Recently, when I’ve had the chance to listen to insurance company annuity wholesalers pitch their variable annuity riders, I’ve been hearing much ado about “reset frequencies” and the relative benefits of monthly vs. quarterly or daily vs. annual adjustments. Recall that the reset frequency of a guaranteed living benefit is the length of time that must elapse before the insurance company adjusts — and potentially increases — the guaranteed base of the contract. All else being equal, if Company A adjusts your base monthly while Company B only adjusts annually, you are better off with Company A than Company B.
Now, while I certainly agree that a week is longer than a day, the relative value of daily adjustments versus yearly adjustments is not a naïve 365-to-1 or even 256 (trading days)-to-1 ratio. (Yes, I’ve actually heard these arguments ).
Upon hearing such pitches I am usually left with (at least) two unanswered questions: (i) By how much are you economically better off with a more frequent re-set? And, (ii) can “all else” really be “equal?”
So, in this column I would like to get to the heart of annuity analytics and carefully delve into the relative merits of more frequent resets. Arm yourself with a sharp pencil, as this one’s going to require some numerical doodling and a straw man.
The Baseline: 5 and 5
Assume you invest $100,000 in a variable annuity at the age of 55, and you allocate the money to a relatively aggressive portfolio — as you should with these things. Assume further that the policy offers a 5% annual guaranteed return on the base, compounding, and a guaranteed 5% lifetime income starting at age 70. This means that at the end of each anniversary year, the insurance company will credit your guaranteed base at least 5% interest; and if the market value of your policy on the anniversary happens to be higher than last year’s base plus 5%, the company will adjust the base to the higher market value. This crediting process continues every year for the many years of accumulation, which for analysis purposes I’ll take to be 15 years. Thus at retirement (age 70) you are guaranteed to be able to withdraw 5% of the guaranteed base value — which by definition will be at least equal to the policy account value.
Notice that so far I haven’t said anything about adjustment frequencies. This (simple) hypothetical product is the canonical guaranteed lifetime withdrawal benefit with annual adjustments. It is the original Model T of the GLWB assembly line.
Now let’s do some math. Given the parameters I’ve specified, at a minimum you are guaranteed $100,000 x (1.05)^15 x 0.05 = $10,394 in lifetime income starting at age 70. Of course, you might get (much) more if the roulette wheel governing your subaccounts co-operates, but how much more can only be resolved in Monte Carlo.
The table accompanying this column gives you an indication of what guaranteed income you might expect at the age of 70 with these annual adjustments. According to statistical simulations, recently conducted by one of my ambitious Ph.D. students, Ling-wu Shao, on average you can expect to have a starting income of $17,200 per year — about $7,000 more than the guaranteed amount. Remember that the 17% income stream is an average across many different scenarios.
The same statistical simulations indicate that there is a 25% chance you might get $25,700 (or even more) of lifetime income per year. (I call this the “good” scenario to distinguish it from the average.) And in the “bad” scenario, you only get $12,600 — or less — in initial income. You can expect this “bad” scenario 25% of the time. Take a moment to understand this important row in the table, which displays results for the annual adjustments before you move on to the impact of the frequency of adjustments, which is lower down in the table.
Now let’s assume that an aggressive company comes along and offers you the following deal: At the end of every year they will not only credit your guaranteed base 5%, but in addition they will examine the market value of the sub-accounts at the end of each one of the last four calendar quarters. And, if any of those account values are greater than the last year’s guaranteed base, the company will adjust your new guaranteed base to the highest of those four numbers. This is quite different from only looking at the end-of-year value. Needless to say, there is a minor chance that December 31st is the highest day of the year, and hence the appeal of being able to pick the best of September 30th, June 30th or March 31st values.
This process is known as a “quarterly adjustment, undertaken annually.” (Some companies actually perform these calculations on a quarterly basis and adjust the guaranteed base four times per year. This is called “stacking”.) Now let’s go further and imagine a situation in which a company looks back to monthly, or even weekly values. It sounds sexy, but what is it worth?
