Risk Topic 3

Frequency

How often

Severity

How bad

What is Measure in risk management?

The process of evaluating exposes to loss by looking at frequency, severity, and expected loss

What is Expected Loss(EL)?

The expected total amount of losses during a given time period

What is the Expected Loss Formula?

Expected loss= expected frequency x expected severity

What does E(F) mean

expected frequency-expected number of losses

What’s ES?

Expected severity- the expected dollar amount of each loss

What does Expected Loss tell us?

The total dollar amount of losses over a given time period

What does risk involve?

Variation around expected losses versus actual losses

What is statistical Probability?

Making probability estimates based on statistics

How can statistical probability be determined?

By looking at past data, making an estimate, or running an experiment and using the results from the collected data

What is the Law of Large Numbers?

Over time, the more data or observations you collect, the closer your results will get to the accurate/ expected result

Law of Large Numbers example

Observing something 3000 times will generally give a more accurate result than observing it only 3 times

Random Variables

Outcome depends on chance/random results (eg. dice, coin flip, car accidents, property fires)

Expected Outcome

Core of Risk Management decision making; variation around it is objective risk

Expected Losses (EL)

what we expect to happen based on experience/data

Actual Losses(AL)

Losses that actually occur

Objective Risk

Variation around expected outcome; measured by range/ spread of possible outcomes (eg. Person A;10 buildings, expects 2 fires, range 0 less than or equal to number of fires less than or equal tp 4.

Person B; 30 buildings expects 9 fires, range 6 less than or equal to number of fires less than or equal to 12

How do you calculate the “probability or chance of loss” ?

Expected losses / Total Cases

How do you calculate “Variation of Actual from Expected Relative to Expected?”

(Actual-Expected)/ Expected

Between two scenarios, which one faces the most objective risk based on relative variation?

The one with the higher percentage of relative variation (eg scenario A at 100% vs. Scenario B at 33%)

What is the goal of using a sample (like 1000 autos out of 100,000) i risk management ?

To look at past data/ information to estimate future outcomes and expected loss per unit

How do you calculate the Expected Loss for all autos?

Expected Loss per Auto x Total

What is the risk when dealing with total expected losses?

Actual total losses will exceed their estimate, resulting in a drain on a firm’s capital

How would a company like Alamo address this risk?

Increase sample size for a more accurate estimate, Set aside more than expected total losses, estimate the accuracy of their guess

What is the main challenge with pricing insurance (gross premium)?

The price should be sufficient to cover all costs but the insurer does not know all the costs until the final insurance claim is settled

What are the 3 components that make up Gross Premium?

Pure premium +risk charge +administrative costs

What is Pure Premium?

The portion of the gross premium calculated as being sufficient to pay for losses only (expected outomes)

What is Estimation RIsk?

An additional risk faced by insurers because their expected loss estimates might be wrong

What is a Risk Charge?

An extra amount charged by the insurer to represent and cover estimation risk

What influences the size or magnitude of the risk charge?

The accuracy of the estimate or guess

What is the basis of insurance forecasting?

Insurers use past information to predict the future

Case 1 Characteristics (Lots of past info)

Examples: Auto, homeowners, most property risks, and life insurance (mortality risk)

Confidence/ Risk : Very confident in the estimate; little estimation risk; very low need for a risk charge

Case 2 Characteristics (Not a lot of past info/ The other extreme)

Example :Terrorism, Olympics (event risk) space shuttle, J-LO, Tom Brady

Markets-Lloyds of London, Surplus Lines Market

Risk/Nature-Lots of estimation risk; high need for a risk charge; just an “educated guess” at best

Case 3 Characteristics(in the “middle”

Examples: natural disasters, floods, certain types of liability risks

Risk/Nature: Some estimation risk is present; intermediate need for a risk charge

How does the size of the risk charge relate to the level of confidence in the estimate?

It varies inversely (oppositely) with the level of confidence in the estimate

What is DAC and what does it include?

DAC is also known as the expense loading

-It includes wages and compensation, marketing/advertising, and state premium taxes

What are state premium taxes and what are the overall administrative costs?

Sales Premium Taxes: Sales tax of an insurance contract, embedded directly into the policy, which depending on the state addsb2-5% of premium

Overall Administrative Costs:Can be anywhere from 20-40% of the overall premium

How do you measure the quality of an estimate using measures of central tendency?

The question asks “how good is it?”

mean: expected outcome (EO) which is a weighted average

What are the measures of dispersion used to check the accuracy/ risk of the guess?

Variance, Standard Deviation, Coefficient of variation

In statistics, what does the mean equal?

The Expected Outcome (EO)

What are the expected outcomes (means) for the two breweries in the example?

Evil Empire is 1.12 kegs per month

Lucky Dog is 1.7 kegs per month

Step 1-set up column tables with Ex(number of damaged kegs) column 2 (the probability of each outcome happening (make sure your probabilities add up to 1.0)

Step 2-multiply across (take each outcome and multiply by its probability)

Step 3- Add them all up (add subtotals from every row together and the final sum is your EXPECTED OUTCOME (mean)

What crucial question does the brew example prompt us to ask next?

Who faces the most risk? (determined by looking at measures of dispersion like variance/ standard deviation around that mean)

What are steps to calculate variance?

1-outcome (list the outcomes)

2-mean (find or list the mean) expected outcomeee

3- difference (subtract the guess from the mean)

4-squared (square that difference

5-probabilites(multiply by the probability)

6-sum it up (add all the rows together )

How do you find Standard Deviation (SD) once you have the variance?

It is simply the square root of the variance

What is COV (coefficient of variation) and why is it important?

It is the true measure of variation (risk/estimation risk)How big the variation (risk) is compared to the average expected loss.

What does a Bigger vs Lower COV mean for estimation risk?

Bigger COV: bigger risk (estimation risk)

Lower COV: lower risk (estimation risk)

Maximum Probable Loss

largest loss that would most likely occur , not always an exact answer -key is how you present it

Can a probability ever be negative? What makes a valid risk distibution?

No probabilities must be between 0 and 100%

A valid risk statement must use valid percentages that sum correctly (a 95% chances of losses is ess than or equal to 1000 and a 5% chance of losses between 1000 and 10000) rather than flawed or negative numbers

COV formula

Formula: Standard Deviation divided by the MEAN