## Understanding Variable Annuities with GMWBs

### March 1, 2011

### by Robert Huebscher

The passive portfolio has a near-100% chance of survival (i.e., not being depleted) until age 73, after which that probability slowly diminishes.

This tells only part of the story, though. We must also consider the amount of income that the VA+GMWB will provide in those instances where the passive portfolio is depleted. This is shown in the graphs below:

**Figure 3a. Median average income for the VA+GMWB based on life span**

Figure 3b. Median terminal income for the VA+GMWB based on life span

Figures 3a and 3b show the median average and terminal nominal and inflation-adjusted income for the VA+GMWB based on life span. Initially, the nominal income is $45,000, based on the payout percentage of 4.5%. For the inflation-adjusted income, we assumed 3% inflation, which has been the average over the last century. The nominal median average income increases at an average rate of approximately 0.5% per year, so it fails to keep pace with an assumed 3% inflation. At age 90, the nominal income would need to be in the 15th percentile of outcomes to keep pace with 3% inflation.

Any sales claim that the VA+GMWB income will keep pace with inflation should be viewed with extreme skepticism. Moreover, its performance will exhibit an undesirable positive correlation to the equity and fixed-income markets; in those cases where the income fails to ratchet up, the investor’s other assets are likely to fare poorly.

Combining the data from the prior two figures, one can determine the cost and benefit of the VA+GMWB based on life expectancy. Until age 73, there is a near-100% chance that the passive portfolio will survive, and the VA+GMWB provides virtually no value.

At age 82, which is the life expectancy for a 60-year old male, the probability of the passive portfolio surviving is 90.42%. If it fails to survive, the median value for the VA+GMWB is $55,208 in average nominal income ($28,719 after adjusting for inflation – equivalent to 63.8% of the purchasing power of the initial $45,000 income).

The probability of the passive portfolio surviving drops to 80% at age 88, at which point the median VA+GMWB average nominal income is $55,701 ($24,346 on an inflation-adjusted basis). The probability drops to 70% at age 95, at which point the median VA+GMWB average income is $55,497 of nominal income and $19,723 of inflation-adjusted income.

At age 113, which is where our mortality table ends, there is still a 21% chance the nominal income would never increase above its initial value of $45,000.

Although accurately computing the cost and benefit of the longevity insurance requires a consideration of life expectancy, the probability the passive account will be depleted, and the likely income the VA+GMWB will provide, one can obtain a high-level estimate. Overall, the passive account has a 9.83% probability of being depleted, but the median average total cash flow for the passive strategy exceeds that of the VA+GWMB strategy by $862,942.

We also computed those values for a hypothetical scenario in which the VA+GMWB payout never increased above its initial value of 4.5%. Our intent here was to show the additional cost and benefit the VA+GMWB offers through the feature of its increased payout amount based on market performance. In this case, the passive account has a 7.22% chance of being depleted and it has a median average of $1,169,050 in additional total cash flow. Thus, by adding the increased payout feature of the VA+GMWB, the investor makes a tradeoff: the chance that the passive portfolio will be depleted increases by 2.61%, but the median total cash flow also increases by $306,108.

Ultimately, the VA+GMWB is handicapped by its fee structure. As Joe Tomlinson, an advisor based in Maine who has studied this product and reviewed this article, put it, “With fees in excess of 3% of assets, most of the equity risk premium is gone, leaving the investor with stock-like volatility and bond-like returns.”

**Three other observations**** **

We considered three other factors, each of which a potential VA+GMWB investor should consider: how the VA+GMWB compares to a SPIA, the size of a potential bequest the VA+GMWB might provide, and whether it is advantageous to purchase it prior to age 60.

Anyone considering the purchase of an annuity should compare its costs and benefits to the most basic annuity offering – the SPIA. A 60-year old male in Massachusetts can purchase an SPIA with a nominal payment of 6.84%. Neither the median average nor the terminal income from the VA+GMWB account reach this level, as can be seen from figures 3a and 3b.

Figure 4 shows the probability of the ending income from the VA+GMWB surpassing the SPIA based on life span.

**Figure 4. Probability the ending income from the VA+GMWB will surpass the SPIA**

Thus, for someone whose goal is solely to maximize his or her lifetime income, the SPIA is superior to the VA+GMWB.