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Understanding Variable Annuities with GMWBs

March 1, 2011

by Robert Huebscher

The results of our model

We computed the internal rates of return (IRRs) for the VA+GMWB and the passive portfolio, taking into account all cash flows – withdrawals from the VA+GMWB, income from the passive account, and the ending balances in the passive and VA+GMWB accounts.  We ran 100,000 simulations, each to a randomly chosen date-of-death based on mortality tables.   Averaging the IRRs over those simulations, the results were as follows:

VA+GMWB 4.08%
Passive portfolio 5.65%

One of the virtues of the VA+GMWB is that it offers a 4.08% IRR; it would not be hard to find variable annuities that offer zero or even negative IRRs. But it still lags behind the passive portfolio’s returns.

While this 157 basis point difference provides a general indication of the relative advantage of the passive approach, however, it lacks mathematical precision, since IRRs cannot be averaged over different time horizons.  The appropriate view is of the IRRs based on life span:

Figure 1.  Median internal rates-of-return (IRRs) for VA+GMWB and passive strategies

Median internal rates-of-return

This figure shows the median IRRs for various life spans, from 61 years up to well past 100.

The overall IRR advantage of the passive portfolio is not surprising, and the lower IRR of the VA+GMWB reflects its higher fees and the cost of the longevity insurance for the scenarios in which the investor would outlive the passive portfolio.  The VA+GMWB investor sacrifices overall return in order to insure against longevity risk.  The passive strategy has a higher IRR for all life spans through 113.

While these IRRs compare the investment properties of the VA+GMWB to the passive portfolio, they do not provide the necessary framework for an investor to assess the cost of the longevity insurance.  That assessment must be based on life expectancy, the probability that the passive portfolio would deplete, and how much insurance the VA+GMWB provides in those instances.

Below are the probabilities that the passive portfolio will match the cash flows of the VA+GMWB.

Figure 2.  Probability the cash flow from the passive portfolio will equal that of the VA+GMWB

Probability the cash flow from the passive portfolio will equal that of the VA+GMWB