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ANNUITIES

Just To Be Clear

The annuities discussed here refer to insurance products where mortality risks are shared. In exchange for a lump-sum payment, the issuer provides a stream of benefits until the owner dies. The benefits are larger than the income that could be earned by each individual buying risk-free bonds because the remaining principal of members of the cohort who die early, subsidize the ongoing payments to those who live longer.

This is completely different from the word 'annuity' used in finance or math or the time-value-of-money equations for 'Present Value of an Annuity' or 'Future Value of an Annuity' . That use of the term refers to a stream of equal payments as well, but there is no transfer of value between population cohorts. That is a concept, not a product. If you find something called an 'annuity calculator' on the web, chances are it is a TVM calculator with nothing at all to do with annuity products.

This page does not pretend to discuss all the issues relevant to annuities. To simplify the ideas, unless stated otherwise presume that the annuities discussed here are Single Premium Immediate Annuities that:

• pay fixed benefits for life,
• start benefits immediately after purchase,
• provide no minimum guaranteed period,
• provide no death benefits,
• provide no increases for inflation, and
• attract no taxes.

Resources

• Canadian quotes from issuers - Globe Investor
• Opportunity cost of delaying a purchase from age 65 to age 75 - ifid's calculation of ILY
• Annuity Choice spreadsheet compares your choice of an immediate purchase vs a delayed purchase vs a deferred purchase.
• Convert a flat income stream to an inflation adjusted one - (spreadsheet)
• 1971 Mortality Tables - used to determine %benefit is taxable for prescribed annuities.
• Example of calculation of taxable income for non-prescribed annuities - spreadsheet
• Life Expectancy Calculator - CAN
• Life Expectancy Calculator - US
• US quotes from issuers - Immediate Annuities.com
• British quotes from issuers - MoneyMadeClear

Risks

Annuities are insurance contracts. They insure against longevity risk - the risk that you live so long that you run out of money. Like most insurance products, their value to the buyer depends on his ability to self-insure - to pay for any losses by himself. Academics have found that people generally distort probabilites in their decision making. Low probability (2%) events like dying by age 65 are weighted at a 6% probability. Conversely, people overweight the probability of living beyond age 99.

The need to get rid of longevity risk decreases as your wealth (relative to spending requirements) increases. The less-wealthy person may be forced to gradually liquidate their nest-egg during retirement. He faces the risk of running out of both income and capital. Longevity insurance is very important to him. The very rich may have enough assets to cover his costs to 150 years old. He don't really need to buy insurance.

There is no hard rule for deciding who is wealthy enough to NOT need annuities. An approximation would be the person whose nest-egg equals ( his yearly living costs including taxes ) times ( his remaining lifespan in years ). All his income needs to cover is the increase in living costs due to inflation. Other people who may put little value on longevity risk are those who receive Defined Benefit pensions, or those with real estate that generates positive cash flows.

Annuities also insure investment returns. Investors who have lost money in the markets are drawn to annuities as a form of professionally-managed-guaranteed-return investment. The annuity's guaranteed benefits makes comparisons with other risky securities difficult, if not completely meaningless. There is no practical way to address this problem unless you restrict your comparison to risk-free government debt, or do a 'gut-feel' analysis.

If all you need for living expenses is a guaranteed return that is slightly higher than current government bond yields, and you want to leave an estate after death, it is common to pair a Prescribed annuity with a term-to-100 life insurance policy. This removes the cost of longevity insurance. If you match the value of the life insurance to the cost of the annuity, the net cashflow is your guaranteed return. You get no tax break from the life insurance premium costs, but the preferential tax on the annuity income (see below) usually means your net after-tax return will be higher than a simple purchase of debt. Be clear you cannot reverse the decision. The principal only becomes available after your death, and the net income payments will not change with changing inflation.

Counterparty risk should not be ignored. This is your risk that the underwriter goes belly-up. The risky issuer should be offering higher benefits as compensation but it is impossible to determine your effective risk - now and in the future. In Canada insurance companies contribute to a fund for covering the contracts of defaulting issuers. But it is not limitless, nor it is backstopped by the taxpayer. In the U.S. annuity divisions of issuers have been sold to Private Equity and Hedge Funds who channel the back-stop-assets into risky securities. The new owners stand to capture all the potential upside, with annuity owners suffering the downside.

