ACST152 Introduction to Actuarial Studies

ACST152 Introduction to Actuarial StudiesLecture 4A in 2015 Retirement Products and Lifetime AnnuitiesLast week we looked at fixed term annuities.

A person retiring with a large lump sum has to plan his spending this money has to last the rest of his life.

He has different options, e.g. :

* level payments : spend $X per annum for the next n years

* increasing payments: spend $Y in year 1 increasing with expected inflation

* spend less than the investment income each year, so that the account balance never falls (perpetuity)

Or choose some other pattern of spendingFixed Term AnnuitiesSam has $500,000 at the date of retirement.He can invest in an account which earns 5% p.aWhat should he do with his money?

He has many different options....

Example: Retirement OptionsHe might decide to withdraw $45,000 pa in arrears until the money runs out, and then rely on the old age pension.

Q. How long will the money last?

Option 1: $45,000 p.a.Let n be the year when he runs out of money.

500,000 < 45,000 [1-1.05^-n] / 0.05

Solve for n

n > 16.62

He will be able to make 16 full withdrawals of $40000 and then a smaller withdrawal in the 17th year. Option 1 AnswerHe might decide that he will spread the money evenly over the next 20 years, and then rely on the old age pension.

Q. How much can he withdraw every year?

Option 2: 20 year plan Let R be the amount withdrawn each year

500,000 = R * [1-1.05^-20]/0.05

R = 40,121.29Option 2 AnswerHe might decide that he will just spend the interest on his account each year. The balance will never decrease. When he dies the balance in the account will be left to his heirs (whoever they are).

Q. How much can he spend every year?

A. $500,000 * 5% = 25,000 p.a.

Note that his real income will be declining each year. Prices are increasing but his income is not.Option 3: ConservativeThere are many other options, e.g.

He could take out an increasing amount each year (so that income increases in line with inflation)

He could take out a decreasing amount each year (as he gets older his lifestyle might become less expensive, e.g. Less travelling)

He could set aside an amount to be left to his children when he dies (bequest)Other OptionsBut any such plan is exposed to various risks

1. Investment Risk: what if you earn less than the expected rate of i per annum ?

2. Inflation Risk: what if prices increase so that you need more money to maintain the same standard of living?

3. Longevity Risk: what if you live longer than expected ?

4. Personal Risks: what if you suddenly need an expensive operation or your home is damaged in a storm and you need expensive repairs? [Some of these risks might be covered by insurance, e.g. Health insurance, home insurance]

3 RisksYou can manage one or more of these risks by buying annuities from life insurance companies

You pay an amount P (single premium)

Life insurance company promises that they will pay you specified amounts every year under specified conditions

Different types of annuities deal with different risks.

Buying AnnuitiesExample: Fixed term level annuity * pays $X per annum for exactly n years-> protects against investment risk

Example: Fixed term increasing annuity * pays $X per annum in the first year,* payments increase by say 3% pa every year, * n payments are made-> protects against investment risk-> allows for inflation

Examples of Retirement ProductsExample: Lifetime annuity * Pays $X per annum every year until you die-> protects against investment risk and longevity risk

Example: Indexed Lifetime annuity * pays $X per annum in year 1, amounts in later years are increase in line with increases in the Consumer Price Index, payable every year until you die-> protects against investment risk and longevity risk and inflation risk

Examples of Retirement ProductsExample: Variable lifetime annuity ( also called a with profits annuity): You receive at least $X each year as long as you live, You might receive more, if the life insurance companys investment returns are higher than i% in the year

A formula is used to calculate your payment each year

The insurer will guarantee that the payments will not fall below $X in any year (even if the investment returns are terrible)

-> Protects against longevity risk and Gives PARTIAL protection against investment risk

Examples of retirement productsPayments made monthly or weekly

Payments increase by f per annum, f is a constant

Payments increase in line with CPI, subject to a maximum increase

Payments have a guarantee period (if you die early - the insurance company pays at least say 10 annual payments)

Payments on joint lives usually husband & wife (variations). E.g. $X payable while both alive, dropping to 75% of X when only one is aliveVariations on Lifetime AnnuitiesSuppose you pay the life insurance company $100,000 as a lump sum at age 65, to buy an indexed lifetime annuity

Q. How much will you receive each year?

This is a job for the actuary..

