### Understanding Variable Annuities with GMWBs

*Peng Chen’s response to this study is published here.*

It’s very tempting: a variable annuity with minimum lifetime payout that can increase – but never decrease – based on market performance. You don’t even have to annuitize; if you die or terminate the agreement, you or your heirs receive the remaining contract value.

That temptation comes in the form of an increasingly popular variable annuity (VA) rider known as a guaranteed minimum withdrawal benefit (GMWB).

I became interested in this product because of a widely publicized study by Peng Chen and his colleagues at Ibbotson Associates. Chen’s research, which was funded by Nationwide Insurance, has been published in the *Journal of Financial Planning *and presented at industry conferences.

Because its performance is tied to market performance, the VA+GMWB is a complex product. In order to understand it, I will look at a key issue that was not addressed in Chen’s study: the amount and cost of the longevity insurance a VA+GMWB provides. But first I will turn to Chen’s central thesis, namely that an investor can reduce longevity risk – and increase income – by taking a portion of the fixed-income assets in a retirement portfolio and replacing them with a VA+GMWB. That thesis is wrong, as I will demonstrate.

The VA+GMWB is not a bad product, and it is not my intent to discourage its use. An investor who understands its costs and benefits in the proper analytical framework may find the VA+GMWB useful. It is my intent to provide that framework.

Michael Edesess, who has a PhD in advanced mathematics and economics, helped design the framework to study this product. He is a visiting fellow at the Hong Kong Advanced Institute for Cross-Disciplinary Studies, as well as a partner and chief investment officer of Denver-based Fair Advisors*.* Louis Mittel, a research assistant with Advisor Perspectives, built the Monte Carlo model for this study.

A more detailed description of the VA+GMWB is provided in an appendix at the end of this article. At a high level, it is an annuity that pays a minimum lifetime withdrawal amount with the added benefit that the amount can increase based on the performance of its subaccounts. It also pays a death/termination benefit equal to the remaining account value.

**The flaws in Ibbotson’s study**** **

Let’s turn first to Peng Chen’s study. Chen is the president of Morningstar’s Global Investment Management Division. His responsibilities include overseeing the research of Ibbotson Associates, which is a subsidiary of Morningstar. Chen’s results deserve scrutiny because of Morningstar’s stature in the investment industry and because many potential investors will rely on them.

In his study, Chen replaced a portion of the fixed-income component of a hypothetical retirement portfolio with a VA+GMWB. He compared the original portfolio to the resulting portfolio using several metrics, including total income, income return (the percentage change of income from year-to-year) and semi-deviation (the standard deviation of negative income returns). On all counts, the resulting portfolio was superior, leading Chen to conclude that the “VA+GMWB offers protection both in terms of market downturns and more importantly retirement income risk.”

Chen used Ibbotson’s projected capital market returns for his study, which included an expected return for bonds of 4.36%; this represented the income (as a percentage of principal) in the original portfolio. The corresponding income from the VA+GMWB was a minimum of 5% of the principal, and this amount can increase (but not decrease) based on market performance. Thus, it was a foregone conclusion that the portfolio containing the VA+GMWB will score better on all three metrics, as Chen’s study verifies.

Chen’s thesis, however, is based on flawed methodology and has limited, if any, practical value.

First, Chen considered only one scenario – that where the investor lived to age 90, which has a probability of approximately 19%. His analysis, unlike ours, does not take into consideration mortality and the possibility that the investor might not live to age 90. Had he considered mortality, he would have replicated our analysis.

In an email exchange, I asked Chen about his decision to ignore mortality in his analysis. He said he was modeling an investor who was “moderately risk-averse,” by which he said he meant an investor who was concerned about outliving their assets at age 90.

But this is a severely incomplete approach. It is analogous to purchasing insurance against an event that has a 19% probability, and then examining only that scenario, as if it had a 100% probability. Only by examining the full range of scenarios with a mortality-based framework can one understand the costs and benefits of the VA+GMWB.

Second, in his robustness check, Chen considered the sensitivity of his results to changes in the fee structure and in the equity/fixed-income allocation. Given his metrics, however, the most important variables to consider would have been the expected return for the fixed-income component of the portfolio and the initial payout percentage for the annuity. The relationship between those two variables will drive income tradeoff in the portfolio with and without the VA+GMWB, and anyone who relies on Chen’s study should analyze this carefully.

By examining only a single mortality assumption and ignoring the sensitivity of the VA+GMWB to changes in his assumed fixed-income return and annuity payout percentage, Chen has provided a narrow analysis that has little, if any, applicability.

The only relevant question when considering the purchase of a VA+GMWB is whether the longevity insurance provided by its guaranteed lifetime income is worth its cost. That decision is unique to every investor, and we have provided the framework to make that choice.

**Modeling the product**** **

Chen’s analysis was based on a “generic” VA+GMWB, not Nationwide’s product. We chose to analyze Nationwide’s Income Architect product. Its key features turned out to be identical to those in Chen’s study, with one important exception – the initial withdrawal percentage is currently 4.5%, not 5% as in Chen’s study. We assumed that the investment would begin at age 60 and withdrawals would begin immediately.

To estimate the cost and benefits of the longevity insurance provided by this product, we compared its returns to those of a passively invested portfolio. In other words, instead of investing $1 million in a VA+GMWB, one could choose to invest those funds in a similarly allocated passive portfolio.

We modeled a 70% equity/30% fixed portfolio, because that allocation provides the maximum benefit to the owner of the VA+GMWB. The probability of the withdrawal amount increasing from its base value is greatest with the most aggressive equity allocation, and the maximum permitted by Nationwide is 70%.

The fee structure of the Nationwide VA+GMWB that we examined was identical to that in Chen’s study. Those fees are 2.4% applied to the contract value and 0.6% applied to high-water mark reached by the contract value (the contract base), resulting in fees in excess of 3%. The passive portfolio had 1% fees, reflecting expense ratios and advisor fees.

As in Chen’s study, we ignored any risk that the insurer might default.

We ran a Monte Carlo simulation using the same capital market assumptions as in Chen’s Ibbotson study. In each iteration, we chose a randomly determined life span based on current mortality tables. That we modeled mortality and Ibbotson did not is a critical difference between the studies, a point I will return to later.

We used the passive portfolio to replicate the cash flows from the VA+GMWB, based on the terms in Nationwide’s prospectus and rider, which are summarized in the appendix. Our goal was to determine the probability that the investor could obtain those identical cash flows from the lower-cost passive portfolio. If the passive portfolio depleted, that indicated that the VA+GMWB was superior in that scenario.

The passive portfolio represents the opportunity cost of investing in a VA+GMWB; it has risk and return characteristics that are identical to the underlying sub-accounts of the VA+GMWB and can be used to replicate its cash flows. Only by considering the probability of the VA+GMWB outperforming the passive account – under the full range of mortality scenarios – can one assess the costs and benefits of the longevity insurance provided by the annuity.