Risk Mangement Topic 3

Measuring Risk

combines how often losses occur (frequency) with how costly they are (severity). Expected loss is their product: EL = E(f) × E(s), the total dollars of loss anticipated over a given period.

Risk

refers to uncertainty, specifically the variation between expected losses and actual losses. The greater this variation, the greater the level of risk involved.

Statistical Probability

estimates likelihood from data, either past records or experimental results. By the Law of Large Numbers, the more observations collected, the closer the estimate gets to the true probability.

Random Variables

is one whose outcome depends on some element of chance, meaning the results occur randomly rather than being predetermined. Common examples include rolling a die, flipping a coin, car accidents, and property fires.

Expected Outcome

Risk management centers on the expected outcome and the variation around it (objective risk); more variation means more risk.

Measurement of Risk

by comparing Expected Loss (EL), the anticipated loss based on experience, data, or estimation, to Actual Loss (AL), what really occurs. The variation between the two determines the level of risk.

Uses of Expected Outcome

The basis for (1) enterprise risk management decisions and (2) insurance pricing, where they determine the gross premium, the price per unit of coverage meant to cover all costs.

Cost of an Insurance Contract

known as the gross premium, is made up of three components: the pure premium, the risk charge, and administrative costs.

Pure Premium

is the portion of the gross premium calculated to be sufficient to cover losses only, based on the expected outcome (EO).

Limitation of Pure Premium

Because the expected outcome must be calculated in advance, the estimate may turn out to be wrong — meaning actual losses may not end up equaling the expected outcome.

AL = EL

Breakeven

AL < EL

Profit

AL > EL

Loss

Risk Charge

is the extra amount charged by the insurer that reflects the estimation risk it takes on — essentially compensating for the uncertainty involved in estimating the pure premium in advance.

Influences the Size of the Risk Charge

The accuracy of the insurer's estimate and its confidence in it. Greater uncertainty raises the charge, and greater confidence lowers it. Clear past data (e.g., a driver's history) makes the estimate more reliable, so the charge is lower.

Case 1: Lots of Past Information (One Extreme)

the insurer has a large amount of past information to draw on, as with auto, homeowners, most property risks, and life insurance (mortality risk). Because of this, the insurer is very confident in its estimate and faces little estimation risk, so there is very little need for a risk charge.

Case 2: Not A Lot of Past Information (the other extreme)

the insurer has very little past information to draw on, as with terrorism, the Olympics, "event risk," the space shuttle, and celebrity-specific coverage like J-Lo or Tom Brady. Because the insurer's estimate is just an educated guess at best, there is a lot of estimation risk and a high need for a risk charge. These unusual risks are often placed through Lloyd's of London and the surplus lines market.

Case 3: In The Middle

the insurer has a moderate amount of past information to draw on, as with natural disasters, floods, and certain types of liability risks. Because some estimation risk is present, there is an intermediate need for a risk charge. The size of the risk charge varies inversely with the level of confidence in the estimate: when confidence is high, the risk charge is low, and when confidence is low, the risk charge is high.

Administrative Cost - aka the expense loading

are the part of the gross premium that covers the insurer's cost of doing business: wages, marketing, advertising, and state premium taxes. Taxes are built into the policy and add roughly 2 to 5% of the premium, and total administrative costs can run 20 to 40% of the premium.

Measuring the Quality of the Estimate

"How good is it?" It is done using two types of measures: a measure of central tendency (the mean) and measures of dispersion (variance, standard deviation, and coefficient of variation).

Measure of Central Tendency

is the mean, which is the same as the expected outcome and is calculated as a weighted average.

Measures of Dispersion

indicate the accuracy of the guess, or how spread out outcomes are around the expected outcome. The three main measures are variance, standard deviation, and the coefficient of variation.

Coefficient of Variation (COV)

is the standard deviation divided by the mean. A higher COV means more risk, which makes COV the true measure of risk, since it expresses the variation relative to the expected outcome.

Maximum Possible Loss

is the largest dollar loss that could occur from a single event or exposure under the worst-case circumstances, regardless of how unlikely that event is. It represents the upper limit of severity, such as the total destruction of a building and its contents.

Maximum Probable Loss

is the largest loss that would most likely occur, rather than the worst-case scenario. It is not always an exact answer, so the key is how you present it: as an estimate of the largest realistic loss, not a precise figure.

Gross Premium

price per unit of coverage to insure a particular risk