By now, everyone should have heard of the government's new mandatory retirement initiative, a life annuity scheme dubbed CPF Life.

Ordinarily, I would not have an interest in something like CPF Life. After all, I am not anywhere near retirement age, which means current policy is likely to change by the time it affects me. Also, the Singapore government has the irritating habit of making things mandatory without public consultation or agreement. Bottomline, if it's policy that doesn't directly affect me in the near future and that I have no say in how it's implemented anyway, I'm not likely to pay any attention to it.

My mother, however, is near retirement age, and she asked me to explain to her how CPF Life works. Well, actually her question was more along the lines of "Should I sign up for CPF Life now so I can get the $4000 L-bonus?"

[Figures, dangle a financial incentive and awaken the kiasu instinct in the older generation of Singaporeans to get them to climb onboard the CPF Life bandwagon.]

So after my mother asked, I decided to dig deeper into CPF Life and take a hard look at this retirement policy. It doesn't hurt that I also have a much better knowledge of actuarial science than the average person (better even than the typical finance professional I suspect).

The main questions I wanted to ask were, what's the L-bonus, how much is it actually worth, and more broadly, is CPF Life a worthwhile investment, because make no mistake, a life annuity is a form of investment, and not just insurance against longevity risk.

In the remainder of my post, I will assume that the reader already understands how CPF Life works. If not, I refer the reader to Guide A and Guide B from the CPF Board. I will be referencing information in these 2 guides as well in my discussion below, so even if you're thoroughly familiar with Guides A and B, if you're interested in reading further, you should open these 2 guides now in your browser (in separate tabs of course).

First up, an annuity is properly defined as a series of payments, while CPF Life is more correctly called a life annuity. However, the link I have provided to Wikipedia's entry on "annuity" is still a useful read for those unfamiliar with the concept of the present value of money.

Throughout this post, where I have written "annuity", I mean "life annuity". Also, this post will deal only with the Life Income Plan in CPF Life. The reason for this is that the presence of a bequest in the other CPF Life plans complicates calculations.

The first question we need to ask is, how does one value an annuity, because this will decide whether CPF Life is worth joining. The problem with valuing annuities is that payments are uncertain over time, since for most of us, we are blessed/cursed with not knowing the moment of our deaths. Hence, it is uncertain how many monthly payments each annuitant will receive over his/her lifetime.

Therefore, for the purpose of valuing annuities, actuaries speak of an *expected present value*, rather than just the present value that other finance professionals use. The EPV of an annuity is a function of monthly payments, interest rate and the probability distribution of human lifespan. The formula for calculating the EPV of a life annuity is:

This is a rather intimidating formula, so I will go through it slowly.

M is the monthly payment (hence there is a coefficient of 12 in front), the funny "a" symbol with the 2 dots, subscript x and superscript (12) is an annuity term used only in actuarial science, and x is the age of the annuitant at the time of the first payment. The superscript denotes the number of times payments are made in a year, hence the 12 in the parentheses.

On the right-hand side, breaking up the annuity term into its components, kpx denotes the probability that someone alive at age x will still be alive at age x+k, v^k is the discount term involving the prevailing interest rate, and the product of these terms is summed from k=0 to k=omega, where omega is usually the maximum age human beings live to. Typical values of omega range from 100-120. The subtraction of 11/24 is an adjustment made for monthly rather than annual payments.

Values of M and v are available from page 6 of CPF Guide A . However, where does one get values for kpx for k=1 to k=omega to value the annuity? (by definition, 0px=1).

Answer: Actuaries whose professional job is to calculate these things rely on figures from life tables, which are data tables from which one derives these life probabilities.

Published life tables for Singapore's resident population may be found here.

From the life tables, for a given value of k,

kpx = (number of lives alive at age x+k)/(number of lives alive at age x)

From here, it's quick work on an Excel spreadsheet to calculate the EPV of an annuity. Note that I used the **2006 male** life tables for my calculations.

From page 6 of CPF Guide A, we have 4 examples of the Life Income Plan, 2 for an RA balance of $20,000, and another 2 for an RA balance of $40,000. Each pair is further divided up into one with an interest rate of 3.75% and one with an interest rate of 4.25%, for a total of 4 plans as mentioned above.

My calculations indicate that:

EPV $20,000 RA, 3.75% = $17,279

EPV $20,000 RA, 4.25% = $17,217

EPV $40,000 RA, 3.75% = $34,222

EPV $40,000 RA, 4.25% = $34,126

The first thing you would notice is that an RA balance always purchases less than the EPV of the corresponding annuity. This is perfectly normal. The reason for this is that administrative costs are incurred in setting up annuity policies, and annuity managers, out of prudence, typically provide for some kind of buffer or contingency in the funding of the annuity scheme (after all, there is a wide variation in when exactly people drop dead).

The EPV of an annuity, in actuarial parlance, is termed the risk premium. It is the expected cost of claims under an insurance policy (which in this case, is an annuity policy). Private insurers selling annuities will typically charge considerably more than the risk premium as they need to cover administrative costs, commissions as well as provide for a profit margin.

In contrast, the CPF board is a government entity, which obviates the need for profit, and since it already manages CPF accounts for all Singaporeans, additional administrative overhead would presumably be negligible. The small difference in risk premiums for the CPF Life Income Plans, as calculated above, relative to the cost of purchasing the annuities, is a reflection of these considerations.

