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?