3. Special Topics I Risk Management

1. Risk Identification

2. Risk Measurement

3. Risk Evaluation

4. Risk Treatment

5. Risk Monitoring

We focus on 2/3/4

Pure Risk

• Only results in losses (downside risk)

• Underlying cause often firm specific, e.g. lightning strike

• Can be covered with insurance contracts • Reduces total wealth in society

Speculative Risk

• Gains and losses are possible

• Underlying cause often more general, e.g.

changes in preferences

• Often reduced with financial derivatives • Redistribution of wealth

-> Traditional focus of risk management on pure risk

• Risk control: (real) investment decision: determines the probability distribution of payoffs Installing sprinklers, safety measures for products

• Risk financing: risk transfer decision: determines how the risk is split up between Insurance, derivatives, equity (cash)

• What is the objective?

Should firms try to reduce the volatility of the stock price, EBIT or ROE? Should firms care about these risks – why and when?

• What are the differences between different risk transfer instruments?

Insurance or derivatives versus holding cash

Insurance versus derivatives

Options versus futures

Various risk measures available, the use of which makes sense for different questions, for instance:

The variance and standard deviation map negative and positive deviations from the expected value, i.e. risks and chances: useful, e.g., in the portfolio selection context

Downside risk measures only take the downside risk into account: useful, if a downside risk is particularly detrimental, for instance the insolvency risk of a firm

In the following:

• Closer look at the Value-at-Risk and the Expected Shortfall

• Two important (downside) risk measures used in banking and insurance

Die Subadditivitätsbedingung besagt, dass das Risikomaß bei zwei Portfolios nach deren Zusammenführung nicht größer sein sollte als die Summe der Risikomaße jedes einzelnen Portfolios.

The Question Being Asked in Value at Risk (VaR):

“What loss level is such that we are 𝛼 *100% confident it will not be exceeded in N business days?”

VaR and Regulatory Capital

• Regulators have used VaR to calculate the capital they require banks to keep

• The market-risk capital has been based on a 10-day VaR estimated where the confidence

level is 99%

• Credit risk and operational risk capital are based on a one-year 99.9% VaR

• Insurance supervision in the EU is based on the VaR-idea: Solvency capital required to assure a 99.5% survival probability of an insurance company during the next year.

Advantages of VaR

• It captures an important aspect of risk in a single number

• It is easy to understand

Downfalls of VaR

• Can deliver undesirable results when used as a measure to limit risk

• VaR does not provide any information about the average magnitude of losses beyond the VaR level. It only estimates the maximum potential loss at a given confidence level. In contrast, Expected Shortfall provides insight into the average loss magnitude if the VaR threshold is breached. This additional information is valuable in assessing the potential impact of extreme events.

Advantages

• Expected value and variance characterize distribution completely

• Sum of normally distributed random variables is normally distributed

• Correlation characterizes dependency between normally distributed random variables fully

Drawbacks

• Becomes negative with a positive probability (problem when mapping damage distributions)

• In reality, we observe:

• asymmetric distributions

• more weight at the edges ("heavy tails")

• more complex dependencies

Insurance is the most common method firms use for risk financing.

• What is an insurance contract?

A contract (voluntarily agreed or regulated by law) between two parties, i.e.

• the insurance company

• the policyholder

According to the terms specified by the contract, the insurance company covers (i.e. finances) the specified loss in case it occurs during the contract period,

either fully or in part.

In return, the policyholder pays an insurance premium to the insurance company.

• Property insurance: to insure their assets against hazards such as fire, storm damage, vandalism, earthquakes and other natural and environmental risks

• Business Liability Insurance: A type of insurance that covers the costs that result if some aspect of a business causes harm to a third party or someone else’s property

• Business Interruption Insurance: A type of insurance that protects a firm against the loss of earnings if the business is interrupted due to fire, accident, or some other insured peril

• Key Personnel Insurance: A type of insurance that compensates a firm for the loss or unavoidable absence of crucial employees in the firm

When the NPV from selling insurance is zero because the price of insurance equals the present value of the expected payment, we say the price for the insurance is actuarially fair

Consider again the oil refinery. The risk of fire is specific to this firm and, therefore, diversifiable.

• By pooling together the risks from many policies, insurance companies can create very- low-risk portfolios.

• In other words, the risk of fire has a beta of zero, so it will not command a risk premium. In thiscase rL = rf equalstherisk-freeinterestrate.

But not all insurable risks have a beta of zero:

• Some risks, such as hurricanes and earthquakes may be difficult to diversify completely.

• For risks that cannot be fully diversified, the cost of capital 𝑟L will include a risk premium.

By its very nature, insurance for non-diversifiable hazards is generally a negative beta asset (it pays off in bad times).

• Thus, the risk-adjusted rate 𝑟 for losses is less than the risk-free rate 𝑟f, leading to a higher insurance premium in the actuarially fair insurance premium equation.

• Although firms that purchase insurance earn a return 𝑟L < 𝑟f on their investment, because of the negative beta of the insurance payoff, it is still a zero-NPV transaction.

• In a perfect capital market, there is no benefit to the firm from any financial transaction, including insurance.

• Insurance is a zero-NPV transaction that has no effect on value.

• The value of insurance comes from reducing the cost of market imperfections.

• Therefore, we consider the potential benefits of insurance with respect to the following market imperfections:

a. Bankruptcy and Financial Distress Costs

b. Issuance Costs

c. Tax Rate Fluctuations

d. Debt Capacity

e. Managerial Incentives

f. Risk Assessment

• When a firm borrows, it increases its chances of experiencing financial distress

• Financial distress may impose significant direct and indirect costs on the firm (agency costs such as excessive risk taking and underinvestment)

• By insuring risks that could lead to distress, the firm can reduce the likelihood that it will incur these costs.