It is common practice for individual underwriters to spread their own risk wider by themselves buying re-insurance. You should check the company's credit rating even though that will change over the 40 years of your policy. If you are making a large purchase, spread it between different issuers. It has been suggested that you should buy from either a very small issuer or one that is too-big-to-fail. The industry fund should be large enough to cover the smaller book of contracts of the small issuer, and the taxpayer will bail out the too-big-to-fail issuer's contracts. But again, the status quo won't last the life of the contract.

Social risks . E.g. elder abuse should be considered at least, before rejecting with "My family would never do that." Hitting up grandma to 'co-sign my loan', to fund 'this great idea', to 'just get me back on my feet', etc. is probably not infrequent. Locking away your money where it cannot be touched in an annuity may be good protection.

E.g. when the first spouse of a couple gets ill, there is huge pressure for the healthy spouse to insist that 'no cost be spared' - even if it bankrupts her or leaves her with no money for her own later illness, which she must handle without a built-in care-giver. The pre-existence of an annuity safe-guards her support and prevents the issue from arising.

E.g. Cyber-warfare is a reality everyone should consider. Imagine that the world-wide internet were compromised. Stock portfolios could conceivably become worthless. An annuity cheque in the mail every month with a contractual agreement would feel pretty good.

Loss aversion makes annuities less attractive to many people. This is where a $1 loss is considered twice as bad as a $1 gain. In this case people ask "What is the probability that I die before recovering the investment cost?". Instead of seeing the product as risk-reducing, they see it as gambling on their own death. This is why most Immediate annuities sold include a guarantee period. The guarantee makes the product seem less risky. In reality the person could accomplish the same thing by purchasing a series of strip bonds along with a Deferred annuity.

These people are segregating their mental accounting. They look at the product in isolation. It makes more sense to consider it as integral with all the other retirement purchases, benefits and spending - to consider its effect on your ending $$ wealth.

A close cousin to the insurance company's annuity is a Reverse Mortgage where you borrow against the principal value of your home. Although borrowing a lump-sum is most common, you can also structure deals that pay benefits that provide an income stream until the end of the contract. Assuming you stay in your home until close to death, this product incorporates longevity insurance, as well as protection from market returns.

You might mentally consider yourself to have 'sold' your home to pay for this income stream, just like you pay cash to buy a normal annuity. But there is a big difference between the products if you die early. Where as owners of an annuity die broke because all the principal is lost, the owner of a Reverse Mortgage need only pay back the borrowings and accrued interest. If little time has past, then there will be equity remaining.

Here is an interesting paper discussing the different types of Reverse Mortgages from the issuer's point of view .

Factors Determining Annuity Prices

Supply and Demand: Issuers know that most buyers will compare quotes from competitors. They will compete by offering higher benefits to offset their corporation's lower credit rating or because they are more motivated to gain market share. Differentiating their product with bells-and-whistles attracts certain sub-sets of buyers. It has been claimed that the value of extras (like inflation protection and guarantee periods) doesn't justify their price, but without insider information it is impossible to judge. It may be that there is seasonality to pricing due to the annual rush to convert RRSPs into RRIFs. It is at this time that most people make their annuity purchase.

Interest Rates: The issuer takes your purchase price and buys a portfolio of debt. The rate of return on that debt will be the bedrock of the annuity's pricing. Bond yields have declined since the 1970's inflation. That is at least part of the reason for the 16% (men) and 18% (women) decrease in benefits from October 2000 to October 2010 (ifid table). But bond yields cannot decline forever. They may even increase.

Annuity pricing is much less influenced by interest rates than most people think. Charaput et al found that 30 year mortgage rates are better at explaining changes in annuity prices than are risk-free Treasury bonds. It appears that companies delay changing their prices for fear of losing market share, and in order to see the longer-term rate trends. Compared to a 16-week change of 1% in the mortgage rate, annuity prices for 65 yr-olds change about 5%. (Duration = 5). The price changes are very sticky when rates fall, but react more swiftly when rates rise.

Mortality Rates: Annuities depend on people dying, the faster the better, except for you of course. Their pricing depends on actuaries predicting your probability of dying 20, 30, 40 years ahead of time. Each company develops their own proprietary mortality tables. There are publicly available tables for the general population, but these do not represent the reality faced by annuity issuers.