So as far as annuities go, the CPF Life *is* actually a good deal [it is so rare that I have something good to say about a government policy!]. It is a much better deal than private annuity plans which are more expensive from a valuation standpoint. Also, CPF Life, unlike a private plan, is unlikely to go insolvent.

However, some caveats:

The main problem I have with CPF Life is the lack of transparency and guarantee. The footnotes on page 6 of Guide A states "The payout range ... does not represent the lower and upper limits of the payout ... monthly payout may be adjusted every year to take into account factors such as CPF interest rate and mortality experience."

Great, this basically defeats the purpose of buying an annuity. The whole point of buying insurance is to pass on the longevity risk to the insurance company at an expense which represents profit to the company. People buy insurance for certainty and peace of mind in an uncertain world. All the fine print here in Guide A provides an escape valve for the CPF Board to reduce payments to retirees who would otherwise expect to be on a fixed income. I do not use the word "reduce" here frivolously. Central bank response around the world to the ongoing financial crisis is to slash interest rates close to 0, which would tend to reduce monthly annuity payments. Improving mortality experience in the future (that is, people living longer) is almost certain due to advances in medicine over time. That is a second reason why annuity payments are likely to be reduced.

Next, the lack of transparency and guarantee brings me to the reason why I calculated risk premiums only for the Life Income Plans. With the pitiful amount of information available in Guides A and B on how bequests are calculated, there is no way I can accurately calculate the risk premia for all the other CPF Life plans which involve bequests. Based on the monthly payouts given on page 6, I can only guesstimate that the other CPF Life plans also represent fairly good deals from a valuation standpoint. But I cannot stand by this assertion as I have no hard figures to back me up.

Lastly, just because CPF Life seems like a wonderful annuity scheme doesn't mean that annuities are the right investment for everyone. Annuities may not be suitable for those in ill-health, or for those (including myself) who are concerned with that ever-present scourge called inflation. Bottomline, if you like annuities, you could do a lot worse than CPF Life, but that doesn't mean annuities are an ideal choice for you. Every person will need to consider their own financial and personal situation before purchasing an annuity.

Personally, I think longevity risk is a real problem and the government is right to consider it at the policy level. However, I also suspect that CPF Life is not meant as a solution to longevity risk per se in our population, but is a manifestation of policy tokenism.

Simply put, the government must do something about our rapidly aging population, and CPF Life, just like Eldershield, is a token effort to show that the government is *doing* something. But the monthly payouts are pitifully low (particularly if we factor in the effects of inflation over time) and the very fact that all these schemes and policies are both mandatory and *self-funded* are indicative that the government has no desire to *own* the problems. Despite us paying our taxes and the government running huge budget surpluses (even after paying our ministers million-dollar salaries, *and* throwing money at "investments"), the government is still fearful of draining its abundantly filled coffers on something like healthcare and retirement care. Instead, it discriminatingly spends on education and economic development, which while worthy causes in their own right, more obviously provide a return on investment (which is why the government has no problem spending there).

PS: the L-bonus is a top-up of the RA that the government makes to eligible citizens for the purchase of an annuity plan. Simply substitute an amount of L-bonus in the EPV term on the LHS of the equation I have provided, and you will be able to calculate the M term instead. In practice, an L-bonus of $4,000 increases the monthly payout by approximately an additional $20 per month.

## 1 comment:

At some point last year, I was contemplating if my Mum should be enrolled for CPF Life. Yes, as you pointed out, I wanted the carrot - the L-bonus. The caveat is she has to be enrolled before she reaches 56 years of age.

Yet, the L-bonus receivable is dependent on FOUR factors: age, annual income, property value and Retirement Acct (RA) balance. CPF's website provides a table that approximates the amount of bonus one can receive based on annual income and property value. And that's it. It offers no discernible way of computing a more accurate number after factoring in one's age and RA balance. I guess I could get a more accurate number if I email them.

It's ridiculous that to get a paltry bonus of maximum $4K, one has to get his figures correct on 4 qualifying criteria and then write in to verify. If you are not particularly savvy with the Internet and/or have only primary school education, "good luck" is probably what the govt would say. There's absolutely no transparency on how the exact number can be derived. A calculator on the website would be useful. And if one's RA balance is already very low, after comprehending what's going on and getting a response from CPF, you probably end up with a couple of hundreds in bonus.

And mind you, the bonus may not be even worth the early entry. By joining the scheme by 56 yrs of age, you effectively hand over your RA to the govt, to be added to the pool of monies for CPL Life. So...until you can draw on CPF Life at 65 years, there's 9 years you don't get a single cent. At interest rates of 4% + 1% (extra interest) for 9 years, your RA can generate more than the absolute value of the bonus if you continuously top it up and let it compound.

It's so typical of our govt. To make us navigate bureaucracy just to get a few dollars. The common refrain: they wouldn't want to raid the reserves unless for emergencies. Meanwhile, the population is ageing. The older generation is also not as financially literate as we are. With budgetary surpluses, you would expect the govt to loosen the purse strings and help the older folks a little more. Just the older folks. Not the entire population. I guess that's too much to ask.

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