Sections 3 & 4 Flashcards
What are the 3 measures of central tendency?
Mean, Median & Mode
How do you calculate the MEAN and interpret the effect of extreme values.
Commonly known as the average. It’s the sum of all values divided by the number of observations. Highly susceptible to extreme values or outlying observations (AKA skewness).
How do you calculate the MEDIAN and interpret the effect of extreme values on each measure.
The midpoint of the observations ranked in order of value. Median lies between the bottom half of the observations and the top half of the observations. When there is an even number of observations, the median is the average of the two middle values. This measure of central tendency reduces the impact of extreme values or outliers.
How do you calculate a MODE and interpret the effect of extreme values.
Is the observation that occurs most often in the sample; it has the highest frequency of occurrence. There may be none, one, or more than one mode. Outliers have NO impact on the mode.
What are the two measures of dispersion?
Range & Central Tendency
What is the range and how is it measured by Risk Managers?
It is the difference between the largest and smallest values. IT is a number not a range. It is useful as it captures the total extent of variation or dispersion from the central tendency.
How do you calculate Standard Deviation and explain how they are used by risk managers.
The square root of the variance (how data points differ from the mean). It is a measure of how far a set of data re spread from the mean (average) value.
Shows how far data points are from the mean. Small standard deviation indicates the data points are close together with little variance, while a large standard deviation indicates the data is not grouped together.
Describe the role of the standard deviation in a normal distribution and explain the differences between a normal and skewed distribution.
Normal distribution is often called a bell curve, the mean, median and mode have the same value at the high point of the graph. Empirical rule states that nearly all values will lie within 3 standard deviations of the mean in a normal distribution. In risk management, many distributions aren’t normal. (could be right skewed - tail on right). Skewness is asymmetrical. Skewness is defined as the measure of the degree of asymmetry or distortion from a symmetrical bell curve of a frequency distribution.
Draw a simple histogram showing individual losses versus annual totals.
- Sort the data in ascending order
- Select the number and size (range) of bins (groups of data). Generally it is best to use three to five bins of equal size.
- Sort the data into the selected bins.
- Calculate percentages. Divide the number of occurrences in each bin by the total number of occurrences.
- Draw the graph. The ranges of losses (bins) are on the X-axis. Percentages (probabilities) of those losses occurring on the Y-Axis.
Forecast future losses by describing and calculating confidence intervals and simple linear regression.
View pages 93 & 94
Explain the different types of claim reserves and summarize why reserves are important to a risk manager.
- Case Reserve - these are generally set by a claims adjuster on individual claims. It’s an estimate of what the claim could ultimate cost and is based on the information available at that time.
- IBNR - (Incurred but not reported) - Actuaries look at reserves in aggregate to determine if they sufficiently reflect the total ultimate losses that are expected. These must be held for claims payments that have been incurred but not reported, for claims that reopen, claims in transit and for additional adverse development of known claims. They are made up of the following for the Gross IBNR 1) Adverse Development (provision for future adjustments of case reserves) 2) Reopened Claims Reserve (The provision for claim files that are closed but may reopen), 3) Incurred but not Reported (Claims that have occurred but have not been reported to the carrier) 4. Reported but not recorded (RBNR) Claims that have been reported to the insurer but have not yet been recorded on the insurer’s books.
Loss Adjustment Expenses
1) ALAE (Allocated Loss Adjustment Expenses)expenses that are directly assigned to or arise from a particular claim
2) ULAE (Unallocated Loss Adjustment Expenses) expenses not specifically allocated or charged for a particular claim.
By making sure the assets are large enough to cover all liabilities, the company can ensure all reserves are sufficiently covered.
Calculate Ultimate Losses for An Organization
The difference between incurred losses and paid losses, provided from the RMIS system are the estimated current case reserves The information misssing from the loss runs are the IBNR losses. In order to calculate IBNR reserves actuaries must first determine loss development factors (LDFs). They are calculated using a methodology known as loss triangulation. The purpose of calculating loss development factors is so they may be applied to a current valuation of incurred losses to determine an estimate of ultimate losses. Current year is the most unknown.
Explain the necessary data requiring adjustment prior to loss forecasting.
- Adjust for inflation - data must be adjusted to reflect current prices. The oldest data requires the most adjustment.
- Adjust for exposures. If a company is growing or shrinking, it is important to factor the changing exposures into our forecasts. Risk managers can select any exposure base or exposure until that makes sense and appropriate for the analysis.
Steps to calculate Forecasted losses
- Calculating Loss Rate by Year - Divide indexed ultimate losses by revenue to obtain loss rate.
- Selecting the Appropriate Loss Rate for Renewal Forecasting -The goal is to select a value that best estimates next year’s losses. Could pick a number that averages the past five policy years etc..
- Forecasting Losses (Fully Developed Loss Rate) x (# of projected exposures next period) = Projected Developed Ultimate Losses or Loss Pick)