The people buying annuities self-select for health and an expected long life. Nobody buys longevity insurance when they expect to die soon. (Although if you have a poor medical history you can buy special annuities with higher benefits.) This chart compares the probability of dying in any particular year between the general population and a population of annuity-buyers. Note at age 70 the probability of an annuity buyer dying is almost half that of the general population. Half the cohort has died by the age of 83 in the general population, but not till 86 for annuity-buyers.

These tables get changed over time as society gets healthier. If you delay an annuity purchase you may find the benefits have decreased because the company is experiencing fewer deaths. Or maybe the epidemic of diabetes will result in higher death rates in the near future. The OSFI 2010 presentation has very interesting charts showing changing mortality and changing rates of change for Canadians, especially pages 5, 9 and 12.

The issuers can only afford to pay you more than the market rate for bonds because they distribute the remaining principal from members of your cohort who die. If the bond portfolio earns a 5% return, and 2% of your cohort die in the year, the company can distribute 7% to the people remaining alive (roughly). The pricing of products available to younger people reflects little benefit from mortality credits because few people that age die. The probability of death only starts becoming meaningful after about age 65, so the buyer gains little from annuities purchased before that age.

The graph above represents cumulative benefits from two points of view - the owner and the issuer. The top line reflects the cumulative value of benefits received from the POV of the individual owner. Each year's benefit equals all the others, and the cumulative total increases in a straight line. The lower line reflects the issuer's POV. As the years go by fewer of the original cohort are left alive, so the issuer's yearly outlay shrinks. The cumulative outlays line flattens out. The outlay added each year equals
( the quoted benefit paid to each person ) multiplied by ( the percentage of the cohort still alive- per the table above).
The difference between the two lines equals the mortality credit - the remaining principal value of those who die that accrues to those remaining alive. When taxation is discussed below you will see that non-prescribed annuities are taxed 'from the POV of the issuer' - the bottom line.

Life Expectancy

'Life Expectancy' is not the same as asking when 50% of you will have died. The 50% number gives you the statistical median. For Life Expectancy you want the average or statistical mean. The total person-years remaining for your cohort is divided by the size of your cohort today. Think of it as the ratio of the area under the survivorship curve BEYOND your age, divided by the height of the line AT your age. In the chart below the area under the curve, beyond age 60 is 17,647. The surviving cohort at age 60 was 868. The life expectancy at age 60 was 17,647 / 868 = 20 years. This is from the 1971 mortality table spreadsheet.

The number of that same cohort of 60-year-olds (only 868 remaining of the origial 1,000 births) that die each year is a function of both the rising probability of dying, and also the declining size of the cohort.

Is the Price Right?

The pricing of annuities can be looked at from the point of view of the buyer or the issuer. Some people claim that the insurance company is laughing all the way to the bank and the products are a rip-off. But from the issuer's POV, pricing in Canada was very fair in 2009. The table below shows the money's-worth-ratio for different countries. This measures the total benefits paid out as a ratio of the original funding, assumed to earn the risk-free Treasury return. A ratio greater than 1 shows benefits paid greater than costs. Of the two columns only Annuitants column is relevant because it reflects the mortality table for those who self-select to buy annuities. ( paper by N. Nielson for C D Howe).

From the POV of the buyer, most discussions present generalized conclusions that completely ignore the product's price. But like all financial products, it is the price you pay that determines your profits. The industry norm is to quote monthly benefits for a standard $100,000 purchase. So instead of comparing the product's price, you compare the yields. Same thing. Price determines yield - yield determines price.

People typically under-estimate the power of compound interest. At the extreme, they wrongly value annuities with NO discounting. E.g. An annuity that pays $8,000 a year where they expect to live another 20 years is valued at $160,000. The market pricing of the actual product would always look like a great deal.

Just like other investments, you evaluate an annuity by comparing it to your other investment opportunities. But the annuity's yield is not directly comparable to other securities' yields, because part of each payment is a return of the purchase price. When you die there is no remaining value, but there is no knowing when that will be. Think of an annuity like a mortgage. The payments are a blend of interest and principal. To make any comparison to other products you need to calculate its implicit interest rate (i%).