• When a firm experiences losses, it may need to raise cash from outside investors by issuing securities.

• Issuing securities is an expensive endeavor: underwriting fees, transaction costs and costs from underpricing due to adverse selection as well as potential agency costs due to reduced ownership concentration.

• Insurance provides cash to the firm to offset losses, reducing the firm’s need for external capital thus reducing issuance costs.

When a firm is subject to graduated income tax rates, insurance can produce tax savings if the firm is in a higher tax bracket when it pays the premium than the tax bracket it is in when it receives the insurance payment in the event of a loss.

• The benefit arises because the grower is able to shift income from a period in which it has a high tax rate to a period in which it has a low rate.

• This tax benefit of insurance can be large if the potential losses are significant enough to have a substantial impact on the firm‘s marginal tax rate.

• Firms limit their leverage to avoid financial distress costs.

• Because insurance reduces the risk of financial distress, it can relax the trade-off between leverage and financial distress costs and allow the firm to increase its use of debt financing.

• Recall, that debt financing provides important advantages for the firm, including lower corporate tax payments due to the interest tax shield, lower issuance costs, and lower agency costs.

• By eliminating the volatility that results from perils outside management’s control, insurance turns the firm’s earnings and share price into informative indicators of management’s performance.

• Therefore, the firm can increase its reliance on these measures as part of performance- based compensation schemes, without exposing managers to unnecessary risks.

• In addition, by lowering the volatility of the stock, insurance can encourage concentrated ownership by an outside director or investor who will monitor the firm and its management.

• Insurance companies specialize in assessing risk and will often be better informed about the extent of certain risks faced by the firm than the firm’s own managers.

• This knowledge can benefit the firm by improving its investment decisions. Requiring the firm to purchase fire insurance, for example, implies that the firm will consider differences in fire safety, through their effects on the insurance premium, when choosing a warehouse. Otherwise, the managers might overlook such differences.

• Insurance firms also routinely monitor the firms they insure and can make value-enhancing safety recommendations.

• When insurance premiums are actuarially fair, using insurance to manage the firm‘s risk can reduce costs and improve investment decisions.

• In reality, market imperfections exist that can raise the cost of insurance above the actuarially fair price and offset some of these benefits.

Three main frictions may arise between the firm and its insurer:

a) Transferring the risk to an insurance company entails administrative and overhead costs. The insurance company must employ sales personnel who seek out clients, underwriters who assess the risks of a given property, appraisers and adjusters who assess the damages in the event of a loss, and lawyers who can resolve potential disputes that arise over the claims.

Insurance companies will include these expenses when setting their premiums.

b) Adverse selection: A firm’s desire to buy insurance may signal that it has above-average risk. If firms have private information about how risky they are, insurance companies must be compensated for this adverse selection with higher premiums.

c) Agency costs are a third factor that contributes to the price of insurance.

Moral Hazard: When purchasing insurance reduces a firm’s incentive to avoid risk. For example, after purchasing fire insurance, a firm may decide to cut costs by reducing expenditures on fire prevention.

• Screen applicants to assess their risk as accurately as possible

• Investigate losses to look for evidence of fraud or deliberate intent

Insurance companies also structure their policies in such a way as to reduce these costs, by including:

• Deductibles: A provision of an insurance policy in which an initial amount of loss is not covered by the policy and must be paid by the insured

• Policy Limits: The provisions of an insurance policy that limit the amount of loss that the policy covers regardless of the extent of the damage.

These provisions mean that the firm continues to bear some of the risk of the loss even after it is insured. In this way, the firm retains an incentive to avoid the loss, reducing moral hazard.

Also, because risky firms will prefer lower deductibles and higher limits (because they are more likely to experience a loss), insurers can use the firm’s policy choice to help identify its risk and reduce adverse selection.

The Insurance Decision

• For insurance to be attractive, the benefit to the firm must exceed the additional premium charged by the insurer.

• Insurance is most likely to be attractive to firms that are currently financially healthy and are paying high current tax rates.

• They will benefit most from insuring risks that can lead to cash shortfalls or financial distress and that insurers can accurately assess and monitor to prevent moral hazard.

• Are only a few specialized insurers available?

• Is the risk complex and is it difficult to determine the realized loss?

• Is the counterparty risk high?

• Has the firm a comparative advantage in bearing the risk?

• Does the firm understand (know) the risk better than an insurer?

• Does the firm control the level of risk (and are the firm’s activities difficult to enforce)?

• Is it possible to accommodate the risk at low cost?

The more questions a firm answers with yes, the more likely it is that it will not insure the risk.

In a perfect capital market, purchasing insurance does not add value to the firm. It can add value in the presence of market imperfections, but market imperfections are also likely to raise the premiums charged by insurers. For insurance to be attractive, the benefit to the firm must exceed the additional premium charged by the insurer.

For these reasons, insurance is most likely to be attractive to firms that are currently financially healthy, do not need external capital, and are paying high current tax rates. They will benefit most from insuring risks that can lead to cash shortfalls or financial distress, and that insurers can accurately assess and monitor to prevent moral hazard.

Full insurance is unlikely to be attractive for risks about which firms have a great deal of private information or that are subject to severe moral hazard. Also, firms that are already in financial distress have a strong incentive not to purchase insurance—they need cash today and have an incentive to take risk because future losses are likely to be borne by their debt holders.