Our main question of interest, remember, is how the frequency of adjustments impacts the expected income, and our table presents results for various frequencies.
To make sure you understand this process — and how it might not be as beneficial as it is alluring — I offer the following example. Assume you start with $100,000 in the policy and during the first quarter of the year your sub-account investments decline by 20%, in the second quarter they decline by a further 10%, in the third quarter the investments increase by 10% and in the fourth and final quarter the investments increase by 20%.
The third and fourth quarters were great and much better than 5%. But a product that offers quarterly adjustments would credit your guaranteed base with (only) the 5% at the end of the year, which leads to a guaranteed base of $105,000. The fact that the third and fourth quarter earned 10% and 20% respectively do not affect the guaranteed base, because the trajectory of your account over the four quarters was $100,000 to $80,000 (drop of 20%) to $72,000 (drop of 10%) to $79,200 (increase of 10%) and then $95,040 (increase of 20%). At no point did the account value exceed $105,000 or even $100,000 — so all you are credited is 5%. In fact, in year No. 2 the subaccount investment values must grow by at least (105,000/95,040)-1 = 10.48% by the end of any one of the quarters for the “quarterly deal” you’ve been offered to have any value. Sure. It can happen, especially in volatile markets, but the odds don’t favor it.
Numerical minutiae and details aside, the table in this article illustrates the average, good and bad retirement incomes you can anticipate at age 70 — as a function of the adjustment frequencies.
For example, if the insurance company adjusts the base values quarterly (see row 3 in the table), you can expect $17,900 in income at retirement, while a company that does this weekly (row 7) leads to a median value of $18,600. Notice the (inter-quartile) range between the 75th percentile and the 25th percentile. Conclusion: The more frequent the adjustments, the greater the potential range of incomes.
Now take a look at the right-most column (“Relative Value”) in the table. Looking at the “good” scenario, you can see that a weekly adjustment to the guaranteed base (with stacking – this is row 8) is about 10% more valuable than a simple annual adjustment (row 2) from the perspective of anticipated income. In contrast, a company that adjusts the guaranteed base once every three years (row 1) provides about 15% less income (and value) compared to the Model T baseline (row 2).
Remember, greater update frequency exposes insurance companies to more risk — all else being equal — which many companies learned all too well recently. The reason I point to tri-annual adjustments in particular is that Canadian companies selling products in Canada to Canadians only offer this adjustment frequency, in contrast to the U.S. where even daily adjustments are available. This fact provides yet another perspective on the conservative nature of Canadian financial institutions — an orientation which served them well during the recent financial crisis.
Apples to Oranges
All that said, the simulations and the summary table I’ve provided undoubtedly indicate that more frequent adjustments are marginally better in the economist’s world of ceteris paribus. But in reality, everything else is rarely equal. How so? Consider the following questions: What if the product with weekly adjustments is charging an extra 50 basis points per year for this privilege? Or, what if said company forces you into an asset allocation model — with lousy funds, no less — that limits your equity exposure to only 60% and effectively reduces your projected growth rate? Then is weekly still better than monthly or quarterly? Fortunately, the same methodology I described above can be used to make these comparisons, although time and space limit my ability to display all the permutations.
Just as one example, a product that offers a guaranteed 6% credit to the base and lifetime income, but only adjusts the account annually, is financially equivalent to a product that offers (only) 5% credit and lifetime income, but with monthly adjustments. Likewise, a product that only credits the 5% for 10 years — but adjusts the guaranteed base weekly — is actually worse than a product that adjusts the base annually, but allows a credit for the full 15 years. There are many more such examples but my main point is all else is rarely equal.
The numbers provided in this column are quite case-specific, but some general and qualitative insights do emerge. Here’s the big one: The marginal value of more frequent adjustments — measured in terms of expected lifetime income — can be quantified in the low single digits. Building on that insight, when you factor in the implicit and often hidden costs associated with greater frequencies, and the statistical fact that a majority of policyholders will never consume the guaranteed lifetime income, one can make the argument that a day is just as long as a month in the long-term universe of variable annuities.