Use the Present Value of an Annuity ( PVA ) function on your calculator. You already know two of the inputs :
PV = the $100,000 purchase price, and
Pmt = the monthly benefits quoted by the salesman (times 12).
n = the number of years until you die (lifespan) is a subjective input.

The longer lifespan you use, the higher the resulting i% and the more attractive the annuity will appear. Your choice of lifespan depends on how much value you put on longevity insurance (discussed above). If you are the rich person, who benefits little from longevity insurance, you could use your own expected lifespan. Add (say) 10 years to your parent's age at death, or 20 years to your grandparent's. The less wealthy person should use a lifespan that is super safe - at least to age 100.

Do NOT use the average lifespan for people your age. Averages are relevant to the issuer, but not to you. The variability around that average is huge. Think of a bell curve. Two thirds of people would die within +/- one standard deviation of the expected. From the chart below a 70 year old's life expectancy falls between +/- 50% of the average. Using the same Social Security Table above the life expectancy of that 70-year-old was 13.6 years. So the range of highly probable life expectancies is between 6.8 and 20.4 years. A VERY wide range.

Once you have calculated the implicit interest rate (i%), compare that rate to the yields of super safe government bonds that are laddered with different maturities. Or if you are willing to assume some investment risk, compare to the total returns you expect from other investments. But beware of the risk mismatch. The annuity insures your rate of return as well as longevity risk, so your comparative investment should also be on the safe side.

Should You Delay A Purchase?

Even if you decide that it makes sense to buy an annuity today, you may find it better to delay the purchase. There are two ways to evaluate this choice. Both ways model the results of a choice between buying an annuity today, or instead, investing somewhere in the interim and then buying the annuity at a later date. If necessary in the interim, the alternate investment is gradually sold, so that cash flows are equal between the choices. The following is an example showing HOW to evaluate the choice. The process is automated in the Annuity Choice spreadsheet.

There are four unquantified risks in the decision that must be considered.

1. He may die in the intervening 10 years. Does he care himself? Probably not because ... he is dead. That is the only logical reaction. His beneficiaries would much prefer he had NOT bought the annuity because all value evaporates on death. But that is only hindsight. They would much prefer he HAD bought the annuity if during the delay he loses all his money in poor investments - leaving them to support him. From the beneficiary's POV the risks offset each other.

   Many do care though. It is this fear of dying early and losing all your principal that prevents many people from buying annuities. This fear is the reason the issuers provide the option of a guaranteed minimum period. But the value you personally place on this risk is purely subjective. Logically there is little to justify the market price for this risk implicit in products with guarantee periods.

2. He may face a need for money in the interim that exceeds his normal-course budget. If he gets sick, not only will his life expectancy fall (and the value to him of an annuity), he may face bills that are larger than the annuity's benefits. You should ignore the possible change in life expectancy. Hindsight is perfect. The whole point of annuities is that you don't know, ahead of time, who will die young and who won't. You share the risk. That is the benefit of annuities.

   The need to spend more money than the benefits provide is faced by most everyone, not just the person who gets sick in the (say) 10 year delay period. High medical costs at the end of life will affect many of us who linger with dementia or stroke. Advisors seems to ignore this reality. Baby boomers frequently presume the taxpayer will cover all their expenses. Maybe family members will provide the support and pay the bills. The problem is solved, not by delaying the purchase of an annuity, but by not spending all your capital on annuities. You should keep a portion of your capital invested in your home, or securities for these large expenses later in life.

3. The annuity pricing for the 75 year old may have changed by the time of purchase 10 years later. Will people be living longer or shorter? As at 2010 the interest rates determining benefits are at all time lows ... surely they can only go up from here ... there is no room to go any lower. But then the same thing has been said by most people for eight years.

4. Preferred shares (or any other alternate investment) have values determined by the market. Unlike bonds, perpetual preferreds do not guarantee you a surrender value. Interest rate changes will impact the pricing of preferreds MORE than the pricing of the later annuity. There is a mis-match of risk between these choices. You should not accept the risky choice unless the expected benefit from delaying is LARGE.

Moshe Milevsky has come up with another way to evaluate the decision to delay a purchase. He compares two annuities - an immediate annuity with a guarantee period equal to the 10 year delay, and the annuity paid to the older person. He reconciles the difference ensuring the cash flows are equal for each option. From this he calculates the rate of return you must earn from any alternate investment to make you indifferent between the choices.

