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Understanding Variable Annuities with GMWBs

March 1, 2011

by Robert Huebscher

Incidentally, the SPIA has a lower IRR (2.60%) than the VA+GMWB (4.08%), when measured in a mortality-based framework as in figure 1.  With the SPIA, however, all the cash flow goes to the annuitant.  The VA+GMWB has a death benefit, so a good portion of its return goes to the annuitant’s heirs, not the annuitant.

The comparison between the SPIA and the VA+GMWB, while informative, is imperfect.   The SPIA is a pure annuity; it cannot be terminated, and it does not pay a death benefit.  The VA+GMWB can be terminated (in some cases – although not with Nationwide’s – with a penalty) and it pays a death benefit.

Since the VA+GMWB pays a death benefit equal to the remaining contract value, we can also look at the estimated bequest it offers:

Figure 5.  Median terminal values for VA+GMWB and passive strategy

Median terminal values for VA+GMWB and passive strategy


These are nominal values, not adjusted for inflation.  Notably, the median ending contract value for the VA+GMWB is zero after age 88.

We calculated the present value of the bequest shown in figure 5, after adjusting for mortality.  We chose a discount rate of 3%, reflecting a premium over of the risk-free rate to allow for Nationwide’s creditworthiness, and the present value was $519,984.  Investors should carefully consider the fact that roughly half of their investment in a VA+GMWB is likely to be passed on to their heirs and, moreover, weigh the tax consequences of that decision against other ways that money could be gifted.

Nationwide’s product has two variations.  One can invest at age 55 and receive an initial payout of 5% (instead of 4.5%) beginning at age 60, or one can invest at age 50 and receive a beginning payout of 5.5% at age 60.  These two options offer superior returns to investing at age 60:

Age at Investment Beginning Payout % IRR
50 5.5% 4.55%
55 5.0% 4.33%
60 4.5% 4.08%

These IRRs are a first approximation of the relative merits of these investments, and they indicate that investing earlier provides better longevity insurance at a lower cost, as compared to investing at age 60; a full analysis would require replicating the figures above.  The passive portfolio will have the same return characteristics regardless of whether the investment begins at age 50, 55 or 60.

The broader lessons

We are not the first to examine Chen’s research.  Bob Veres criticized Chen in a 2008 article that appeared in Financial Planning.  Veres rightly pointed to the tax inefficiencies of the VA+GMWB as compared to the passive portfolio and to its lack of inflation protection. 

He also questioned whether industry-funded research, such as Chen’s, can be objective.  That point bears reinforcement.

The movie Inside Job offers a disturbing case study of industry-funded research gone awry.  Frederick Mishkin, a former Federal Reserve Governor, was paid $124,000 by Iceland’s Chamber of Commerce to study the stability of Iceland’s banking system in May of 2006, prior to the financial crisis.  “The economy has already adjusted to financial liberalization,” Mishkin concluded, “which was already completed a long time ago, while prudential regulation and supervision is generally quite strong.”

Iceland’s economy collapsed less than two years after Mishkin’s report, due in large part to lax regulation and insufficient supervision.

It is inconceivable that industry-funded research would ever be published if it failed to support the thesis of its sponsor.  This study and Veres’ article are examples of the level of scrutiny that should be applied to such research before relying on any of its findings.

Even if one were to pay no heed to industry-funded research, the complexity of the VA+GMWB should be sufficient to raise significant concerns.  I needed the help of a trained mathematician and economist and the construction of a Monte Carlo model to accurately and comprehensively understand the product.  Who can an advisor, much less an unsophisticated investor, turn to for similar support?

The British economist John Kay has been critical of overly complex financial products.  He wrote about the dangers posed by “kickout bonds,” but he could have just as easily been writing about the VA+GMWB.  “The idea that small savers are equipped to assess the risk associated with these products by reading the small print is absurd,” he said, “as absurd as the notion that consumers can protect their families through do-it-yourself toxicology assessments of the food they buy.”

As I noted at the outset, the VA+GMWB is not a bad product, in that it offers a 4.08% median IRR, which will compare favorably to many, perhaps most, other annuities.  But it is very complex, and I am sure this article will not be the last word on its merits.   The decision to buy an annuity, like any other investment product, comes down to relative risk and the cost of mitigating that risk.  This analysis should demonstrate that risk can’t be boiled down to standard deviation or to the contrived measures that Chen employed. 

As Michael Edesess told me, “In a sense, all risk is longevity risk – the risk that you'll run out of money before you finish your spending program.  The probability of that event occurring may be the best measure of risk, which needs to be compared with the expected cost.”   Our study can make that comparison. Chen’s can't.

Appendix – A description of the VA+GMWB

The guaranteed minimum wealth benefit (GMWB) is a rider applied to a variable annuity (VA).  Our model operated as follows:

  • The purchaser invests a fixed amount ($1,000,000 at age 60, in our example) and receives a payout percentage (e.g., 4.5%). 
  • The funds are invested in VA sub-accounts with a 70% equity/30% fixed income allocation. 
  • The account balance and contract base are initially set to $1,000,000
  • At the end of each year
    • The income amount is determined by multiplying the contract base by the payout percentage
    • The account balance is reduced by the income amount and by the fees.  The fees are 2.4% applied to the account balance and 0.6% applied to the contract base.
    • The account balance is adjusted up or down based on the performance of the sub-accounts.  The account balance cannot be less than zero.
    • If the resulting account balance is greater than the contract base, the contract base is reset to the account balance
  • The investment is terminated by the death of the investor or if it is canceled by the investor.  In this case, the investor (or his or her heirs) is paid the remaining account balance.