Actuarial Present Value Actuarial Present Value and Sensitivity Analysisand Sensitivity Analysis
What does an Actuary do?What does an Actuary do?
Areas of Actuarial WorkAreas of Actuarial WorkLife InsuranceProperty and Casualty Insurance
(P&C)Health InsurancePensionConsulting
Life InsuranceLife InsuranceLife companies principally serve two
functions◦ to insure against financial loss in result of death◦ to save and invest money for retirement
Less exposed to risk than P&C companies
Invested in longer term assets
Types of ProductsTypes of Products◦Term Life, Whole Life, Universal and
Variable Universal◦Fixed, Deferred, and Variable
Annuities◦Asset Management, Mutual Funds
Why do companies use life Why do companies use life tables?tables?
To help predict the amount that will be paid out in claims (known as liabilities)
Example:◦ Tom, aged 22, buys a one year, $250,000 term
policy◦ Expected claims equals total amount at risk
times the probability of claim◦ Expected claims = $250,000*0.000987=$246.75
Note that $246.75 is the average amount of claims expected by the insurance company
Actual claims may differ substantially
The Collective Risk PoolThe Collective Risk PoolThe basis of insuranceA large number of people buy an insurance
productOnly some of them will be affected – The risk is
shared among the groupThe company is able to predict total claim
amounts of the entire risk pool accurately
The Time Value of MoneyThe Time Value of MoneyA dollar today is worth more than a
dollar one year from now◦At 7 % interest, $1.00 becomes
$1.07 one year from now, but $1 received one year from now is worth: $1.00/1.07=$0.93
PV = FV/ (1+i)^t
Whole Life ExampleWhole Life ExampleSuppose Tom, aged 22, buys a
$250,000 whole life policy.◦His expected number of years left is
56.5◦That means on average, the company
will pay out $250,000 in 56.5 years. ◦PV = FV/ (1+i)^t◦The present value of this liability is
thus: $250,000/(1.07)^(56.5)=$5,467.09
Limitations of these Limitations of these examplesexamplesThe probabilities I used were taken
from data representing ALL of the U. S. population◦Mortality rates are known to differ
according to certain socioeconomic, demographic, gender, and health factors
◦Companies must draw up their own life tables based on their own customer base
The actual modeling process of these life policies is much more complex than indicated
Where does the Actuary Where does the Actuary come in all of this?come in all of this?I worked in an area of the company
known as Corporate Actuarial◦Statutory income statements and
balance sheets
Actuarial Present ValueActuarial Present Value3 basic components of valuing an
insurance policy◦Expected present value of premiums
(known as assets)◦Expected claims (liabilities)◦Cost of selling the contract by
insurance salesmen (called “financial representatives”)
Total Value=Expected value of assets – Expected value of liabilities – acquisition costs
My First Project: Sensitivity My First Project: Sensitivity AnalysisAnalysisThe value of a contract changes over
timePV = FV/ (1+i)^tAssumptions that can change the value
of an insurance contract◦Mortality Rates: causes change in present
value of liabilities due to when claims are paid out
◦ Interest Rates: causes change in how much future dollars are worth – generally affects assets more, but not always
◦Managing interest rate risk is known as duration analysis
Sensitivities to be tested:Sensitivities to be tested:Mortality/Morbidity: Mortality/Morbidity rates
were scaled up and down by 10% in the ALFA model
Interest/Discount rates: Up and down 1% from 7%
Equity Rate: Increased/Decreased rates premiums grew at up and down 1%
Lapse/Termination rates: Up and down by10%
Rates chosen to provide input for an upcoming audit of the firm’s financial statements
AppendixAppendixBellis, Claire et al., Understanding Actuarial
Management: The Actuarial Control CycleBlack, Kenneth Jr. and Harold Skipper Jr., Life InsuranceEaston, Albert E. and Timothy F. Harris, Actuarial
Aspects of Individual Life Insurance and Annuity Contracts
Hull, John C., Options, Futures, and Other Derivatives
ConclusionConclusionThanks for comingAny Questions?