He calls this the Implied Longevity Yield ILY - a misleading choice of names. A value for the risk of dying (the first risk above) in the interim period is integrated by the implicit pricing for the guarantee. But this market valuation of the risk may not equal your personal valuation. He has published the historical ILY calculations for a delay from age 65 to age 75 on this webpage.

Deferred Annuities

A lot of the risks faced by delaying the purchase of an annuity are reduced with the product called a Deferred Annuity. You pay today and the benefits are set at the time of purchase but they don't start until a later date. The following assumes that the product does NOT involve adding additional savings in the interim before the benefits start. Consider.

• You get the benefit of the larger yield paid for older purchasers.
• You get that rate set so that they cannot change it in the interim.
• The price for the policy is discounted for paying ahead of time, so your investment at the start is smaller.
• The $$ at risk in the alternate investment that funds the interim cash needs (until the annuity's benefits start) is smaller than in the option to delay a purchase.
• The pricing of the policy allows you to benefit from mortality credits from deaths in your cohort in the interim before your benefits start.
• The cash paid upfront grows in value inside the plan tax free.

This choice will almost always trump the choice to delay a purchase. It will hurt to think about dying before receiving a cent, but the smaller investment helps with that mental hurdle. The Annuity Choice spreadsheet includes this option.

Annuity Ladders

Instead of buying your whole quota of annuity at once, you can stagger purchases of smaller amounts over time. The delayed purchase addresses the buyer's reluctance to commit capital that may turn out to be needed for some big-ticket item, or his reluctance to commit capital that may disappear tomorrow if he dies. Laddering may reduce the risk of regret.

Beware of advice that prescribes set percentage top-ups based on supposed historical data. The decision to ladder is exactly the same as the decision to delay. The math is the same, and the risks are the same. Some people claim that laddering reduces interest rate risk and is comparable to laddering your debt holdings. But risk refers to the unknown. With any delay in purchase you face unknown changes to interest rates and other variables. If product prices fall in the interim you get a better deal by waiting. But of course there is the other possibility that product prices rise.

Inflation Protection

The insurance industry offers some products where the benefits increase with the CPI. But

• They often have provisions that any increases will not exceed (say) 6% inflation. Exactly when you need the coverage, they don't work.
• Other products provide for set (say) 3% yearly increases in the benefit regardless of CPI inflation. These do not offset inflation risk. Risk refers to the unknown. These products only manage cash flows with investment return insurance.
• Inflation protected products do not qualify for the preferential tax treatment of Prescribed Annuities. The higher tax may wipe out any additional benefits from inflation protection.
• Product pricing is said to be 'not worth it'. The retail purchaser will not really be able to put a value of the risk reduction. Just like for RealReturn Bonds, the buyer pays a premium for the risk reduction that may be larger than the rest of the population values it.

You can evaluate the worth of these products using the Spending spreadsheet. As an example take the 65 year old male above who can buy an indexed annuity with a 5% yield. Assume he wants $500 a month or $6,000 a year. That means his annuity would cost $120,000 ((6,000/0.05).

For the spreadsheet variables use
Inflation of (say) 2%,
Principal = $120,000 (the cost of the annuity),
0% tax rate (because taxes must be paid out of the annuity payment),
35 years to death because if you DIY you must cover off all eventualities.

Now play with the Rate of Return variable to see what you would have to earn, steadily and completely safely, to generate a $6,000 yearly withdrawal (in the Die Broke scenario). It is only when you earn 5.5% that you can spend $6,061 yearly. You certainly could not generate that 5.5% with Treasury bonds. If you consider stocks paying a growing dividend to be a safe alternative to annuities, remember that the yield will cover only a portion of that. See the box on the Got Enough page to see how high yield portfolios can fail.

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You can manage inflation yourself using the ladder concept. The following idea is not self-insurance against inflation. It only manages the cash flows for expected inflation - not un-expected higher inflation. You can manage your need for an increasing cost of living by not spending all the benefits from your regular annuity in the early years. Set aside and invest a portion of each payment. Periodically use the cash to buy another annuity. The benefits from both policies would equal your inflation-adjusted cost of living. With this strategy you are assuming the same investment risk and other risks as in any delay decision. But the dollars involved here are much smaller than in the decision to delay the initial purchase. You can model the amount required to be saved using this spreadsheet. You can use the same spreadsheet to evaluate the pricing of an inflation-indexed annuity product.

