital requirements and subsequently the economic capital. The model Capital Required illustrates the problem.
Secondly, we will determine what the transfer of the two main risks (by insurance and hedging) mean for the economic capital of the firm. We will show that insurance and hedging can in fact be seen as a form of "off-balance-sheet capital".
Our firm of interest is SlakerBrewery, an American beer brewery that exclusively brews beer for the UK market. It has a contract for the next year of 1 million cases at 10 pounds per case. Its capital to produce the beer is expected to be a minimal 10% of sales, most likely 12% and maximum 15%.
In addition, SlakerBrewery is exposed to two main types of risk; exchange risk and liability risk. The current exchange rate is 1.6 pounds per dollar, and has a volatility of 10%. On average, the company expects one lawsuit per two years for an amount of minimal $1000, most likely $10,000 and maximal $10 million.
The graph in the model shows that for 20,000 scenarios the minimum amount of capital it needs to stay in business is $1,361,000; this is equal to the operational capital. In 1% of the scenarios, the required capital is more than $5,556,000, which means that this is the economic capital of the firm. Of the economic capital, $1,361.000 is operational capital and $5,556,000 - $1,361,000 = $4,195,000 is risk capital. Finally, considering the long tail at the right of the 99% percentile SlakerBrewery decides to keep another $1,000,000 signalling capital. In total, the amount of required capital is therefore $6,556,000.
After doing this analysis, the management of SlakerBrewery asks you to do another analysis in which they would take an insurance policy against the liability claims and they would hedge the exchange risk. The premium of the insurance policy was set equal to the expected losses + 10% (the insurer's profit). The resulting distribution of the firm's required capital is shown below. The minimum capital required now is $1,771,000; this is equal to the operational capital. In 1% of the scenarios, the required capital is more than $2,455,000, which means that is the economic capital of the firm. Of the economic capital, $1,771,000 is operational capital and $2,455,000 - $1,771,000 = $684,000 is risk capital. Finally, considering the "smaller tail" at the right of the 99% percentile SlakerBrewery decides to keep only $100,000 signalling capital. In total, the amount of required capital is therefore $2,555,000.
This simple example illustrates that the insurance and hedging basically provided a form of "off-balance-sheet financing" to the firm. Simulation of the firm provided a useful way to determine the capital requirements.
Techniques are available to find the optimal financing strategy for a firm, taking into account both paid-up capital (capital that appears on the balance sheet; retain the risk) and off-balance sheet capital (such as insurance; transfer the risk). As these techniques fall beyond the scope of the current example, we refer to e.g. Culp (2002) for overviews of these techniques. For all of these techniques, risk analysis can provide insight and subsequent support corporate decisions making.
The links to the Capital Required software specific models are provided here: