Lecture 4
Loss forecasting and Financial Analysis
In Risk Management
Objectives
Understand and explain the various tools employed in forecasting losses
Show how financial analysis can be applied to risk management decisions
Describe other risk management tools
Loss forecasting
Probability analysis
The chance of a loss is the possibility of occurrence of an adverse event. The ratio of the number of events(E) likely to occur to the number of exposure units(N) is called the probability (P) of occurrence
. E.g. A fleet of 630 vehicles is such that on average 42 vehicles suffer physical damage each year. What is the probability that a vehicle will suffer physical damage in a given year.
Types of events
Independent events: Two events are independent if
the occurrence of one does not affect the occurrence or
non-occurrence of the other. The university of Ghana
Business School has two campuses, one at the main
campus site and the other one at the new site. The
probability of a fire outbreak in one of the campuses
will not affect the occurrence of fire outbreak on the
other campus. There is the possibility of the two
occurring simultaneously. If the probability of having
fire on main campus is P(M)=0.35 and the probability
of fire at the new site P(N)= 0.12. The probability of
having fire on both campuses =P(M)*P(N)=0.35*0.12
Type of Events
Dependent events: If two events are dependent the
occurrence of one has effects on the occurrence of the other. In the example above if the two campuses were on the same premises and close and fire occurs in one, the probability that the other one will also catch fire will be increased. The main campus and the new campus
may have probabilities of catching fire as 0.12 and 0.35 respectively. However the occurrence of fire at the main could increase the probability of fire on the new campus to 0.65. This probability is stated as the probability of fire at the new site given that fire had occurred at the main campus. The combined probability of a fire
outbreak =
Types of events
Mutually exclusive events: Two events are mutually exclusive if the occurrence of one prevents the
occurrence of the other. If a building is exposed to fire and flood. The probability that the building is
destroyed by fire means that it can not be destroyed by flood.
Mr. Kesedovo insured his house against fire and
flood. The probability that the house is destroyed by fire is 0.3 and the probability of destruction by flood is 0.45. What is the probability that it is destroyed by
i) fire or flood ii) at least one of the perils
Types of events
Regression analysis
It models the relationship between two variables for the purposes of prediction.
Dependent variable(response variable) is the variable that changes as a result of changes in the other variable called the independent(predictor) variable. Where the independent variable is one, the regression is simple regression and where there is more than one independent variable, is called multiple regression.
The number of claims(dependent) variable in a worker
compensation policy will depend on the number of
employees(independent variable). The number of claims
for a fleet of vehicles will depends on the number of
vehicles and the mileage driven
Regression
The above example can be represented mathematically as shown below
CZ claim size(number of claims)
NE number of employees
NV number of vehicles
M mileage driven
, constant
error term
Loss distribution
It is a compilation of losses and their corresponding
probabilities. It can be used to calculate, mean, standard deviation and used to predict future loss severity and
frequency. The losses will follow any of the following distributions binomial, poisson, normal etc.
The when the number of losses is high(greater than 30) the normal pobability distribution can be used to model.
Standard variate is the mean and s is standard deviation
Example; the number of weather losses is normally
distributed with mean 16 and a standard deviation of 3.
What is the probability that the number of weather losses will be between 16 and 22?
Loss distribution
from the normal distribution table 2.00 corresponds to 0.4772. The probability of the number of weather losses being between 16 and 22 is 48%
Example
Assume the number of fire losses in Accra is normally distributed with mean 400 and standard deviation of 80. what is the probability that
i) more than 400 losses will occur?
ii) between 460 and 520 losses will occur?
iii) above what number of losses do the higest 10% of losses occur?
Time value of money
Time value of money
Valuing cash flows in different time periods taking into consideration the interest earning capacity of money.
Annuity
Present value factor
annuity immediate(ordinary annuity or annuity in arrears)
annuity due or annuity in advance
Example
You are offered to insurance policy options as follows”
Option 1. Annual premium= GHC 90,000 with a deductible of GHC5,000 per claim
Option 2. Annual premium of GHC35,000 with a deductible of GHC 10,000 per claim.
The loss distribution is as shown below
Expected number of losses Expected size of Loss
12 GHC 5,000
6 GHC10,000
2 over GHC 10,000
Example
Premiums are paid at the start of the year and deductibles made at the end of the year. If the appropriate interest rate is 5%. Which option will you choose as a risk manager?
Solution
Total deductible for option 1
Total deductible Option 2
Option 2 is better because the PV of outgos is less than option1
Loss control investments
They are investments undertaken with the
aim of reducing the severity and frequency of losses. They are normal budgeting decisions such the NPV and IRR.
The NPV is calculated as the sum of the PVs of inflows less the present value of outflows
A project is worthwhile if the NPV is positive.
The IRR is the rate at which NPV is zero
Project with high values of IRR are preferable
Cash flows of a project normally come as
estimates of future benefits such as increased revenues, reduced spending, or a
combination of the two
Whereas is easy to quantify some forms of revenues it becomes challenging to value other aspects of a project’s benefits such as employee morale, reduced pain and suffering, public perception and lost productivity in
replacing and old worker.
Other risk management tools
Risk management information system
Computerised data base where risk management data is stored and analysed and used for prediction and control of future loss level. Data on property and liability is availble for analysis
Risk management Intranet
A local website connection where risk management information is deposited for use my interested parties within the organaistation
Risk maps