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When married couples buy joint coverage they face the decision whether the surviving spouse's benefits should decrease, remain the same, or increase. In most cases they should increase, unless you have inflation-proofed the benefits.

• By the time of the first spouse's death inflation will have eaten into the value of the original benefits. An increase would partially rectify the situation.
• A presumption is commonly made that one person can live cheaper than two. But will that be true? Other than food and medicines what expenses will be reduced? And what about the additional costs to the survivor of paying people to do some of the (eg) repair chores previously done by the now dead spouse?
• Consider the costs of health care. Chances are that the first-to-die was cared for gratis by the spouse. The second spouse will have to pay for care.

Canadian Taxes on Annuity Benefits

The decision to buy an annuity, and also the decision to defer purchase should be made on an after-tax basis, like all financial decisions. Annuities are taxed under three different systems.

1. Purchases made with RRSP or RRIF money end up being treated like any other investment in those accounts. All the benefits received are fully taxed as income.

2. Prescribed Annuities have a simple formula for determining the portion of the benefit that is taxable. It is set and can be calculated ahead of time.
   • Start with the 1971 Tables that are prescribed by the Tax Act.
   • Look up your age (when purchasing) and the life expectancy for that age.
   • Divide the annuity's purchase price by that longevity, to determine the yearly amortization of cost.
   • Subtract that amortization from the yearly benefits.
   • The rest of the benefits are taxable income.
   • For every year after, the taxable income will be that exact same $$ amount.

   Example
   A 70 year old male buy a $ 100,000 annuity with benefits of $ 8,460 yearly.
   Look up on line for age 70 shows life expectancy of 13.76 years.
   The purchase price $ 100,000 divided by 13.76 years = $ 7,267 amortization yearly
   The taxable income = 8,460 benefit less the 7,267 amortization = $ 1,193

   
   
3. Non-Prescribed Annuities are a lot more complicated. So complicated that you will not be able to tell ahead of time what your taxable income will be. It varies over time (getting smaller) and depends on the issuer's proprietary mortality table - which they will not publish. As an almost universal rule you should accept that Prescribed annuities are taxed at lower rates than non-Prescribed - as shows in the graph above. The lines don't cross until you are older than 100. The taxable income in the first year may be very low because the issuing costs are allocated to you for a deduction. If you ask about taxable income and they tell you the amount for the first year only, consider it meaningless.

   Taxable income is calculated according to an amortization table that is very similar to the table you know for a mortgage. But in this case the table reflects the point of view of the issuer, not the owner. The portion of the benefit coming from the capital of people who have died is not taxed. Neither is the return of your own capital taxed. To understand the calculation you have to follow an actual spreadsheet's calculations.

   

Buy with RRSP or Non-registered Cash?

Canadians' decision to buy an annuity is usually made around age 70, when the RRSP must be rolled into an RRIF. If your assets are all inside an RRSP then there is no question - the annuity is bought with RRSP cash.

But when you hold assets both inside and outside an RRSP, you must decide which to use for the purchase. The simplicity of holding an annuity instead of an RRIF may outweigh any tax considerations. As a very general rule taxes are slightly higher when a Prescribed annuity is bought with RRSP cash. But that conclusion may reverse if a longer lifespan is assumed because the minimum withdrawal from the RRSP increases in later years (depending on your presumed rate of return). If the annuity has bells-and-whistles that make it Non-Prescribed then it is generally better bought with RRSP cash in order to avoid the much-higher taxable income.

Your conclusions will depend on assumptions about an unknown future. The following example shows you how to model the decision. You must use your own assumptions.

There are other issues to consider.
a) Annuity products designed for purchase from RRSPs may have lower benefits, making Option B look even better.
b) The marketable securities invested outside the RRSP in Option A may be held for many years without selling - so not triggering taxes and lowering the effective tax rate. This makes Option A look better.
c) If not all the cash flow is spent - with some reinvested to take care of inflation - the marginal tax rate on the income from those reinvested assets may be different in each Option.
c) If you worry about taxes reducing the value of your estate, after you die, then Option A looks better. In Option B, the remaining securities inside the RRSP will be considered taxable income on death.

Interesting Reading

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