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Principles of Risk Management and Insurance 13th Edition(1).doc

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Principles of Risk Management and Insurance 13th Edition(1).doc

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  • April 11, 2023
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Loss ForecasTIng 81



Assigning probabilities to individual and joint the corresponding number of workers compensation
events and analyzing the probabilities can assist the claims during the year. In the second panel of
risk manager in formulating a risk treatment plan. Exhibit 4.6, the number of claims is plotted against
payroll. Regression analysis provides the coordinates
19
of the line that best fits the points on the chart. This
Regression Analysis
line will minimize the sum of the squared deviations
Regression analysis is another method for forecasting of the points from the line. Our hypothesized relation-
losses. Regression analysis characterizes the relationship ship is as follows:
between two or more variables and then uses this char-
acterization to predict values of a variable. One Number of
variable—the dependent variable—is hypothesized to be workers
= B0 + (B1 * Payroll [in thousands])
a function of one or more independent variables. It is not compensation
difficult to envision relationships that would be of inter- claims
est to risk managers in which one variable is dependent
on another variable. For example, consider workers where B0 is a constant and B1 is the coefficient of the
compensation claims. It is logical to hypothesize that the independent variable.
number of workers compensation claims should be posi- The regression results provided at the bottom of
tively related to some variable representing employment Exhibit 4.6 were obtained using spreadsheet software.
(such as the number of employees, payroll, or hours The coefficient of determination, R-square, ranges
worked). Likewise, we would expect the number of from 0 to 1 and measures the model fit. An R-square
physical damage claims for a fleet of vehicles to increase value close to 1 indicates that the model does a good
as the size of the fleet increases or as the number of miles job of predicting Y values. By substituting the esti-
driven each year by fleet vehicles increases. mated payroll for next year (in thousands), the risk
The first panel in Exhibit 4.6 provides data for a manager estimates that 509 workers compensation
company’s annual payroll in thousands of dollars and claims will occur in the next year.



Exhibit 4.6
Relationship between Payroll and Number of Workers Compensation Claims

Workers Claims
Payroll in compensation 500
Year thousands claims
2004 $ 400 18 400
2005 520 26
2006 710 48
2007 840 96 300
2008 1200 110
2009 1500 150
2010 1630 228 200
2011 1980 250
2012 2300 260
100
2013 2900 300
2014 3400 325
2015 4000 412
$500 $1000 $1500 $2000 $2500 $3000 $3500 $4000
Payroll (in thousands of $)
2
Regression results: Y = –6.1413 + .1074 X, R = .9519 Predicted
number of claims next year, if the payroll is $4.8 million:
Y = –6.1413 + (.1074 × 4800)
Y = 509.38

,82 CHAPTER 4 / Enterprise Risk Management and Related Topics

, important deci-sions, adjust dollar values to
including whether to reflect the earning of
Forecasting Based on retain or transfer loss interest. A lengthy discourse
Loss Distributions expo-sures, which on the time value of
money is beyond the
insurance coverage bid is 20
Another useful tool for scope of this text.
best, and whether to
the risk manager is loss Instead, we will limit our
invest in risk-control
fore-casting based on treatment to the
projects. The risk valuation of single cash
loss distributions. A loss
manager’s decisions are flows.
distribution is a
based on economics—- Suppose you open a
probability distribution
weighing the costs and bank account today and
of losses that could
benefits of a course of deposit $100. The value
occur.
action to see whether it of the account today—
Forecasting by using loss
is in the economic the present value—is
distributions works well
interests of the company $100. Further assume
if losses tend to follow a
and its stock-holders. that the bank is willing
specified distribution and
Financial analysis can be to pay 4 percent interest,
the sample size is large.
applied to assist in risk compounded annually,
Knowing the parameters
management decision on your account. What is
that specify the loss
making. To make the account bal-ance one
distribution (for
decisions involving cash year from today? At that
example, mean, standard
flows in different time time, you would have
deviation, and frequency
periods, the risk manager your original $100, plus
of occurrence) ena-bles
must employ time value an additional 4 percent
the risk manager to
of money analysis. of $100, or $4 in
estimate the number of
events, severity, and interest:
confidence intervals. The Time Value of
Many loss distributions Money
can be employed, $100 + ($100
Because risk * .04) = $104
depending on the pat-
management decisions
tern of losses. As noted
will likely involve cash Factoring, you
at the start of the chapter,
flows in different time would have:
a problem set for this
periods, the time value
chapter is provided at the
of money must be $100 * (1 +
com-panion website. The
considered. The time .04) =
first section of the
value of money means $104
problem set discusses
that when valuing cash
loss forecasting based on
flows in different time Thus, if you
the normal distri-bution,
periods, the interest- multiply the starting
a widely used
earning capacity of amount (the present
distribution. To access
money must be taken value, or PV) by 1 plus
the prob-lem set, visit the
into consideration. A the interest rate (i), it
site at:
dollar received today is will give you the amount
pearsonhighered.com/rej
worth more than a dollar 1 year from today (the
da.
received one year from future value, or FV):
today because the dollar
Financial Analysis in received today can be PV * (1
invested imme-diately to + i) =
Risk Management
earn interest. Therefore, FV
Decision Making
when evaluating cash
Risk managers must flows in different time If you wish to know
make a number of periods, it is important to the account balance after

, 2 years, simply multiply Because you are earning
the balance at the end of interest on interest (com-
the first year by 1 plus pound interest), the
the interest rate. In this operation through which
way, we arrive at the a pre-sent value is
simple formula for the converted to a future
future value of a present value is called
amount: compounding.
Compounding also
n
PV(1 + i) = FV, works in reverse.
w Assume that you know
h the value of a future cash
e flow, but you want to
r
e know what the cash flow
is worth today, adjusting
“ for the time value of
n money. Dividing both
” sides of our
compounding equation
i by (1 + i) yields the
s
following expression:
t FV
h PV
e
=
n (1
u
m + i)n
b
e
r

o
f

t
i
m
e

p
e
r
i
o
d
s

In the second year,
not only will you earn
interest on the original
deposit, but you will also
earn interest on the $4 in
interest you earned in the
first period.

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