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.

**Reset Frequencies**

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?