Using LIFE TABLES (Mortality Tables)And Contingent Payments TheoryAnnuity RatesThe customer has:No investment riskNo inflation risk (if the amount of the annual payment increases in line with inflation)No longevity risk even if you live much longer than the average life expectancy, the insurer keeps paying

BUT : Q. what are the drawbacks ??Advantages of lifetime annuities1. Payments stop when you dieE.g. Save up $100,000 in superBuy lifetime annuity, Die the next day

Q. Is this a problem ??Bequest motive ??

To alleviate this problem, some life insurers offer policies with guarantee periods, i.e. they guarantee that they will pay at least, say, 5 years payments (even if you die before the end of 5 years).Disadvantages of annuities2. No liquidityThe amount paid in each year is fixed.If you need extra money for some reason (family emergency?), cant get it out.

Q. Could you ask the life insurer to cancel your annuity and give the remaining money back (surrender)?

Disadvantages of annuities3. No surrenders

You cant usually change your mind, cancel your annuity, and ask for the rest of the money to be paid back to you

Life insurers dont usually let you surrender annuities

Q. WHY ?

If so, as soon as you got sick (diagnosed with serious disease) you would surrender and ask for money back

Some will let you surrender if you can prove you are in good health

Surrendering annuities4. Trusting the insurance company

You hand over all your life savings to the insurance company....

Can you be sure that the life insurance company will still be around to pay you your benefits in 40 years (when you are 105?)

Disadvantages of AnnuitiesHistorically before regulation Several life insurers went brokeSome were simply scams {collected all your money and then disappeared}

> Life Insurance Act 1945 led to improvements

Over last 50 years, only two Australian life insurers have gone broke (sister companies : Regal and Occidental, in 1991 an interesting fraud case)

Other insurers have sometimes been in difficulties, but have survived.

AustraliaOther countries have had more problems

e.g. In USA about 1% of life insurers go broke on average each year (547 insurers between 1976-2002)

Rate of insolvency varies over time, e.g. GFC has led to several recent insolvencies

The UK, Japan, and Korea have also had serious problems with insolvent insurers over the last 10-20 years

Other countries ?1. What makes life insurance companies get into trouble? (poor quality actuaries...?)

2. What regulations exist to make sure that insurers keep their promises to customers?

After the break we will look at life insurance regulationQuestions to considerTo prevent life insurance companies from going broke-> minimum capital requirements

Capital = money put in by shareholders and/or retained past profits

Life insurance companies are required to hold large amounts of capital in case anything goes wrong. If the company becomes insolvent:Policyholders get paid firstShareholders get paid if there is anything left over

Capital Requirements5. Cost. The price for buying an annuity tends to be quite high....

Q. Why are they so expensive ?

A1. The life insurance company is taking a lot of risk. Life insurance companies are risk averse. You have to pay them to take risk. And the higher the risk, the more you have to pay them....

A2. The life insurance companies must hold high levels of capital in order to reduce the risk of insolvency. The shareholders who provide this capital must be paid dividends.

Disadvantages of AnnuitiesFor the reasons given above, lifetime annuities are NOT very popular in Australia (poor sales).

Most retired people prefer to keep retirement savings in an account-type product.

They take the investment risk, inflation risk, and longevity risk

The govt thinks this is a problem and would like to encourage people to buy more lifetime annuities.

Why?

PopularityScenario 1: Joe and Bob both age 65.Both have $500,000 in accounts

Joe dies early, leaves lots of money to kids

Bob lives to 100, runs out of money at age 80, must rely on government social security system (old age pension = OAP) to survive.

Govt cost: 20 years of OAPGovernment PerspectiveScenario 2: Joe and Bob both age 65.Both buy lifetime annuitiesJoe dies early, leaves $0 to kidsBob lives to 100 and continues to receive annuity

Life insurer uses profits from Joes annuity to pay for losses on Bobs annuity.

Govt cost: nil

Government PerspectiveMany countries REQUIRE people to buy lifetime annuities (or similar products which spread income over expected lifetime).Not ALL your super, but some

This is currently under consideration in Australia.

Politically very unpopular???

Should lifetime annuities be compulsory?Ageing Australia-> Financial Services Inquiry-> ConclusionWe need better products to help people manage their longevity risks

Better products to cope with longevity risk ?